MC-PDFT#
DFT for strong correlation#
Let’s start by looking at how well standard DFT performs for strong correlation. Here for simplicity, we will use the textbook example of H\(_2\) dissociation. We also compute Hartree-Fock and full CI for comparison.
import matplotlib.pyplot as plt
import multipsi as mtp
import numpy as np
import veloxchem as vlx
# HF, BLYP and CI calculation of H.
mol_str = """
H 0.0000 0.0000 0.0000
"""
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
molecule.set_multiplicity(2)
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz", ostream=None)
scf_drv = vlx.ScfUnrestrictedDriver()
scf_drv.ostream.mute()
scf_results = scf_drv.compute(molecule, basis)
E_H_hf = scf_drv.get_scf_energy()
scf_drv.xcfun = "BLYP"
scf_results = scf_drv.compute(molecule, basis)
E_H_blyp = scf_drv.get_scf_energy()
space = mtp.OrbSpace(molecule, scf_drv.mol_orbs)
space.fci()
CIdrv = mtp.CIDriver()
ci_results = CIdrv.compute(molecule, basis, space)
E_H_FCI = CIdrv.get_energy()
# HF, BLYP and CI calculations of H2 dissociation
mol_template = """
H 0.0000 0.0000 -H2dist
H 0.0000 0.0000 H2dist
"""
scf_drv = vlx.ScfRestrictedDriver()
dft_drv = vlx.ScfRestrictedDriver()
scf_drv.ostream.mute()
dft_drv.ostream.mute()
dft_drv.xcfun = "BLYP"
distlist = [
0.5,
0.6,
0.65,
0.7,
0.75,
0.8,
0.9,
1,
1.2,
1.4,
1.5,
1.6,
1.7,
2,
2.5,
3,
4,
]
E_hf = []
E_blyp = []
E_FCI = []
# Scan over O-H distances
for dist in distlist:
mol_str = mol_template.replace("H2dist", str(dist / 2))
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz", ostream=None)
scf_results = scf_drv.compute(molecule, basis)
E_hf.append(scf_drv.get_scf_energy() - 2 * E_H_hf)
dft_results = dft_drv.compute(molecule, basis)
E_blyp.append(dft_drv.get_scf_energy() - 2 * E_H_blyp)
space = mtp.OrbSpace(molecule, scf_drv.mol_orbs)
space.fci()
ci_results = CIdrv.compute(molecule, basis, space)
E_FCI.append(CIdrv.get_energy() - 2 * E_H_hf)
plt.figure(figsize=(6, 4))
plt.title("Energy during H2 dissociation")
x = np.array(distlist)
y1 = np.array(E_FCI) * 627.5
y2 = np.array(E_hf) * 627.5
y3 = np.array(E_blyp) * 627.5
plt.plot(x, y1, label="FullCI")
plt.plot(x, y2, label="RHF")
plt.plot(x, y3, label="BLYP")
plt.axhline(y=0, color="k", linestyle="--")
plt.xlabel("H2 distance")
plt.ylabel("Energy (kcal/mol)")
plt.legend()
plt.tight_layout()
plt.show()
Around the equilibrium distance, BLYP performs remarkably well. Actually, since we are only using a small DZ basis set, it is likely that the FullCI curve is too high and the true answer is closer to the BLYP curve. On the other hand, approaching dissociation, BLYP follows the same trend as Hartree-Fock and goes above the 0 which represents the energy of the 2 separate hydrogens, though with a significantly smaller error than Hartree-Fock.
One way to at least partly fix this issue is by using so-called broken symmetry. By default the DFT calculation respect the symmetry of the system as well as the spin symmetry, but you can explicitely break this symmetry by starting from a guess with one \(\alpha\) electron on one hydrogen and one \(\beta\) electron on the other one.
# Broken-symmetry BLYP calculation of H2
bs_drv = vlx.ScfUnrestrictedDriver()
bs_drv.ostream.mute()
bs_drv.xcfun = "BLYP"
bs_drv.guess_unpaired_electrons = "1(1), 2(-1)" # alpha on atom 1 and beta on atom 2
E_bs = []
# Scan over O-H distances
for dist in distlist:
mol_str = mol_template.replace("H2dist", str(dist / 2))
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz")
bs_results = bs_drv.compute(molecule, basis)
E_bs.append(bs_drv.get_scf_energy() - 2 * E_H_blyp)
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
y4 = np.array(E_bs) * 627.5
fig, ax = plt.subplots()
ax.plot(x, y1, label="FullCI")
ax.plot(x, y3, label="BLYP")
ax.plot(x, y4, label="BS-BLYP")
ax.axhline(y=0, color="k", linestyle="--")
ax.set_xlabel("H2 distance")
ax.set_ylabel("Energy (kcal/mol)")
ax.legend()
axin = ax.inset_axes([0.5, 0.2, 0.4, 0.4])
axin.set_xlim(1.4, 1.9)
axin.set_ylim(-50, -10)
axin.plot(x, y1, label="FullCI")
axin.plot(x, y3, label="BLYP")
axin.plot(x, y4, label="BS-BLYP")
ax.indicate_inset_zoom(axin)
plt.show()
The broken-symmetry BLYP result is here a very good match to the FullCI. Looking in more details, we can see that the energt first follows exactly the one from restricted BLYP, but has a bifurcation point where the broken-symmetry solution becomes lower in energy.
While symmetry-breaking often leads to reasonable energies, it is not always ideal. First, in more complicated systems, the intermediate region may still be poorly described, but also, the resulting wavefunction may not be physical and suffers from spin-contamination. Plotting the spin-densities before and after the bifurcation point, it is easy to see that they differ significantly in nature, implying that we do not really have a smooth transition between the restricted and symmetry-breaking regime.
# Plotting densities along the bond axis (z)
n = 100
z = np.linspace(-4, 4, n, endpoint=True)
coords = np.zeros((n, 3))
coords[:, 2] = z
# Before the bifurcation
mol_str = """
H 0.0000 0.0000 -0.75
H 0.0000 0.0000 0.75
"""
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz")
bs_tensor = bs_drv.compute(molecule, basis)
vis_drv = vlx.VisualizationDriver()
rho1_a = vis_drv.get_density(coords, molecule, basis, bs_drv.density, "alpha")
rho1_b = vis_drv.get_density(coords, molecule, basis, bs_drv.density, "beta")
# After the bifurcation
mol_str = """
H 0.0000 0.0000 -0.85
H 0.0000 0.0000 0.85
"""
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz")
bs_tensor = bs_drv.compute(molecule, basis)
vis_drv = vlx.VisualizationDriver()
rho2_a = vis_drv.get_density(coords, molecule, basis, bs_drv.density, "alpha")
rho2_b = vis_drv.get_density(coords, molecule, basis, bs_drv.density, "beta")
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(8, 4))
fig.suptitle("Density profile")
ax1.plot(z, rho1_a, label="alpha 1.5 Å")
ax1.plot(z, rho1_b, label="beta 1.5 Å")
ax2.plot(z, rho2_a, label="alpha 1.7 Å")
ax2.plot(z, rho2_b, label="beta 1.7 Å")
ax1.legend()
ax2.legend()
plt.show()
Passing the bifurcation point, we suddenly go from equal spin densities on each side to mostly \(\alpha\) on the left and \(\beta\) on the right.
There is thus still a need to develop a DFT framework that can properly handle strong correlation.
Pair-density functional theory#
It is interesting to note that the issue with strong correlation is only present because we use spin-densities. If we were using only the total density (which is what the fundamental theorems of DFT suggest), then H\(_2\) would dissociate to the correct limit even with restricted DFT, and this would be true for any (reasonable) functional. The issue at dissociation is because the restricted wavefunction is not spin-polarized while the open-shell fragments are, and thus they have different energies.
However, the reason most modern DFT uses spin-densities is because it usually gives better results, and in particular, it can distinguish between a triplet and open-shell singlet while these two states tend to have very similar densities.
Still, in the absence of magnetic field (or relativistic effect), it is actually unphysical to spin-polarize, since space is isotropic. This has led to attempts to find another variable that is more physical that the spin-densities but carries more information that just the total density.
The on-top pair-density \(\Pi(r)\) has been the most promising idea. This quantity is simply the pair-density \(\rho_2(r_1,r_2)\) but for \(r_1 = r_2 = r\). In other words, it represents the probability of having two-electrons in the same point in space (“on-top” of each other, hence the name).
\[\Pi(r) = \rho_2(r,r)\]
Let’s see how this variable behaves in H2 at short and long distance for a simple MCSCF wavefunction.
# Function to compute the on-top pair-density
def get_ontop(coords, molecule, basis, space, TwoDM):
vis_drv = vlx.VisualizationDriver()
orbital_values = []
for i in space.active_orbitals:
values = np.array(
vis_drv.get_mo(
coords, molecule, basis, space.molecular_orbitals, i, "alpha"
)
)
orbital_values.append(values)
den_i = vlx.AODensityMatrix([space._get_inactive_density()], vlx.denmat.rest)
rho_i = np.array(vis_drv.get_density(coords, molecule, basis, den_i, "alpha"))
norb = space.n_active
ontop = 2 * rho_i**2
for i in range(norb):
for j in range(norb):
for k in range(norb):
for l in range(norb):
ontop += (
TwoDM[i, j, k, l]
* orbital_values[i]
* orbital_values[j]
* orbital_values[k]
* orbital_values[l]
)
return ontop
mol_str = """
H 0.0000 0.0000 -0.4
H 0.0000 0.0000 0.4
"""
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz", ostream=None)
bs_tensor = bs_drv.compute(molecule, basis)
space = mtp.OrbSpace(molecule, bs_drv.mol_orbs)
space.cas(2, 2)
mcscf_drv = mtp.McscfDriver()
mcscf_drv.compute(molecule, basis, space)
den = vlx.AODensityMatrix([mcscf_drv.get_total_density()], vlx.denmat.rest)
rho1 = np.array(vis_drv.get_density(coords, molecule, basis, den, "alpha"))
ontop1 = get_ontop(
coords, molecule, basis, space, mcscf_drv.ci_driver.get_active_2body_density(0)
)
mol_str = """
H 0.0000 0.0000 -1.0
H 0.0000 0.0000 1.0
"""
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz", ostream=None)
bs_tensor = bs_drv.compute(molecule, basis)
space = mtp.OrbSpace(molecule, bs_drv.mol_orbs)
space.cas(2, 2)
mcscf_drv = mtp.McscfDriver()
mcscf_drv.compute(molecule, basis, space)
den = vlx.AODensityMatrix([mcscf_drv.get_total_density()], vlx.denmat.rest)
rho2 = np.array(vis_drv.get_density(coords, molecule, basis, den, "alpha"))
ontop2 = get_ontop(
coords, molecule, basis, space, mcscf_drv.ci_driver.get_active_2body_density(0)
)
fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(8, 4))
fig.suptitle("Density profile")
ax1.plot(z, rho1, label="rho 0.8 Å")
ax1.plot(z, ontop1, label="Pi 0.8 Å")
ax2.plot(z, rho2, label="rho 2.0 Å")
ax2.plot(z, ontop2, label="Pi 2.0 Å")
ax1.legend()
ax2.legend()
plt.show()
Close to the equilibrium, there is a significant on-top pair-density in the middle of the bond, reflecting the fact that both electrons are likely to be there simultaneously. On the other hand, in the outside of the molecule, there is still a significant density but a low on-top pair-density. This means that in these regions, there is a high likelihood of having an electron but not both simultaneously: correlation pushes the electrons to rather be on opposite side of the molecule.
Towards bond dissociation, the on-top pair-density is very small, reflecting the fact that at this point, the electrons are almost completely on opposite sides with little overlap.
Unlike the spin densities, the on-top pair-density is well defined and in particular, the on-top pair-density of two fragments at infinite distance is the same as the on-top pair-density for each fragment computed separately. So bond dissociation, and strong correlation in general, are not an issue for functionals of this variable.
But in addition, what makes this variable very promising is that for a single determinant:
\[ \Pi(r) = 2\rho_\alpha(r) \rho_\beta(r)\]
This can be easily understood if we look at the totally uncorrelated case, the Hartree Product, for which the pair-density is equal to the product of one-electron densities:
(4)#\[\begin{align}
\Pi^\mathrm{Hartree}(r) &= \rho^\mathrm{Hartree}_2(r,r)\\
&= \rho^2(r) \\
&=\left(\rho_\alpha(r) + \rho_\beta(r)\right)^2\\
&= \rho_\alpha^2(r) + \rho_\beta^2(r) + 2\rho_\alpha(r) \rho_\beta(r)
\end{align}\]
The first two terms correspond to the probability of having two electrons of same spin in the same point in space, which is non-zero in an uncorrelated Hartree product but 0 in a Slater Determinant, hence the above equation.
With this equation as well as \(\rho = \rho_\alpha + \rho_\beta\), we have two equations linking two pairs of variable, and thus, there is as much information in the density and on-top pair-density as there is in the spin-densities. In other words, you can translate any functional of the spin-densities to become a functional of the density and on-top pair-density in a way that they give exactly the same result for a single determinant.
A way to do this in practice is to invert the system of equations. This gives us a quadratic equation which has two solutions:
\[\rho^\mathrm{eff}_{\alpha/\beta} = 0.5 \left(\rho \pm \sqrt{\rho^2 - 2\Pi} \right)\]
We arbitrarily choose the \(\alpha\) to be the larger of the two solution. Let’s plot these effective spin-densities. Note that the quantity under the radical can be negative, and for now we just remove this problem by setting these cases to 0.
fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(8, 4))
fig.suptitle("Density profile")
ax1.plot(
z, 0.5 * (rho1 + np.sqrt(np.maximum(rho1**2 - 2 * ontop1, 0))), label="rho_a 0.8 Å"
)
ax1.plot(
z, 0.5 * (rho1 - np.sqrt(np.maximum(rho1**2 - 2 * ontop1, 0))), label="rho_b 0.8 Å"
)
ax2.plot(
z, 0.5 * (rho2 + np.sqrt(np.maximum(rho2**2 - 2 * ontop2, 0))), label="rho_a 2.0 Å"
)
ax2.plot(
z, 0.5 * (rho2 - np.sqrt(np.maximum(rho2**2 - 2 * ontop2, 0))), label="rho_b 2.0 Å"
)
ax1.legend()
ax2.legend()
plt.show()
This result appears weird at first, because the \(\alpha\) density we obtain is clearly larger than the \(\beta\), which we do not expect in a singlet. Here it is important to remember that these are only “effective” densities which correspond to the physical spin densities only in a single determinant. In addition, we arbitrarily chose the larger one to be the \(\alpha\), and you could easily imagine that on the right-side we could choose the reverse and the result would then look more like the broken-symmetry result.
Looking more in details, we see that this predict an approximately equal amount of \(\alpha\) and \(\beta\) density in the middle of the bond, corresponding to our observation above that this is where the probability of having both electrons simultaneously is the largest. By contrast, in the outer regions, the \(\alpha\) density becomes very large compared to the \(\beta\), which is reminescent of the broken-symmetry solution we found earlier, reflecting the correlation effects in this region. However, unlike the broken-symmetry solution, this distribution retains the left-right symmetry of the system.
Let us briefly come back to the problem of negative number under the radical. The on-top pair-density is bounded \(0<\Pi(r)<\rho^2(r)\) and for a closed-shell single determinant case, \(\Pi = 2\rho_\alpha \rho_\beta = 0.5 \rho^2\). This means the quantity under the radical is positive if the probability of finding two electrons in the same space is lower than that of a closed-shell single determinant, which is often the case since correlation tends to reduce this probability. But it may not always be so, locally, and in particularly in the middle of the bond here, where it would give a complex number. This is however not a problem in practice, as if we simply blindly apply the usual density functional expressions on a complex density, we get an increased energy, which is what we would expect from having a high probability of two electrons in the same place.
Multiconfigurational pair-density functional theory#
The section above tried to motivate why the density and on-top pair-density are good variables to use within a functional, becoming thus a pair-density functional. The issue of course is that we do not know the on-top pair-density, and if we compute it from the spin-densities in a Hartree-Fock or DFT calculation, we have not gained anything. However, we can compute these with a level of theory like MCSCF which is able to dissociate properly but lacks dynamical correlation. This is the basis for so-called multiconfigurational pair-density functional theory. The idea is then to use the MCSCF densities in an analogue to the Kohn-Sham energy expression:
\[E = \langle \Psi_\mathrm{MCSCF}| \hat{h} + \hat{J} | \Psi_\mathrm{MCSCF}\rangle + \int F(\rho^\mathrm{eff}_\alpha, \rho^\mathrm{eff}_\beta) dr \]
This is implemented in MultiPsi by first computing the MCSCF and then using the compute_pdft function. We use the tBLYP functional which is simply the “translation” of the BLYP functional.
# MC-tBLYP calculation of H.
mol_str = """
H 0.0000 0.0000 0.0000
"""
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
molecule.set_multiplicity(2)
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz", ostream=None)
scf_drv = vlx.ScfUnrestrictedDriver()
scf_drv.ostream.mute()
scf_results = scf_drv.compute(molecule, basis)
space = mtp.OrbSpace(molecule, scf_drv.mol_orbs)
mcscf_drv = mtp.McscfDriver()
mcscf_results = mcscf_drv.compute(molecule, basis, space)
E_H_tBLYP = mcscf_drv.compute_pdft(molecule, basis, "tBLYP")
# MC-tBLYP calculation of H2 dissociation
mol_template = """
H 0.0000 0.0000 -H2dist
H 0.0000 0.0000 H2dist
"""
scf_drv = vlx.ScfRestrictedDriver()
mcscf_drv = mtp.McscfDriver()
E_tblyp = []
# Scan over O-H distances
for dist in distlist:
mol_str = mol_template.replace("H2dist", str(dist / 2))
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz", ostream=None)
scf_results = scf_drv.compute(molecule, basis)
space = mtp.OrbSpace(molecule, scf_drv.mol_orbs)
space.cas(2, 2)
mcscf_results = mcscf_drv.compute(molecule, basis, space)
E_tblyp.append(mcscf_drv.compute_pdft(molecule, basis, "tBLYP") - 2 * E_H_tBLYP)
y5 = np.array(E_tblyp) * 627.5
fig, ax = plt.subplots()
ax.plot(x, y1, label="FullCI")
ax.plot(x, y3, label="BLYP")
ax.plot(x, y4, label="BS-BLYP")
ax.plot(x, y5, label="MC-tBLYP")
ax.axhline(y=0, color="k", linestyle="--")
ax.set_xlabel("H2 distance")
ax.set_ylabel("Energy (kcal/mol)")
ax.legend()
axin = ax.inset_axes([0.5, 0.2, 0.4, 0.4])
axin.set_xlim(1.4, 1.9)
axin.set_ylim(-50, -10)
axin.plot(x, y1, label="FullCI")
axin.plot(x, y3, label="BLYP")
axin.plot(x, y4, label="BS-BLYP")
axin.plot(x, y5, label="MC-tBLYP")
ax.indicate_inset_zoom(axin)
plt.show()
The MC-tBLYP result is very similar to the BLYP result at equilibrium distance but has the correct dissociation limit and a gentler curve in the intermediate region, which is where it differs most from the BS-BLYP result.
Of course, there is no specific reasons to use MCSCF densities. These densities have only correlation within the active space and are therefore not the true or best densities. We can instead try to optimize the wavefunction so that it minimizes the MC-PDFT energy expression. This variational MC-PDFT can be obtained in MultiPsi by simply setting the functional in the MCSCF driver.
# Variational MC-tBLYP calculation of H.
mol_str = """
H 0.0000 0.0000 0.0000
"""
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
molecule.set_multiplicity(2)
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz", ostream=None)
scf_drv = vlx.ScfUnrestrictedDriver()
scf_drv.ostream.mute()
scf_results = scf_drv.compute(molecule, basis)
space = mtp.OrbSpace(molecule, scf_drv.mol_orbs)
mcscf_drv = mtp.McscfDriver()
mcscf_drv.xcfun = "tBLYP"
mcscf_results = mcscf_drv.compute(molecule, basis, space)
E_H_tBLYP = mcscf_drv.get_energy()
# Variational MC-tBLYP calculation of H2 dissociation
mol_template = """
H 0.0000 0.0000 -H2dist
H 0.0000 0.0000 H2dist
"""
mol_str = mol_template.replace("H2dist", str(0.5))
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz")
scf_drv = vlx.ScfRestrictedDriver()
scf_results = scf_drv.compute(molecule, basis)
space = mtp.OrbSpace(molecule, scf_drv.mol_orbs)
space.cas(2, 2)
mcscf_drv = mtp.McscfDriver()
mcscf_drv.xcfun = "tBLYP"
mcscf_results = mcscf_drv.compute(molecule, basis, space)
E_tblyp = []
# Scan over O-H distances
for dist in distlist:
mol_str = mol_template.replace("H2dist", str(dist / 2))
print(mol_str)
molecule = vlx.Molecule.read_molecule_string(mol_str, units="angstrom")
basis = vlx.MolecularBasis.read(molecule, "cc-pvdz")
mcscf_results = mcscf_drv.compute(molecule, basis, space)
E_tblyp.append(mcscf_drv.get_energy() - 2 * E_H_tBLYP)
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 1
Number of virtual orbitals: 4
This is a restricted open-shell Hartree-Fock wavefunction
Equivalent to a CASSCF: CAS(1,1)
CI expansion:
-------------
Number of determinants: 1
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -0.496396614 0.0e+00 2.2e-03 1 0:00:00
2 -0.496403222 -6.6e-06 1.6e-04 1 0:00:00
3 -0.496403255 -3.3e-08 9.6e-10 1 0:00:00
4 -0.496403255 -3.3e-16 8.1e-15 1 0:00:00
** Convergence reached in 4 iterations
5 -0.496403255 1.4e-15 6.4e-15 1 0:00:00
Final results
-------------
* State 1
- Energy: -0.49640325498824395
- S^2 : 0.75 (multiplicity = 2.0 )
- Natural orbitals
1.00000
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.000 Energy: -0.11565 a.u.
( 1 H 1s : 0.58) ( 1 H 2s : 0.51)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.000 Energy: 0.51785 a.u.
( 1 H 1s : 1.24) ( 1 H 2s : -1.28)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 1.31509 a.u.
( 1 H 1p+1: 0.35) ( 1 H 1p-1: -0.94)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 1.31509 a.u.
( 1 H 1p+1: 0.94) ( 1 H 1p-1: 0.35)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.31509 a.u.
( 1 H 1p0 : -1.00)
Dipole moment for state 1
---------------------------
X : -0.000000 a.u. -0.000000 Debye
Y : -0.000000 a.u. -0.000000 Debye
Z : 0.000000 a.u. 0.000000 Debye
Total : 0.000000 a.u. 0.000000 Debye
Total MC-PDFT time: 00:00:00
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Self Consistent Field Driver Setup
====================================
Wave Function Model : Spin-Restricted Hartree-Fock
Initial Guess Model : Superposition of Atomic Densities
Convergence Accelerator : Two Level Direct Inversion of Iterative Subspace
Max. Number of Iterations : 50
Max. Number of Error Vectors : 10
Convergence Threshold : 1.0e-06
ERI Screening Scheme : Cauchy Schwarz + Density
ERI Screening Mode : Dynamic
ERI Screening Threshold : 1.0e-12
Linear Dependence Threshold : 1.0e-06
* Info * Nuclear repulsion energy: 0.5291772109 a.u.
* Info * Overlap matrix computed in 0.00 sec.
* Info * Kinetic energy matrix computed in 0.00 sec.
* Info * Nuclear potential matrix computed in 0.00 sec.
* Info * Orthogonalization matrix computed in 0.00 sec.
* Info * SAD initial guess computed in 0.00 sec.
* Info * Starting Reduced Basis SCF calculation...
* Info * ...done. SCF energy in reduced basis set: -1.095959327021 a.u. Time: 0.01 sec.
* Info * Overlap matrix computed in 0.00 sec.
* Info * Kinetic energy matrix computed in 0.00 sec.
* Info * Nuclear potential matrix computed in 0.00 sec.
* Info * Orthogonalization matrix computed in 0.00 sec.
Iter. | Hartree-Fock Energy | Energy Change | Gradient Norm | Max. Gradient | Density Change
--------------------------------------------------------------------------------------------
1 -1.100056242572 0.0000000000 0.02692675 0.00838888 0.00000000
2 -1.100153689745 -0.0000974472 0.00051916 0.00017723 0.00493758
3 -1.100153764817 -0.0000000751 0.00001420 0.00000490 0.00030702
4 -1.100153764873 -0.0000000001 0.00000000 0.00000000 0.00000815
*** SCF converged in 4 iterations. Time: 0.01 sec.
Spin-Restricted Hartree-Fock:
-----------------------------
Total Energy : -1.1001537649 a.u.
Electronic Energy : -1.6293309758 a.u.
Nuclear Repulsion Energy : 0.5291772109 a.u.
------------------------------------
Gradient Norm : 0.0000000003 a.u.
Ground State Information
------------------------
Charge of Molecule : 0.0
Multiplicity (2S+1) : 1.0
Magnetic Quantum Number (M_S) : 0.0
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 2.000 Energy: -0.52504 a.u.
( 1 H 1s : -0.38) ( 1 H 2s : -0.23) ( 2 H 1s : -0.38)
( 2 H 2s : -0.23)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.000 Energy: 0.14359 a.u.
( 1 H 1s : 0.20) ( 1 H 2s : 1.36) ( 2 H 1s : -0.20)
( 2 H 2s : -1.36)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.53961 a.u.
( 1 H 1s : -0.78) ( 1 H 2s : 0.74) ( 2 H 1s : -0.78)
( 2 H 2s : 0.74)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.79480 a.u.
( 1 H 1s : -0.95) ( 1 H 2s : 1.47) ( 1 H 1p0 : 0.20)
( 2 H 1s : 0.95) ( 2 H 2s : -1.47) ( 2 H 1p0 : 0.20)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.28713 a.u.
( 1 H 1p+1: 0.61) ( 2 H 1p+1: 0.61)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.28713 a.u.
( 1 H 1p-1: 0.61) ( 2 H 1p-1: 0.61)
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.143566377 0.0e+00 5.4e-02 4 0:00:00
2 -1.148744377 -5.2e-03 6.1e-03 5 0:00:00
3 -1.148804711 -6.0e-05 1.6e-02 4 0:00:00
4 -1.149285428 -4.8e-04 2.0e-03 4 0:00:00
5 -1.149310085 -2.5e-05 1.0e-03 4 0:00:00
6 -1.149314174 -4.1e-06 5.7e-05 4 0:00:00
7 -1.149314195 -2.1e-08 2.3e-05 1 0:00:00
8 -1.149314199 -4.1e-09 8.7e-06 4 0:00:00
** Convergence reached in 8 iterations
9 -1.149314200 -5.1e-10 3.3e-06 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.149314199926862
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.98226 0.01774
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.982 Energy: -0.33023 a.u.
( 1 H 1s : 0.40) ( 1 H 2s : 0.21) ( 2 H 1s : 0.40)
( 2 H 2s : 0.21)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.018 Energy: 0.11039 a.u.
( 1 H 1s : -0.76) ( 1 H 2s : -0.39) ( 2 H 1s : 0.76)
( 2 H 2s : 0.39)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.35559 a.u.
( 1 H 1s : -0.77) ( 1 H 2s : 0.74) ( 2 H 1s : -0.77)
( 2 H 2s : 0.74)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.44574 a.u.
( 1 H 1s : 0.73) ( 1 H 2s : -1.96) ( 2 H 1s : -0.73)
( 2 H 2s : 1.96)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.01604 a.u.
( 1 H 1p+1: -0.49) ( 1 H 1p-1: 0.39) ( 2 H 1p+1: -0.49)
( 2 H 1p-1: 0.39)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.01604 a.u.
( 1 H 1p+1: -0.39) ( 1 H 1p-1: -0.49) ( 2 H 1p+1: -0.39)
( 2 H 1p-1: -0.49)
Dipole moment for state 1
---------------------------
X : 0.000010 a.u. 0.000025 Debye
Y : 0.000015 a.u. 0.000039 Debye
Z : 0.000235 a.u. 0.000596 Debye
Total : 0.000235 a.u. 0.000598 Debye
Total MC-PDFT time: 00:00:01
H 0.0000 0.0000 -0.25
H 0.0000 0.0000 0.25
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.052521357 0.0e+00 2.5e-01 4 0:00:00
2 -1.077746302 -2.5e-02 1.1e-01 4 0:00:00
3 -1.082349570 -4.6e-03 3.7e-03 1 0:00:00
4 -1.082358066 -8.5e-06 1.2e-04 1 0:00:00
5 -1.082364708 -6.6e-06 2.1e-04 4 0:00:00
6 -1.082364599 1.1e-07 3.7e-04 1 0:00:00
7 -1.082365046 -4.5e-07 2.0e-04 4 0:00:00
8 -1.082365361 -3.2e-07 1.8e-04 4 0:00:00
9 -1.082365882 -5.2e-07 1.9e-04 4 0:00:00
10 -1.082366076 -1.9e-07 1.1e-04 4 0:00:00
11 -1.082366110 -3.4e-08 1.9e-05 4 0:00:00
12 -1.082366111 -1.2e-09 4.4e-06 1 0:00:00
** Convergence reached in 12 iterations
13 -1.082366111 3.4e-10 2.5e-06 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.0823661110355856
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.99459 0.00541
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.995 Energy: -0.42354 a.u.
( 1 H 1s : -0.43) ( 2 H 1s : -0.43)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.005 Energy: 0.56953 a.u.
( 1 H 1s : 1.17) ( 1 H 2s : 0.44) ( 2 H 1s : -1.17)
( 2 H 2s : -0.44)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.26170 a.u.
( 1 H 1s : -0.62) ( 1 H 2s : 0.72) ( 2 H 1s : -0.62)
( 2 H 2s : 0.71)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.49397 a.u.
( 1 H 1s : -0.37) ( 1 H 2s : 3.50) ( 1 H 1p0 : 0.29)
( 2 H 1s : 0.37) ( 2 H 2s : -3.50) ( 2 H 1p0 : 0.29)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.03346 a.u.
( 1 H 1p+1: 0.54) ( 2 H 1p+1: 0.54)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.03348 a.u.
( 1 H 1p-1: -0.54) ( 2 H 1p-1: -0.54)
Dipole moment for state 1
---------------------------
X : 0.000004 a.u. 0.000010 Debye
Y : 0.000000 a.u. 0.000000 Debye
Z : 0.000173 a.u. 0.000441 Debye
Total : 0.000174 a.u. 0.000441 Debye
Total MC-PDFT time: 00:00:01
H 0.0000 0.0000 -0.3
H 0.0000 0.0000 0.3
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.140699969 0.0e+00 7.1e-02 4 0:00:00
2 -1.142676262 -2.0e-03 2.0e-02 4 0:00:00
3 -1.142880436 -2.0e-04 2.9e-04 1 0:00:00
4 -1.142880613 -1.8e-07 2.4e-05 1 0:00:00
5 -1.142880728 -1.1e-07 3.7e-05 4 0:00:00
6 -1.142880744 -1.6e-08 1.6e-05 3 0:00:00
7 -1.142880752 -8.4e-09 1.8e-06 4 0:00:00
** Convergence reached in 7 iterations
8 -1.142880752 2.3e-10 3.2e-07 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.1428807519481459
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.99327 0.00673
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.993 Energy: -0.39893 a.u.
( 1 H 1s : 0.42) ( 2 H 1s : 0.42)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.007 Energy: 0.45658 a.u.
( 1 H 1s : -1.09) ( 1 H 2s : -0.39) ( 2 H 1s : 1.09)
( 2 H 2s : 0.39)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.28012 a.u.
( 1 H 1s : -0.65) ( 1 H 2s : 0.72) ( 2 H 1s : -0.65)
( 2 H 2s : 0.72)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.47279 a.u.
( 1 H 1s : -0.42) ( 1 H 2s : 2.99) ( 1 H 1p0 : 0.29)
( 2 H 1s : 0.42) ( 2 H 2s : -2.99) ( 2 H 1p0 : 0.29)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.01948 a.u.
( 1 H 1p-1: 0.53) ( 2 H 1p-1: 0.53)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.01948 a.u.
( 1 H 1p+1: 0.53) ( 2 H 1p+1: 0.53)
Dipole moment for state 1
---------------------------
X : -0.000001 a.u. -0.000002 Debye
Y : 0.000006 a.u. 0.000015 Debye
Z : 0.000262 a.u. 0.000666 Debye
Total : 0.000262 a.u. 0.000666 Debye
Total MC-PDFT time: 00:00:01
H 0.0000 0.0000 -0.325
H 0.0000 0.0000 0.325
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.157198837 0.0e+00 3.0e-02 4 0:00:00
2 -1.157569007 -3.7e-04 9.0e-03 4 0:00:00
3 -1.157610561 -4.2e-05 6.4e-05 1 0:00:00
4 -1.157610575 -1.5e-08 8.0e-06 1 0:00:00
5 -1.157610614 -3.9e-08 2.0e-05 4 0:00:00
6 -1.157610618 -4.4e-09 1.2e-05 1 0:00:00
** Convergence reached in 6 iterations
7 -1.157610623 -4.6e-09 4.8e-06 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.1576106228624798
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.99246 0.00754
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.992 Energy: -0.38799 a.u.
( 1 H 1s : -0.42) ( 2 H 1s : -0.42)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.008 Energy: 0.40306 a.u.
( 1 H 1s : 1.05) ( 1 H 2s : 0.38) ( 2 H 1s : -1.05)
( 2 H 2s : -0.38)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.28957 a.u.
( 1 H 1s : -0.66) ( 1 H 2s : 0.72) ( 2 H 1s : -0.66)
( 2 H 2s : 0.72)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.46548 a.u.
( 1 H 1s : -0.47) ( 1 H 2s : 2.79) ( 1 H 1p0 : 0.28)
( 2 H 1s : 0.47) ( 2 H 2s : -2.80) ( 2 H 1p0 : 0.28)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.01397 a.u.
( 1 H 1p+1: -0.34) ( 1 H 1p-1: -0.45) ( 2 H 1p+1: -0.34)
( 2 H 1p-1: -0.45)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.01397 a.u.
( 1 H 1p+1: -0.45) ( 1 H 1p-1: 0.34) ( 2 H 1p+1: -0.45)
( 2 H 1p-1: 0.34)
Dipole moment for state 1
---------------------------
X : 0.000000 a.u. 0.000001 Debye
Y : 0.000004 a.u. 0.000010 Debye
Z : 0.000296 a.u. 0.000753 Debye
Total : 0.000296 a.u. 0.000753 Debye
Total MC-PDFT time: 00:00:00
H 0.0000 0.0000 -0.35
H 0.0000 0.0000 0.35
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.165420916 0.0e+00 2.7e-02 4 0:00:00
2 -1.165729971 -3.1e-04 8.2e-03 4 0:00:00
3 -1.165764279 -3.4e-05 5.5e-05 1 0:00:00
4 -1.165764286 -7.2e-09 1.0e-05 1 0:00:00
** Convergence reached in 4 iterations
5 -1.165764335 -4.9e-08 2.9e-05 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.1657643354660692
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.99152 0.00848
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.992 Energy: -0.37784 a.u.
( 1 H 1s : 0.41) ( 1 H 2s : 0.16) ( 2 H 1s : 0.41)
( 2 H 2s : 0.16)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.008 Energy: 0.35251 a.u.
( 1 H 1s : -1.01) ( 1 H 2s : -0.38) ( 2 H 1s : 1.01)
( 2 H 2s : 0.38)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.29914 a.u.
( 1 H 1s : -0.68) ( 1 H 2s : 0.72) ( 2 H 1s : -0.68)
( 2 H 2s : 0.72)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.45962 a.u.
( 1 H 1s : -0.51) ( 1 H 2s : 2.63) ( 1 H 1p0 : 0.26)
( 2 H 1s : 0.51) ( 2 H 2s : -2.63) ( 2 H 1p0 : 0.26)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.00965 a.u.
( 1 H 1p+1: -0.44) ( 1 H 1p-1: -0.37) ( 2 H 1p+1: -0.44)
( 2 H 1p-1: -0.37)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.00966 a.u.
( 1 H 1p+1: 0.37) ( 1 H 1p-1: -0.44) ( 2 H 1p+1: 0.37)
( 2 H 1p-1: -0.44)
Dipole moment for state 1
---------------------------
X : -0.000003 a.u. -0.000007 Debye
Y : 0.000000 a.u. 0.000000 Debye
Z : 0.000221 a.u. 0.000563 Debye
Total : 0.000221 a.u. 0.000563 Debye
Total MC-PDFT time: 00:00:00
H 0.0000 0.0000 -0.375
H 0.0000 0.0000 0.375
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.168853647 0.0e+00 2.4e-02 4 0:00:00
2 -1.169112740 -2.6e-04 7.4e-03 4 0:00:00
3 -1.169140865 -2.8e-05 5.0e-05 1 0:00:00
4 -1.169140864 7.6e-10 3.7e-06 1 0:00:00
** Convergence reached in 4 iterations
5 -1.169140933 -6.9e-08 2.9e-05 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.1691409331842537
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.99043 0.00957
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.990 Energy: -0.36845 a.u.
( 1 H 1s : -0.41) ( 1 H 2s : -0.17) ( 2 H 1s : -0.41)
( 2 H 2s : -0.17)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.010 Energy: 0.30407 a.u.
( 1 H 1s : 0.96) ( 1 H 2s : 0.38) ( 2 H 1s : -0.96)
( 2 H 2s : -0.38)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.30871 a.u.
( 1 H 1s : -0.70) ( 1 H 2s : 0.73) ( 2 H 1s : -0.69)
( 2 H 2s : 0.72)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.45561 a.u.
( 1 H 1s : 0.56) ( 1 H 2s : -2.48) ( 1 H 1p0 : -0.24)
( 2 H 1s : -0.56) ( 2 H 2s : 2.48) ( 2 H 1p0 : -0.24)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.00668 a.u.
( 1 H 1p+1: -0.53) ( 1 H 1p-1: -0.23) ( 2 H 1p+1: -0.53)
( 2 H 1p-1: -0.23)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.00670 a.u.
( 1 H 1p+1: 0.23) ( 1 H 1p-1: -0.53) ( 2 H 1p+1: 0.23)
( 2 H 1p-1: -0.53)
Dipole moment for state 1
---------------------------
X : -0.000006 a.u. -0.000015 Debye
Y : 0.000005 a.u. 0.000013 Debye
Z : 0.000273 a.u. 0.000693 Debye
Total : 0.000273 a.u. 0.000693 Debye
Total MC-PDFT time: 00:00:00
H 0.0000 0.0000 -0.4
H 0.0000 0.0000 0.4
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.168787524 0.0e+00 2.2e-02 4 0:00:00
2 -1.169005343 -2.2e-04 6.7e-03 4 0:00:00
3 -1.169028405 -2.3e-05 4.1e-05 1 0:00:00
4 -1.169028405 2.0e-12 3.3e-06 1 0:00:00
** Convergence reached in 4 iterations
5 -1.169028485 -8.0e-08 3.4e-05 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.169028485352779
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.98919 0.01081
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.989 Energy: -0.35972 a.u.
( 1 H 1s : 0.41) ( 1 H 2s : 0.18) ( 2 H 1s : 0.41)
( 2 H 2s : 0.18)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.011 Energy: 0.25869 a.u.
( 1 H 1s : -0.92) ( 1 H 2s : -0.38) ( 2 H 1s : 0.92)
( 2 H 2s : 0.38)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.31822 a.u.
( 1 H 1s : -0.71) ( 1 H 2s : 0.73) ( 2 H 1s : -0.71)
( 2 H 2s : 0.73)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.45263 a.u.
( 1 H 1s : -0.61) ( 1 H 2s : 2.35) ( 1 H 1p0 : 0.21)
( 2 H 1s : 0.61) ( 2 H 2s : -2.36) ( 2 H 1p0 : 0.21)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.00523 a.u.
( 1 H 1p+1: 0.52) ( 1 H 1p-1: 0.28) ( 2 H 1p+1: 0.52)
( 2 H 1p-1: 0.28)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.00523 a.u.
( 1 H 1p+1: -0.28) ( 1 H 1p-1: 0.52) ( 2 H 1p+1: -0.28)
( 2 H 1p-1: 0.52)
Dipole moment for state 1
---------------------------
X : -0.000001 a.u. -0.000002 Debye
Y : 0.000006 a.u. 0.000015 Debye
Z : 0.000259 a.u. 0.000659 Debye
Total : 0.000259 a.u. 0.000659 Debye
Total MC-PDFT time: 00:00:00
H 0.0000 0.0000 -0.45
H 0.0000 0.0000 0.45
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.161128629 0.0e+00 3.7e-02 5 0:00:00
2 -1.161808476 -6.8e-04 1.1e-02 4 0:00:00
3 -1.161869221 -6.1e-05 1.0e-04 1 0:00:00
4 -1.161869236 -1.4e-08 9.0e-06 1 0:00:00
5 -1.161869579 -3.4e-07 7.2e-05 4 0:00:00
6 -1.161869641 -6.1e-08 2.2e-05 4 0:00:00
7 -1.161869653 -1.2e-08 1.3e-05 4 0:00:00
8 -1.161869653 -6.2e-10 2.8e-06 1 0:00:00
** Convergence reached in 8 iterations
9 -1.161869653 -3.5e-11 1.9e-06 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.1618696533991333
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.98614 0.01386
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.986 Energy: -0.34398 a.u.
( 1 H 1s : -0.40) ( 1 H 2s : -0.20) ( 2 H 1s : -0.40)
( 2 H 2s : -0.20)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.014 Energy: 0.17736 a.u.
( 1 H 1s : 0.83) ( 1 H 2s : 0.39) ( 2 H 1s : -0.83)
( 2 H 2s : -0.39)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.33713 a.u.
( 1 H 1s : -0.74) ( 1 H 2s : 0.73) ( 2 H 1s : -0.74)
( 2 H 2s : 0.73)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.44911 a.u.
( 1 H 1s : 0.68) ( 1 H 2s : -2.14) ( 1 H 1p0 : -0.17)
( 2 H 1s : -0.68) ( 2 H 2s : 2.14) ( 2 H 1p0 : -0.17)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.00720 a.u.
( 1 H 1p+1: 0.52) ( 1 H 1p-1: 0.32) ( 2 H 1p+1: 0.52)
( 2 H 1p-1: 0.32)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.00721 a.u.
( 1 H 1p+1: 0.32) ( 1 H 1p-1: -0.52) ( 2 H 1p+1: 0.32)
( 2 H 1p-1: -0.52)
Dipole moment for state 1
---------------------------
X : 0.000007 a.u. 0.000018 Debye
Y : 0.000012 a.u. 0.000030 Debye
Z : 0.000237 a.u. 0.000604 Debye
Total : 0.000238 a.u. 0.000605 Debye
Total MC-PDFT time: 00:00:01
H 0.0000 0.0000 -0.5
H 0.0000 0.0000 0.5
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.148779644 0.0e+00 3.1e-02 5 0:00:00
2 -1.149275807 -5.0e-04 8.4e-03 4 0:00:00
3 -1.149313834 -3.8e-05 6.1e-05 1 0:00:00
4 -1.149313851 -1.7e-08 6.9e-06 1 0:00:00
5 -1.149314144 -2.9e-07 6.6e-05 4 0:00:00
6 -1.149314192 -4.8e-08 1.8e-05 4 0:00:00
7 -1.149314200 -7.3e-09 9.9e-06 4 0:00:00
** Convergence reached in 7 iterations
8 -1.149314200 -4.6e-10 1.9e-06 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.1493142001660388
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.98225 0.01775
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.982 Energy: -0.33023 a.u.
( 1 H 1s : 0.40) ( 1 H 2s : 0.21) ( 2 H 1s : 0.40)
( 2 H 2s : 0.21)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.018 Energy: 0.11032 a.u.
( 1 H 1s : -0.76) ( 1 H 2s : -0.39) ( 2 H 1s : 0.76)
( 2 H 2s : 0.39)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.35559 a.u.
( 1 H 1s : -0.77) ( 1 H 2s : 0.74) ( 2 H 1s : -0.77)
( 2 H 2s : 0.74)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.44580 a.u.
( 1 H 1s : 0.73) ( 1 H 2s : -1.96) ( 2 H 1s : -0.73)
( 2 H 2s : 1.96)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.01603 a.u.
( 1 H 1p+1: -0.49) ( 1 H 1p-1: 0.39) ( 2 H 1p+1: -0.49)
( 2 H 1p-1: 0.39)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.01604 a.u.
( 1 H 1p+1: -0.39) ( 1 H 1p-1: -0.49) ( 2 H 1p+1: -0.39)
( 2 H 1p-1: -0.49)
Dipole moment for state 1
---------------------------
X : 0.000010 a.u. 0.000025 Debye
Y : 0.000015 a.u. 0.000039 Debye
Z : 0.000235 a.u. 0.000598 Debye
Total : 0.000236 a.u. 0.000600 Debye
Total MC-PDFT time: 00:00:01
H 0.0000 0.0000 -0.6
H 0.0000 0.0000 0.6
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.117019706 0.0e+00 4.7e-02 5 0:00:00
2 -1.118299607 -1.3e-03 1.0e-02 4 0:00:00
3 -1.118361209 -6.2e-05 1.2e-04 1 0:00:00
4 -1.118362130 -9.2e-07 1.3e-04 4 0:00:00
5 -1.118362287 -1.6e-07 2.9e-05 4 0:00:00
6 -1.118362304 -1.7e-08 1.1e-05 4 0:00:00
7 -1.118362304 -1.5e-10 2.0e-06 1 0:00:00
** Convergence reached in 7 iterations
8 -1.118362304 -3.6e-11 6.1e-07 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.1183623041338813
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.97103 0.02897
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.971 Energy: -0.30735 a.u.
( 1 H 1s : -0.39) ( 1 H 2s : -0.24) ( 2 H 1s : -0.39)
( 2 H 2s : -0.24)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.029 Energy: 0.01021 a.u.
( 1 H 1s : 0.65) ( 1 H 2s : 0.40) ( 2 H 1s : -0.65)
( 2 H 2s : -0.40)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.39129 a.u.
( 1 H 1s : -0.82) ( 1 H 2s : 0.75) ( 2 H 1s : -0.82)
( 2 H 2s : 0.75)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.44069 a.u.
( 1 H 1s : 0.77) ( 1 H 2s : -1.69) ( 2 H 1s : -0.77)
( 2 H 2s : 1.69)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.05216 a.u.
( 1 H 1p+1: 0.57) ( 1 H 1p-1: 0.32) ( 2 H 1p+1: 0.57)
( 2 H 1p-1: 0.32)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.05217 a.u.
( 1 H 1p+1: -0.32) ( 1 H 1p-1: 0.57) ( 2 H 1p+1: -0.32)
( 2 H 1p-1: 0.57)
Dipole moment for state 1
---------------------------
X : 0.000004 a.u. 0.000009 Debye
Y : 0.000008 a.u. 0.000020 Debye
Z : 0.000203 a.u. 0.000517 Debye
Total : 0.000204 a.u. 0.000517 Debye
Total MC-PDFT time: 00:00:01
H 0.0000 0.0000 -0.7
H 0.0000 0.0000 0.7
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.086880553 0.0e+00 3.5e-02 5 0:00:00
2 -1.087620796 -7.4e-04 6.3e-03 4 0:00:00
3 -1.087643410 -2.3e-05 1.3e-04 1 0:00:00
4 -1.087643431 -2.0e-08 9.1e-06 1 0:00:00
5 -1.087643830 -4.0e-07 9.4e-05 4 0:00:00
6 -1.087643871 -4.1e-08 2.1e-05 1 0:00:00
7 -1.087643878 -6.5e-09 1.3e-05 4 0:00:00
** Convergence reached in 7 iterations
8 -1.087643878 -3.8e-11 1.2e-05 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.0876438777327968
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.95315 0.04685
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.953 Energy: -0.28914 a.u.
( 1 H 1s : 0.38) ( 1 H 2s : 0.27) ( 2 H 1s : 0.38)
( 2 H 2s : 0.27)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.047 Energy: -0.05684 a.u.
( 1 H 1s : -0.59) ( 1 H 2s : -0.39) ( 2 H 1s : 0.59)
( 2 H 2s : 0.39)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.42504 a.u.
( 1 H 1s : -0.87) ( 1 H 2s : 0.77) ( 2 H 1s : -0.87)
( 2 H 2s : 0.77)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.43766 a.u.
( 1 H 1s : -0.80) ( 1 H 2s : 1.50) ( 2 H 1s : 0.80)
( 2 H 2s : -1.50)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.04502 a.u.
( 1 H 1s : 0.26) ( 1 H 1p0 : -0.62) ( 2 H 1s : 0.26)
( 2 H 1p0 : 0.62)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.10184 a.u.
( 1 H 1p+1: -0.18) ( 1 H 1p-1: 0.66) ( 2 H 1p+1: -0.18)
( 2 H 1p-1: 0.66)
Dipole moment for state 1
---------------------------
X : 0.000010 a.u. 0.000025 Debye
Y : 0.000005 a.u. 0.000014 Debye
Z : 0.000025 a.u. 0.000064 Debye
Total : 0.000028 a.u. 0.000070 Debye
Total MC-PDFT time: 00:00:01
H 0.0000 0.0000 -0.75
H 0.0000 0.0000 0.75
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.073560812 0.0e+00 1.4e-02 5 0:00:00
2 -1.073683015 -1.2e-04 2.4e-03 4 0:00:00
3 -1.073686144 -3.1e-06 4.9e-05 1 0:00:00
4 -1.073686146 -2.4e-09 2.2e-06 1 0:00:00
** Convergence reached in 4 iterations
5 -1.073686198 -5.2e-08 3.6e-05 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.0736861977839989
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.94069 0.05931
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.941 Energy: -0.28139 a.u.
( 1 H 1s : -0.38) ( 1 H 2s : -0.28) ( 2 H 1s : -0.38)
( 2 H 2s : -0.28)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.059 Energy: -0.08157 a.u.
( 1 H 1s : 0.56) ( 1 H 2s : 0.39) ( 2 H 1s : -0.56)
( 2 H 2s : -0.39)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.43712 a.u.
( 1 H 1s : -0.81) ( 1 H 2s : 1.43) ( 2 H 1s : 0.81)
( 2 H 2s : -1.43)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.43979 a.u.
( 1 H 1s : 0.89) ( 1 H 2s : -0.77) ( 2 H 1s : 0.90)
( 2 H 2s : -0.78)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.00945 a.u.
( 1 H 1s : -0.21) ( 1 H 1p0 : 0.63) ( 2 H 1s : -0.21)
( 2 H 1p0 : -0.63)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.12654 a.u.
( 1 H 1p+1: -0.64) ( 1 H 1p-1: -0.25) ( 2 H 1p+1: -0.64)
( 2 H 1p-1: -0.25)
Dipole moment for state 1
---------------------------
X : -0.000005 a.u. -0.000012 Debye
Y : -0.000000 a.u. -0.000000 Debye
Z : 0.000011 a.u. 0.000027 Debye
Total : 0.000012 a.u. 0.000030 Debye
Total MC-PDFT time: 00:00:00
H 0.0000 0.0000 -0.8
H 0.0000 0.0000 0.8
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.060834921 0.0e+00 1.2e-02 5 0:00:00
2 -1.060927904 -9.3e-05 1.9e-03 4 0:00:00
3 -1.060929937 -2.0e-06 3.5e-05 1 0:00:00
4 -1.060929939 -1.5e-09 1.3e-06 1 0:00:00
** Convergence reached in 4 iterations
5 -1.060929976 -3.7e-08 3.1e-05 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.0609299759850996
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.92513 0.07487
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.925 Energy: -0.27431 a.u.
( 1 H 1s : 0.38) ( 1 H 2s : 0.29) ( 2 H 1s : 0.38)
( 2 H 2s : 0.29)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.075 Energy: -0.10202 a.u.
( 1 H 1s : -0.54) ( 1 H 2s : -0.39) ( 2 H 1s : 0.54)
( 2 H 2s : 0.39)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.43772 a.u.
( 1 H 1s : -0.82) ( 1 H 2s : 1.37) ( 2 H 1s : 0.82)
( 2 H 2s : -1.37)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.45146 a.u.
( 1 H 1s : 0.91) ( 1 H 2s : -0.78) ( 2 H 1s : 0.91)
( 2 H 2s : -0.78)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 0.99641 a.u.
( 1 H 1p0 : 0.65) ( 2 H 1p0 : -0.65)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.14891 a.u.
( 1 H 1p+1: -0.64) ( 1 H 1p-1: -0.26) ( 2 H 1p+1: -0.64)
( 2 H 1p-1: -0.26)
Dipole moment for state 1
---------------------------
X : -0.000002 a.u. -0.000005 Debye
Y : -0.000002 a.u. -0.000005 Debye
Z : -0.000005 a.u. -0.000012 Debye
Total : 0.000006 a.u. 0.000014 Debye
Total MC-PDFT time: 00:00:00
H 0.0000 0.0000 -0.85
H 0.0000 0.0000 0.85
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.049377798 0.0e+00 1.1e-02 5 0:00:00
2 -1.049448418 -7.1e-05 1.6e-03 4 0:00:00
3 -1.049449776 -1.4e-06 2.3e-05 1 0:00:00
4 -1.049449777 -7.6e-10 6.1e-07 1 0:00:00
** Convergence reached in 4 iterations
5 -1.049449803 -2.6e-08 2.6e-05 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.0494498033566835
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.90585 0.09415
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.906 Energy: -0.26777 a.u.
( 1 H 1s : -0.38) ( 1 H 2s : -0.30) ( 2 H 1s : -0.38)
( 2 H 2s : -0.30)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.094 Energy: -0.11880 a.u.
( 1 H 1s : 0.52) ( 1 H 2s : 0.38) ( 2 H 1s : -0.52)
( 2 H 2s : -0.38)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.43938 a.u.
( 1 H 1s : -0.83) ( 1 H 2s : 1.32) ( 2 H 1s : 0.83)
( 2 H 2s : -1.32)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.45872 a.u.
( 1 H 1s : 0.92) ( 1 H 2s : -0.78) ( 2 H 1s : 0.92)
( 2 H 2s : -0.78)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.00427 a.u.
( 1 H 1p0 : 0.66) ( 2 H 1p0 : -0.66)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.16807 a.u.
( 1 H 1p+1: 0.66) ( 1 H 1p-1: 0.24) ( 2 H 1p+1: 0.66)
( 2 H 1p-1: 0.24)
Dipole moment for state 1
---------------------------
X : -0.000003 a.u. -0.000007 Debye
Y : -0.000007 a.u. -0.000018 Debye
Z : -0.000001 a.u. -0.000003 Debye
Total : 0.000008 a.u. 0.000020 Debye
Total MC-PDFT time: 00:00:00
H 0.0000 0.0000 -1.0
H 0.0000 0.0000 1.0
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -1.022299527 0.0e+00 2.4e-02 5 0:00:00
2 -1.022652787 -3.5e-04 3.5e-03 4 0:00:00
3 -1.022659725 -6.9e-06 6.0e-05 1 0:00:00
4 -1.022659729 -3.3e-09 7.0e-07 1 0:00:00
** Convergence reached in 4 iterations
5 -1.022659836 -1.1e-07 5.3e-05 1 0:00:00
Final results
-------------
* State 1
- Energy: -1.0226598364942843
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.81873 0.18127
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.819 Energy: -0.25002 a.u.
( 1 H 1s : 0.38) ( 1 H 2s : 0.32) ( 2 H 1s : 0.38)
( 2 H 2s : 0.32)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.181 Energy: -0.15227 a.u.
( 1 H 1s : -0.49) ( 1 H 2s : -0.37) ( 2 H 1s : 0.49)
( 2 H 2s : 0.38)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.45080 a.u.
( 1 H 1s : -0.85) ( 1 H 2s : 1.20) ( 2 H 1s : 0.85)
( 2 H 2s : -1.20)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.45534 a.u.
( 1 H 1s : -0.91) ( 1 H 2s : 0.78) ( 2 H 1s : -0.91)
( 2 H 2s : 0.77)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.10024 a.u.
( 1 H 1p0 : 0.69) ( 2 H 1p0 : -0.69)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.20552 a.u.
( 1 H 1p+1: -0.70) ( 2 H 1p+1: -0.70)
Dipole moment for state 1
---------------------------
X : -0.000005 a.u. -0.000012 Debye
Y : 0.000000 a.u. 0.000001 Debye
Z : 0.000009 a.u. 0.000023 Debye
Total : 0.000010 a.u. 0.000026 Debye
Total MC-PDFT time: 00:00:00
H 0.0000 0.0000 -1.25
H 0.0000 0.0000 1.25
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -0.999662902 0.0e+00 1.8e-02 4 0:00:00
2 -0.999866062 -2.0e-04 1.5e-03 4 0:00:00
3 -0.999867885 -1.8e-06 6.5e-05 1 0:00:00
4 -0.999867891 -5.9e-09 8.1e-06 1 0:00:00
** Convergence reached in 4 iterations
5 -0.999867909 -1.8e-08 2.1e-05 1 0:00:00
Final results
-------------
* State 1
- Energy: -0.9998679085818641
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.55489 0.44511
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.555 Energy: -0.22008 a.u.
( 1 H 1s : -0.39) ( 1 H 2s : -0.34) ( 2 H 1s : -0.39)
( 2 H 2s : -0.34)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.445 Energy: -0.16990 a.u.
( 1 H 1s : 0.45) ( 1 H 2s : 0.36) ( 2 H 1s : -0.45)
( 2 H 2s : -0.36)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.42907 a.u.
( 1 H 1s : 0.88) ( 1 H 2s : -0.78) ( 2 H 1s : 0.88)
( 2 H 2s : -0.78)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.48629 a.u.
( 1 H 1s : -0.89) ( 1 H 2s : 1.09) ( 2 H 1s : 0.89)
( 2 H 2s : -1.09)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.22325 a.u.
( 1 H 1p0 : -0.71) ( 2 H 1p0 : 0.71)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.23230 a.u.
( 1 H 1p+1: -0.60) ( 1 H 1p-1: 0.38) ( 2 H 1p+1: -0.60)
( 2 H 1p-1: 0.38)
Dipole moment for state 1
---------------------------
X : 0.000001 a.u. 0.000003 Debye
Y : 0.000001 a.u. 0.000003 Debye
Z : -0.000016 a.u. -0.000040 Debye
Total : 0.000016 a.u. 0.000040 Debye
Total MC-PDFT time: 00:00:00
H 0.0000 0.0000 -1.5
H 0.0000 0.0000 1.5
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
╰────────────────────────────────────╯
State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
--------------------------------------------------
- Wave function: MC-PDFT
- DFT functional: tBLYP
--------------------------------------------------
Active space definition:
------------------------
Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
---------------------------------------------------------------------
Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -0.993557101 0.0e+00 5.4e-03 4 0:00:00
2 -0.993586946 -3.0e-05 6.5e-04 4 0:00:00
3 -0.993587298 -3.5e-07 5.1e-05 1 0:00:00
4 -0.993587300 -2.8e-09 5.0e-06 1 0:00:00
** Convergence reached in 4 iterations
5 -0.993587315 -1.5e-08 2.3e-05 1 0:00:00
Final results
-------------
* State 1
- Energy: -0.9935873149617616
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.27419 0.72581
Spin Restricted Orbitals
------------------------
Molecular Orbital No. 1:
--------------------------
Occupation: 1.274 Energy: -0.19023 a.u.
( 1 H 1s : 0.40) ( 1 H 2s : 0.35) ( 2 H 1s : 0.40)
( 2 H 2s : 0.35)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.726 Energy: -0.16441 a.u.
( 1 H 1s : -0.43) ( 1 H 2s : -0.36) ( 2 H 1s : 0.43)
( 2 H 2s : 0.36)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.42499 a.u.
( 1 H 1s : 0.86) ( 1 H 2s : -0.82) ( 2 H 1s : 0.86)
( 2 H 2s : -0.82)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.51450 a.u.
( 1 H 1s : -0.90) ( 1 H 2s : 1.01) ( 2 H 1s : 0.90)
( 2 H 2s : -1.01)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.25237 a.u.
( 1 H 1p+1: -0.31) ( 1 H 1p-1: -0.64) ( 2 H 1p+1: -0.31)
( 2 H 1p-1: -0.63)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.25237 a.u.
( 1 H 1p+1: 0.63) ( 1 H 1p-1: -0.31) ( 2 H 1p+1: 0.63)
( 2 H 1p-1: -0.31)
Dipole moment for state 1
---------------------------
X : 0.000000 a.u. 0.000000 Debye
Y : 0.000000 a.u. 0.000000 Debye
Z : -0.000003 a.u. -0.000006 Debye
Total : 0.000003 a.u. 0.000006 Debye
Total MC-PDFT time: 00:00:00
H 0.0000 0.0000 -2.0
H 0.0000 0.0000 2.0
* Info * Reading basis set from file: /opt/miniconda3/envs/echem/lib/python3.10/site-packages/veloxchem/basis/CC-PVDZ
Molecular Basis (Atomic Basis)
================================
Basis: CC-PVDZ
Atom Contracted GTOs Primitive GTOs
H (2S,1P) (4S,1P)
Contracted Basis Functions : 10
Primitive Basis Functions : 14
Multi-Configurational Self-Consistent Field Driver
====================================================
╭────────────────────────────────────╮
│ Driver settings │
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State-specific calculation
XC functional: tBLYP
Max. iterations : 50
BFGS window : 5
Convergence thresholds:
- Energy change : 1e-08
- Gradient norm : 0.0001
Integrals in memory
Multi-configurational DFT Settings
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- Wave function: MC-PDFT
- DFT functional: tBLYP
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Active space definition:
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Number of inactive (occupied) orbitals: 0
Number of active orbitals: 2
Number of virtual orbitals: 8
This is a CASSCF wavefunction: CAS(2,2)
CI expansion:
-------------
Number of determinants: 3
MC-PDFT Iterations
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Iter. | Average Energy | E. Change | Grad. Norm | CI Iter. | Time
---------------------------------------------------------------------
1 -0.992627083 0.0e+00 5.1e-03 4 0:00:00
2 -0.992651090 -2.4e-05 1.2e-03 4 0:00:00
3 -0.992652443 -1.4e-06 8.8e-05 1 0:00:00
4 -0.992652516 -7.2e-08 6.1e-05 4 0:00:00
5 -0.992652518 -2.7e-09 2.6e-05 1 0:00:00
** Convergence reached in 5 iterations
6 -0.992652519 -5.0e-10 2.9e-06 1 0:00:00
Final results
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* State 1
- Energy: -0.9926525186787296
- S^2 : 0.00 (multiplicity = 1.0 )
- Natural orbitals
1.05363 0.94637
Spin Restricted Orbitals
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Molecular Orbital No. 1:
--------------------------
Occupation: 1.054 Energy: -0.15719 a.u.
( 1 H 1s : -0.41) ( 1 H 2s : -0.36) ( 2 H 1s : -0.41)
( 2 H 2s : -0.36)
Molecular Orbital No. 2:
--------------------------
Occupation: 0.946 Energy: -0.15112 a.u.
( 1 H 1s : 0.42) ( 1 H 2s : 0.36) ( 2 H 1s : -0.42)
( 2 H 2s : -0.36)
Molecular Orbital No. 3:
--------------------------
Occupation: 0.000 Energy: 0.45665 a.u.
( 1 H 1s : 0.87) ( 1 H 2s : -0.88) ( 2 H 1s : 0.87)
( 2 H 2s : -0.88)
Molecular Orbital No. 4:
--------------------------
Occupation: 0.000 Energy: 0.50852 a.u.
( 1 H 1s : 0.89) ( 1 H 2s : -0.93) ( 2 H 1s : -0.89)
( 2 H 2s : 0.93)
Molecular Orbital No. 5:
--------------------------
Occupation: 0.000 Energy: 1.27565 a.u.
( 1 H 1p0 : 0.69) ( 2 H 1p0 : -0.72)
Molecular Orbital No. 6:
--------------------------
Occupation: 0.000 Energy: 1.27566 a.u.
( 1 H 1p0 : 0.72) ( 2 H 1p0 : 0.69)
Dipole moment for state 1
---------------------------
X : -0.000000 a.u. -0.000000 Debye
Y : 0.000000 a.u. 0.000000 Debye
Z : 0.000000 a.u. 0.000000 Debye
Total : 0.000000 a.u. 0.000000 Debye
Total MC-PDFT time: 00:00:00
y5 = np.array(E_tblyp) * 627.5
fig, ax = plt.subplots()
ax.plot(x, y1, label="FullCI")
ax.plot(x, y3, label="BLYP")
ax.plot(x, y4, label="BS-BLYP")
ax.plot(x, y5, label="MC-tBLYP")
ax.axhline(y=0, color="k", linestyle="--")
ax.set_xlabel("H2 distance")
ax.set_ylabel("Energy (kcal/mol)")
ax.legend()
axin = ax.inset_axes([0.5, 0.2, 0.4, 0.4])
axin.set_xlim(1.4, 1.9)
axin.set_ylim(-50, -10)
axin.plot(x, y1, label="FullCI")
axin.plot(x, y3, label="BLYP")
axin.plot(x, y4, label="BS-BLYP")
axin.plot(x, y5, label="MC-tBLYP")
ax.indicate_inset_zoom(axin)
plt.show()
