The simplest method within the NEO framework is the Hartree-Fock (NEO-HF) method, where the total nuclear-electronic wavefunction is approximated as a product of electronic () and nuclear () Slater determinants composed of electronic and protonic spin orbitals, respectively:
(13.33) |
Here, and are collective spatial and spin coordinates of the quantum electrons and protons. The NEO-HF energy for a restricted Hartree-Fock (RHF) treatment of the electrons and a high-spin open-shell treatment of the quantum protons is
(13.34) |
The , indices denote occupied spatial electronic orbitals, and the , indices correspond to occupied spatial protonic orbitals. In Eq. (13.34), and are conventional electronic core Hamiltonian and two-electron integrals, respectively, and the corresponding terms for quantum protons are defined analogously. The last term in Eq. (13.34) is the Coulomb interaction between the electrons and the quantum protons. The spatial electronic and protonic orbitals [ and ] are expanded as linear combinations of electronic or protonic Gaussian basis functions [ or ]:
(13.35a) | ||||
(13.35b) |
The lower-case Greek letters without and with primes denote basis functions for electrons and protons, respectively, and and are electronic and protonic MO expansion coefficients, respectively.
Analogous to the conventional electronic Hartree-Fock method, the electronic and protonic coefficients are determined by variationally minimizing the energy in Eq. (13.34) via the self-consistent field (SCF) procedure. This procedure leads to a set of coupled electronic and protonic Roothaan equations:
(13.36a) | ||||
(13.36b) |
where and are electronic and protonic overlap matrices, respectively. The electronic and protonic Fock elements in Eqs. (13.36a) and (13.36b) are given by
(13.37a) | ||||
(13.37b) |
The electronic and protonic density matrix elements in Eqs. (13.37a) and (13.37b) are defined as
(13.38a) | ||||
(13.38b) |
The generalization to the unrestricted Hartree-Fock (NEO-UHF) treatment of electrons is accomplished by introducing separate spatial orbitals for and electron spins.
The analytical gradients of the NEO-HF energy
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with respect to the classical nuclear coordinates (or coordinates of the centers of the quantum proton basis functions) are available. These gradients allow geometry optimizations within the NEO framework. The analytical Hessians of the NEO-HF energy with respect to the classical nuclear coordinates are also available.
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The Hessians can identify whether the optimized geometries are minima or transition states on the ground state vibronic potential energy surface.
NEO density functional theory (NEO-DFT)
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,
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is an extension of DFT to multicomponent systems within the NEO framework. The Hohenberg-Kohn theorems have been extended to multicomponent systems, where the reference is expressed as the product of electronic and nuclear Slater determinants composed of Kohn-Sham orbitals. The NEO-DFT total energy is
(13.39) |
In this equation, is the interaction of the electronic and protonic densities with the external potential created by the classical nuclei, and contains the electron–electron, proton–proton, and electron-proton classical Coulomb energies, as well as the noninteracting kinetic energies of the quantum particles. The terms , , and are the electron-electron exchange-correlation functional, the proton-proton exchange-correlation functional, and the electron-proton correlation functional, respectively. The quantities
(13.40a) | ||||
(13.40b) |
are the electron and proton densities, respectively, and and are the electronic and protonic Kohn-Sham spatial orbitals, respectively. These orbitals are obtained by solving two sets of coupled Kohn-Sham equations for the electrons and quantum protons:
(13.41a) | ||||
(13.41b) |
The effective potentials and are obtained by taking the derivative of the total energy expression in Eq. (13.39) with respect to electron density and proton density, respectively. Analogous to NEO-HF, these electronic and protonic Kohn-Sham orbitals are expanded as linear combinations of electronic or protonic Gaussian basis functions ( and ). The extension to open-shell electron systems is analogous to the NEO-UHF method.
The practical implementation of the NEO-DFT method requires an electron-electron exchange-correlation functional, a proton-proton exchange-correlation functional, and an electron-proton correlation functional. Any conventional electron-electron exchange-correlation functional can be used within the NEO-DFT framework.
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J. Chem. Phys.
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Because the proton-proton exchange and correlation are negligible in molecular systems, only the exchange at the NEO-Hartree-Fock level is included to eliminate self-interaction error in the NEO-DFT method. A suitable electron-proton correlation functional is essential for obtaining accurate proton densities and energies, and the epc17-2
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J. Chem. Phys.
(2017),
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,
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J. Phys. Chem. Lett.
(2017),
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and epc19
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functionals are designed to achieve this goal. These two functionals are based on the multicomponent extension of the Colle-Salvetti formalism. The epc17-2 functional is of the local density approximation (LDA) type with the functional form:
(13.42) |
The epc19 functional is its multicomponent generalized gradient approximation (GGA) extension that depends on the electron and proton density gradients and is of the form:
(13.43) |
In addition to the parameters , , and in the epc17-2 functional,
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J. Phys. Chem. Lett.
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the epc19 functional
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has the and parameters and also depends on the proton mass .
Analogous to the NEO-HF analytical energy gradients, the NEO-DFT analytical gradients
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J. Chem. Theory Comput.
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are available for these two functionals,
allowing geometry optimizations on the ground state vibronic potential energy surface. The NEO-DFT analytical Hessians
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J. Chem. Theory Comput.
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are available for the epc17-2 functional or when no electron-proton correlation functional is used and allow characterization of the stationary points.
The essential $rem variables for toggling a NEO-DFT calculation are NEO = TRUE and one of the two options: (1) specify METHOD or (2) specify EXCHANGE and CORRELATION. We inherit Q-Chem’s conventional, electronic DFT library, and therefore METHOD, EXCHANGE, and CORRELATION should be set to a functional listed in Section 5.3. Although it has not been tested across all possible combinations and permutations, NEO-DFT should be able to support the vast majority of the electronic XC functionals listed. Supported JOBTYPE’s include SP, FORCE, OPT, TS, and FREQ. Consult Section 13.5.4 for the full list of variables as well as see the examples in Section 13.5.6. Lastly, the electron-proton correlation functional should be set to one of the supported types:
NEO_EPC
NEO_EPC
Specifies the electron-proton correlation functional.
TYPE:
STRING
DEFAULT:
No default
OPTIONS:
NAME
Use NEO_EPC = NAME, where NAME can be either epc172 or epc19.
RECOMMENDATION:
Consult the NEO literature to guide your selection.
The NEO multistate DFT (NEO-MSDFT) method was developed to describe hydrogen transfer and hydrogen tunneling systems within the NEO
framework.
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,
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J. Phys. Chem. Lett.
(2023),
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Analogous to the conventional electronic MSDFT method,
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pp. 6760.
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,
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,
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,
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(2022),
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the NEO-MSDFT method linearly combines localized NEO-DFT states in a nonorthogonal configuration interaction (NOCI) scheme.
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J. Chem. Phys.
(2005),
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This approach captures the delocalized, bilobal proton densities needed to describe hydrogen tunneling and avoids complications of local minima in orbital space.
Consider a system with transferring protons, where each proton moves in a double-well potential in the Born-Oppenheimer picture. In NEO-DFT calculations, the protonic density tends to localize in one well of a symmetric or nearly symmetric double-well potential instead of delocalizing over both wells. Quantizing each transferring proton with the NEO approach leads to diabatic NEO-DFT states. Each diabatic state has the protonic density of each transferring proton localized in one of the two wells of its corresponding double-well potential. In practice, higher-energy diabatic states can be excluded from the NOCI expansion. The set of all diabatic NEO-DFT states is , where . Each diabatic state is the product of a Kohn-Sham electronic and protonic determinant, as discussed in Section 13.5.2.2.
The adiabatic NEO-MSDFT states are linear combinations of all diabatic NEO-DFT states:
(13.44) | ||||
The coefficients in Eq. (13.44) are determined by solving the matrix eigenvalue problem
(13.45) |
The overlap matrix and effective Hamiltonian matrix contain the overlap and couplings, respectively, between pairs of
localized diabatic states. Note that the diagonal elements of are unity, and the diagonal elements of are the NEO-DFT
energies of the diabatic states. For the sake of brevity, the analytical forms of the off-diagonal terms of these matrices are excluded here but are
given in previous work.
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The limitations of the epc functionals and the resulting inaccuracies of the overlap between two localized NEO-DFT states, as well as the approximate form of the off-diagonal Hamiltonian matrix elements, can be accounted for by applying a simple correction function to the off-diagonal elements of the matrix:
(13.46) |
Users can control the values of and used in NEO-MSDFT calculations, and their default values were determined though a fitting process discussed in our previous work.
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Setting both these parameters to unity produces the original overlap matrix. However, in general the alpha and beta parameters should be kept at their default values unless another parameterization procedure is performed to determine alternative values.
A NEO-MSDFT calculation can be enabled by setting the $rem variable NEO_MSDFT = 1 in addition to the variables in the NEO-DFT subsection (see 13.5.2.2):
NEO_MSDFT
NEO_MSDFT
Enable a NEO-MSDFT calculation
TYPE:
INTEGER
DEFAULT:
0
No NEO-MSDFT calculation.
OPTIONS:
1
Enable a NEO-MSDFT calculation.
0
Disable a NEO-MSDFT calculation.
RECOMMENDATION:
See Section 13.5.2.3 for details on customizing a NEO-MSDFT calculation.
Analytical gradients have also been
implemented,
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allowing users to optimize geometries on specified NEO-MSDFT surfaces by setting JOBTYPE =
OPT. By default, analytical derivative couplings between NEO-MSDFT states are computed directly following an analytical gradient
calculation,
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but this calculation can be disabled. Note that the only gradients and derivative couplings printed out are those pertaining to the ground and
first-excited NEO-MSDFT states, as these are the only states of physical relevance (as explained elsewhere
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).
Users can also request a semi-numerical Hessian calculation by setting IDERIV = 2. Further control of a NEO-MSDFT calculation is given by the $neo_msdft section,
whose job-control options are given below:
OPT_STATE
Controls which NEO-MSDFT state is geometry-optimized when JOBTYPE = OPT
or which NEO-MSDFT surface the semi-numerical Hessian will be calculated on when IDERIV = 2.
INPUT SECTION: $neo_msdft
TYPE:
INTEGER
DEFAULT:
0
Ground-State
OPTIONS:
Indicates optimization/semi-numerical Hessian calculation will occur on the th NEO-MSDFT surface.
RECOMMENDATION:
Ensure that is strictly less than the number of diabatic states included in the adiabatic state expansion of Eq. (13.44).
ALPHA
Sets the parameter used for the overlap correction of Eq. (13.46).
INPUT SECTION: $neo_msdft
TYPE:
FLOAT
DEFAULT:
0.0604
OPTIONS:
User-defined.
RECOMMENDATION:
Keep default value unless another parameterization procedure is performed.
BETA
Sets the parameter used for the overlap correction of Eq. (13.46).
INPUT SECTION: $neo_msdft
TYPE:
FLOAT
DEFAULT:
0.492
OPTIONS:
User-defined.
RECOMMENDATION:
Keep default value unless another parameterization procedure is performed.
NACV
Controls if analytical derivative couplings are calculated following an analytical gradient calculation.
INPUT SECTION: $neo_msdft
TYPE:
INTEGER
DEFAULT:
1
Enables derivative coupling calculation.
OPTIONS:
1
Enables derivative coupling calculation.
0
Disables derivative coupling calculation.
RECOMMENDATION:
None.
DENPLT
Controls the generation of proton density cube files for NEO-MSDFT states.
INPUT SECTION: $neo_msdft
TYPE:
INTEGER
DEFAULT:
-1
Disables generation of proton density cube files.
OPTIONS:
Enables generation of proton density cube files for NEO-MSDFT states .
RECOMMENDATION:
Users can also generate electron density cube files for each of the specified NEO-MSDFT states via the $plots section
(refer to Section 10.5.4.1 for details). Also note that if , a directory neo_msdft_denplt
will be created in the current working directory where all the generated cube files will be written.
CPSCF_THRESH
Controls the convergence criteria for the NEO-CPSCF routine. Solving the NEO-CPSCF equations is required for calculating
the analytical gradients of the NEO-MSDFT energies.
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The NEO-CPSCF routine is considered converged when the error is less than .
INPUT SECTION: $neo_msdft
TYPE:
INTEGER
DEFAULT:
8
OPTIONS:
User-defined.
RECOMMENDATION:
Tightening the NEO-CPSCF convergence will improve the reliability of the analytical gradients.
CPSCF_NSTEPS
Controls the maximum number of NEO-CPSCF iterations permitted. Solving the NEO-CPSCF equations is required for calculating the
analytical gradients of the NEO-MSDFT energies.
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The NEO-CPSCF routine will fail if it does not converge within a CPSCF_NSTEPS number of steps.
INPUT SECTION: $neo_msdft
TYPE:
INTEGER
DEFAULT:
300
OPTIONS:
User-defined.
RECOMMENDATION:
If CPSCF_THRESH is higher than the default, increasing the number of iterations permitted in the NEO-CPSCF routine may be needed.
FDIFF_STEP
Sets the distance each center is perturbed if a semi-numerical Hessian calculation is requested.
INPUT SECTION: $neo_msdft
TYPE:
FLOAT
DEFAULT:
Å
OPTIONS:
User-defined.
RECOMMENDATION:
If INPUT_BOHR = FALSE, then the step size input by the user will be measured in Å. If INPUT_BOHR =
TRUE, then the step size input by the user will be measured in bohr.
As discussed in previous work,
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,
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each quantum transferring proton in NEO-MSDFT is given two basis function centers:
one center localized near the donor and another center localized near the acceptor. When requesting a NEO-MSDFT calculation, in the $molecule
section, each quantum transferring proton must have one center input as a standard H atom center and its other center input as a ghost H atom center.
These centers must be listed consecutively in the $molecule section. Additionally, it is assumed that all ghost H atom centers in the $molecule section
of a NEO-MSDFT calculation belong to a quantum transferring proton.
By default, all possible NEO-DFT diabatic states are included in the adiabatic state expansion of Eq. (13.44). If this is not desired, users can provide an input to the $neo_msdft_diabat_control section to specify which diabatic states to include. This input section takes in an array of Boolean values (input as ones or zeros), where each row is a unique string corresponding to a particular diabatic state. These Booleans refer to whether or not a quantum transferring proton is localized on each proton basis function center in the order in which they appear in the $molecule section. Thus, if the number of diabatic states the user wants to include is and the number of quantum transferring protons is , the $neo_msdft_diabat_control section should contain an array with rows and columns, where the -th row specifies which proton basis function centers have a localized quantum proton in the -th diabatic state. Note that other protons can be quantized with NEO that do not correspond to a transferring proton and therefore are represented by a single proton basis function center; these protons should not be included in the $neo_msdft_diabat_control section. Examples showing how to set up NEO-MSDFT calculations/input files with both one and multiple transferring protons can be found in Section 13.5.6.
The overlap correction of Eq. (13.46) is parameterized to produce accurate proton densities and tunneling splittings when the proton basis function centers are optimized for separate NEO-DFT diabatic states (see the procedures explained in our previous
work).
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,
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However, users may wish to perform geometry optimizations on NEO-MSDFT surfaces instead.
One can either optimize the positions of just the proton basis function centers for fixed geometries of classical nuclei or optimize the positions of both
the classical nuclei and proton basis function centers simultaneously. Both cases require the user to set JOBTYPE = OPT,
but in the former case, the $opt section must be used to freeze the classical nuclei during the optimization (see Section 9.4.3
for details). In either case, the input of the $molecule section serves as an initial guess for the optimization, so users must make an informed guess as
to where to initially place each of the two proton basis function centers for each quantum transferring proton.
In NEO-SCF calculations, the nuclear solution corresponds to the variational nuclear wavefunction (density) for the specific method and basis sets.
The nuclear orbitals in molecular systems
are localized, and therefore the quantized nuclei can be treated as distinguishable when analyzing their position expectation values.
These expectation values are generally not equal to the input coordinates of the NEO nuclear basis function centers.
Control over the position expectation values of the nuclei can be achieved with the constrained (C)NEO approach,
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based on the original NEO method
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and in analogy to the conventional constrained DFT (Section 5.11).
This is accomplished by imposing the following constraint:
(13.47) |
where is the chosen value for the position expectation value for nucleus . For geometry optimizations and vibrational frequency calculations, typically is the position of the NEO nuclear basis function center, as defined by the input coordinates. The constraint is imposed by using Lagrange multipliers. In this case, the protonic part of the coupled Kohn-Sham equations of NEO-DFT (Eq. (13.41b)) becomes:
(13.48) |
where is the Lagrange multiplier. In practice, the value of is optimized numerically to satisfy the constraint in Eq. (13.47).
CNEO calculations can be invoked by setting CNEO = TRUE in addition to the variables for NEO-HF 13.5.2.1 (or NEO-DFT 13.5.2.2):
CNEO
CNEO
Enable a CNEO calculation.
Using CNEO with multiple quantum protons automatically activates the nuclear Hartree product approximation.
TYPE:
LOGICAL/INTEGER
DEFAULT:
FALSE
No CNEO calculation.
OPTIONS:
TRUE (or 1)
Enable a CNEO calculation.
FALSE (or 0)
Disable a CNEO calculation.
RECOMMENDATION:
None.
Analytical CNEO gradients
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and Hessians
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are available, allowing geometry optimizations with
JOBTYPE = OPT and vibrational frequency calculations with JOBTYPE = FREQ.
CNEO can be used with Hartree-Fock or with DFT in conjunction with the epc17-2 or epc19 electron-proton correlation functional and the
electron exchange-correlation functionals available in Q-Chem. Note that using CNEO with multiple quantum protons invokes the nuclear Hartree product approximation (Section 13.5.2.5).
In NEO-HF, the total wavefunction is a product of electronic and nuclear Slater determinants (Section 13.5.2.1); relatedly, in NEO-DFT, the reference is a product of Slater determinants (Section 13.5.2.2). Because the nuclear orbitals in molecular systems are highly localized and the overlap between them is effectively zero, the nuclear exchange interactions are numerically insignificant,
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Chem. Rev.
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and we can treat the quantum nuclei as distinguishable. This means that we can approximate the nuclear wavefunction as a Hartree product instead of a Slater determinant:
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J. Chem. Phys.
(2010),
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(13.49) |
Here, the product is over quantum protons, are the collective spatial and spin coordinates for the quantum protons, and is the spin orbital for the th quantum proton. The total wavefunction is then (see also Eq. (13.33)):
(13.50) |
Note that a high-spin configuration is assumed for the protonic wavefunction, and therefore the protonic spin orbitals can be replaced with spatial orbitals multiplied by the same spin function. For NEO-HF, Eq. (13.50) leads to coupled one-nucleus Roothaan equations instead of one -nucleus Roothaan equation (Eq. (13.36b)). For NEO-DFT, it leads to coupled one-nucleus Kohn-Sham equations (Eq. (13.41b)). Making use of the localized nature of the quantum nuclei, the spatial nuclear orbitals for each nucleus (Eq. (13.35)) are expanded in the local basis set for that nucleus (i.e., different nuclei do not share basis functions).
The nuclear Hartree product approximation can be activated by setting NEO_N_HARTREE_PROD = TRUE in addition to the variables for NEO-HF 13.5.2.1 (or NEO-DFT 13.5.2.2):
NEO_N_HARTREE_PROD
NEO_N_HARTREE_PROD
Enable the nuclear Hartree product approximation.
TYPE:
LOGICAL/INTEGER
DEFAULT:
FALSE
OPTIONS:
TRUE (or 1)
Enable a nuclear Hartree product calculation.
FALSE (or 0)
Disable a nuclear Hartree product calculation.
RECOMMENDATION:
Use simultaneous NEO-SCF for faster convergence.
It is recommended to use the simultaneous NEO-SCF algorithms for faster convergence (Section 13.5.4.3). By default, the Coulomb and exchange self-interaction terms for each nucleus are computed. Similarly to NEO-SCF calculations with one quantum proton, the evaluation of these terms can be turned off with NEO_VPP = FALSE to further accelerate the calculations. Note that this does not change the NEO-SCF energy and the occupied orbitals, but it does affect the nuclear virtual orbitals.
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Chem. Phys. Lett.
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Note that the supported JOBTYPE’s are the same as for CNEO 13.5.2.4 and include SP, FORCE, OPT, TS, and FREQ.
The LR-NEO-TDDFT method
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is a multicomponent extension of the linear response TDDFT method within the NEO framework.
It allows the simultaneous calculation of the electronic and proton vibrational excitation energies. In the (LR)-NEO-TDDFT method,
the linear response of the NEO Kohn-Sham system to perturbative external fields is computed. The NEO-TDDFT working equation is
(13.51) |
where
(13.52) | ||||
(13.53) | ||||
(13.54) | ||||
(13.55) | ||||
(13.56) |
Here, the occupied electronic orbitals are denoted with indices and , whereas the unoccupied electronic orbitals are denoted with indices and . The analogous upper case indices denote protonic orbitals. The solution of Eq. (13.51) provides the electronic and proton vibrational excitation energies , as well as the transition excitation and de-excitation amplitudes, and , respectively. Analogous to the TDDFT method, the Tamm-Dancoff approximation (TDA) can be imposed within the NEO framework, defining the NEO-TDDFT-TDA method that is represented by
(13.57) |
The extension of the NEO-TDDFT and NEO-TDDFT-TDA approaches to open-shell electron systems is straightforward.
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NEO-TDHF and NEO-CIS have similar forms as NEO-TDDFT and NEO-TDA without electron-proton, electron-electron, or proton-proton correlation.
The analytical gradients for NEO-CIS/NEO-TDA/NEO-TDHF/NEO-TDDFT are available,
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enabling geometry optimizations on the excited state vibronic potential energy surfaces. For NEO-TDA and NEO-TDDFT,
analytical gradients are available for the epc17-2 functional or when no electron-proton correlation functional is used.
The transition densities can be analyzed to determine the percentages of electronic and protonic character for each vibronic excited state.
The LR-NEO-TDHF (or TDDFT) method is activated by the following keyword:
RPA
RPA
Do a NEO-TDDFT or NEO-TDHF calculation.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
FALSE
Do a NEO-TDA or NEO-CIS calculation.
TRUE
Do a NEO-TDDFT or NEO-TDHF calculation.
RECOMMENDATION:
Consult the NEO literature to guide your selection.
Furthermore, the variables for NEO-HF 13.5.2.1 (or NEO-DFT 13.5.2.2) should be included. Supported JOBTYPE’s include SP and OPT. Additional customization can be controlled by the following $rem variables:
CIS_N_ROOTS
CIS_N_ROOTS
Sets the number of NEO excited state roots to find by Davidson or display the number of roots obtained by direct diagonalization.
TYPE:
INTEGER
DEFAULT:
0
Do not look for any excited states.
OPTIONS:
Looks for NEO excited states.
RECOMMENDATION:
None
RPA
RPA
Do a NEO-TDDFT or NEO-TDHF calculation.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
FALSE
Do a NEO-TDA or NEO-CIS calculation.
TRUE
Do a NEO-TDDFT or NEO-TDHF calculation.
RECOMMENDATION:
Consult the NEO literature to guide your selection.
DIRECT_DIAG
DIRECT_DIAG
Perform direct diagonalization to obtain all the NEO excitation energies.
TYPE:
INTEGER
DEFAULT:
0
Use Davidson algorithm.
OPTIONS:
1
Do the direct diagonalization.
0
Use Davidson algorithm.
RECOMMENDATION:
Only use this option when Davidson solutions are not stable.
CIS_STATE_DERIV
CIS_STATE_DERIV
This keyword is used to specify for which NEO excited state the gradient or geometry optimization is needed.
TYPE:
INTEGER
DEFAULT:
No default.
OPTIONS:
Looks to calculate gradient or conduct geometry optimization for the th NEO
excited state.
RECOMMENDATION:
Consult the keyword NEO_SET_ESTATE if gradient is desired for a vibronic excited state with dominant electronic character.
NEO_SET_ESTATE
NEO_SET_ESTATE
This keyword is used to specify for which vibronic excited state with dominant electronic character the gradient or geometry optimization is needed.
TYPE:
INTEGER
DEFAULT:
No default.
OPTIONS:
Looks to calculate gradient or conduct geometry optimization for the th NEO
vibronic excited state with dominant electronic character.
RECOMMENDATION:
Make sure enough roots are requested by the CIS_N_ROOTS keyword because the vibronic excited states
with dominant protonic character usually come before.
NEO_SET_OPT
NEO_SET_OPT
Enable a NEO excited state geometry optimization.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
1
Enable a NEO excited state geometry optimization.
0
Disable a NEO excited state geometry optimization.
RECOMMENDATION:
Need to use with CIS_STATE_DERIV. Consult the keyword NEO_SET_ESTATE
if geometry optimization is desired for a vibronic excited state with dominant electronic character.
NEO_ZVEC_LINEAR
NEO_ZVEC_LINEAR
Use linear solver for -vector equations for NEO excited state gradient.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
1
Use linear solver
0
Use iterative conjugate gradient solver
RECOMMENDATION:
Use the default iterative conjugate gradient solver because it is more memory efficient.
NEO_ZVEC_CG_MAXITER
NEO_ZVEC_CG_MAXITER
Controls the maximum number of iterative gradient solver iterations permitted.
TYPE:
INTEGER
DEFAULT:
300
OPTIONS:
Use iterations.
RECOMMENDATION:
None.
NEO_ZVEC_CG_CONV
NEO_ZVEC_CG_CONV
The convergence threshold () for the iterative gradient solver for NEO -vector equations.
TYPE:
INTEGER
DEFAULT:
8
OPTIONS:
Use iterations.
RECOMMENDATION:
None.
SET_SUBSPACE
SET_SUBSPACE
Specify the number of protonic guess vectors for NEO-TDDFT
TYPE:
INTEGER
DEFAULT:
Number of states desired (as set by CIS_N_ROOTS) if the number is smaller than the size of the
protonic subspace (number of protonic occupied orbitals number of protonic virtual orbitals) or
the size of the protonic subspace
OPTIONS:
Use vectors.
RECOMMENDATION:
None.
Real-time NEO time-dependent density functional theory (RT-NEO-TDDFT or RT-NEO for brevity)
is a multicomponent extension of conventional electronic RT-TDDFT
within the NEO framework
1479
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(2020),
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and is an approach that enables the modeling of
nonequilibrium, non-Born-Oppenheimer nuclear-electronic quantum dynamics. This approach assumes the form of the single Slater determinant
product ansatz of the NEO-DFT reference system,
where and are collective spatial and spin coordinates of the quantum electrons and protons,
(or ) is the single particle density matrix and (or )
is the Kohn-Sham matrix for the electrons (or protons), and is the time. The time-dependent Schrödinger equation
(13.58) |
can be propagated according to the set of multicomponent von Neumann equations:
(13.59a) | |||
(13.59b) |
Note that these equations are not propagated independently, but are actually coupled through Fock terms that depend on both particle densities. The electron and proton densities are evolved together in time. The resulting electronic and protonic dipole moments can be obtained at every time step and analyzed via post-processing to provide relevant spectral features. Fourier transformation of these signals from the corresponding time-domain to the frequency-domain can yield both electronic and vibrational spectra that have been shown to agree well with LR-NEO-TDDFT. In addition, this approach provides the nonequilbrium, real-time dynamics of the electronic and protonic densities.
Up to this point, the equations of motion presented above
[Eq. (13.59a) and Eq. (13.59b) assume that the classical nuclei
are held at a fixed geometry throughout the entire simulation.
To combine the real-time dynamics of the electrons and protons together with the mean-field motion of the
classical nuclei, the RT-NEO-TDDFT-Ehrenfest approach has been formulated.
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(2020),
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In this approach, the classical nuclei are evolved according to Newtonian dynamics,
while the nonequilibrium electrons and protons are still being propagated according to Eq. (13.59a) and
Eq. (13.59b), respectively:
(13.60) |
Here we denote and to be the mass and the position, respectively, of the th classical nucleus, and the abbreviated form of the total nuclear gradient expression is . We support both of these approaches, i.e., RT-NEO with fixed classical nuclei and RT-NEO with moving classical nuclei, and we have designated those methods as METHOD = REALTIME and METHOD = EHRENFEST, respectively.
In addition to electrons, it is important that the proton dynamics is adequately described throughout the course of a given trajectory.
This is especially important in cases where proton delocalization may start to occur, such as during a proton transfer reaction or when the
geometry of the classical nuclei is no longer held fixed.
To provide the flexibility for describing proton delocalization, one may use a larger protonic basis set and/or utilize multiple fixed proton basis (FPB) function centers placed at pre-designated positions.
Alternatively, a traveling proton basis (TPB) approach has been formulated and will be made available in a future release.
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153,
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Examples of using either one or multiple FPB function centers can be found in Section 13.5.6) of this manual .
In certain applications, the requirement of using a small time step due to the fast electronic dynamics can prohibit long simulation times.
For systems that are electronically adiabatic, the
electronic Born-Oppenheimer (BO) approximation can be invoked by quenching the electrons to an instantaneous electronic ground state
via the standard self-consistent-field (SCF) procedure instead of
propagating Eq. (13.59a) at every time step:
788
J. Chem. Phys.
(2023),
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(13.61) |
This approach enables the use of a time step that is several orders of magnitude larger than that required for integrating Eq. (13.59a), therefore rendering longer simulation times more tractable. The electronic BO approximation can be invoked for RT-NEO with fixed classical nuclei or for RT-NEO with moving classical nuclei by toggling the methods METHOD = BO-REALTIME or METHOD = BO-EHRENFEST, respectively.
A RT-NEO-HF or RT-NEO-TDDFT calculation can be invoked by setting NEO_TDKS = TRUE in the $rem section. In addition, the variables for NEO-HF 13.5.2.1 (or NEO-DFT 13.5.2.2) should be included, and note that the JOBTYPE $rem variable is not used as it’s not applicable:
NEO_TDKS
NEO_TDKS
Enable a real-time NEO-TDHF or NEO-TDDFT calculation.
TYPE:
LOGICAL
DEFAULT:
FALSE
No RT-NEO calculation.
OPTIONS:
TRUE
Enable a RT-NEO calculation.
FALSE
Disable a RT-NEO calculation.
RECOMMENDATION:
None.
Additional job control is provided in its own input section. The input file for a RT-NEO propagation is illustrated in several examples in Section 13.5.6, however, the available controls are also discussed below. Note that the keywords and field types defined for $tdks (Section 7.4) are not the same parameters as those defined for the $neo_tdks, and vice versa. Only parameters/keywords documented below are supported. The parameters of the jobs are set using options specified in the $neo_tdks input section. The format of the $neo_tdks section is analogous to the $rem section:
$neo_tdks <Keyword> <parameter/option> $end
Note: The following job control variables belong only in the $neo_tdks section. Do not place them in the $rem section.
METHOD
Specifies which RT-NEO dynamics approach will be used to propagate the system.
INPUT SECTION: $neo_tdks
TYPE:
STRING
DEFAULT:
NONE
OPTIONS:
Realtime
Fixed classical nuclei
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(2020),
11,
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Ehrenfest
Moving classical nuclei
1480
J. Chem. Phys.
(2020),
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BO-Realtime
Fixed classical nuclei with electronic BO approximation
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J. Chem. Phys.
(2023),
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pp. 114118.
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BO-Ehrenfest
Moving classical nuclei with electronic BO approximation
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RECOMMENDATION:
None.
DT
Specifies the time step , in atomic units.
INPUT SECTION: $neo_tdks
TYPE:
DOUBLE
DEFAULT:
0.04
OPTIONS:
User-selected.
RECOMMENDATION:
None.
MAXITER
Specifies the maximum number of time steps to simulate.
INPUT SECTION: $neo_tdks
TYPE:
INTEGER
DEFAULT:
NONE
OPTIONS:
User-selected.
RECOMMENDATION:
The total propagation length is .
ELECTRONIC_HOMO_TO_LUMO
Performs a HOMO LUMO excitation for a single electron prior to time propagation.
An unrestricted calculation is performed when this keyword is invoked.
INPUT SECTION: $neo_tdks
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
TRUE
FALSE
RECOMMENDATION:
Should not use in conjunction with the electronically adiabatic approximation.
To perturb the system, a time-dependent electric field pulse can be applied via a dipole coupling term added to the electronic and/or protonic Fock matrices,
(13.62a) | ||||
(13.62b) |
where (or ) is the unperturbed Kohn-Sham matrix and (or ) is the dipole moment matrix for the electrons (or protons). Note that the dipole moment (i.e., and ) have the opposite sign for electrons and protons. Tunable parameters for FIELD_TYPE are provided in the additional keywords found below. For the supported field types below, note that the electric field vector is a quantity whose magnitude is controlled by FIELD_AMP and whose direction is controlled by FIELD_DIRECTION.
Delta simulates a Dirac -function kick with a field that is turned on only at time :
(13.63) |
The amplitude of and its direction are set using FIELD_AMP and FIELD_DIRECTION, respectively.
Gaussian simulates the following impulse field that is turned on at all times :
(13.64) |
The amplitude of and its direction are set using FIELD_AMP and FIELD_DIRECTION, respectively.
The center of the pulse is set using the FIELD_PEAK keyword.
The pulse half-width is set using the FIELD_TAU keyword.
The pulse frequency is set using the FIELD_FREQUENCY keyword.
FIELD_TYPE
The external applied field
INPUT SECTION: $tdks
TYPE:
STRING
DEFAULT:
NONE
OPTIONS:
DELTA
-function kick
GAUSSIAN
Impulse field (Gaussian envelope)
NONE
No field
RECOMMENDATION:
No recommendation.
FIELD_AMP
The amplitude of the external field, in atomic units.
INPUT SECTION: $tdks
TYPE:
DOUBLE
DEFAULT:
0.01
OPTIONS:
NONE
RECOMMENDATION:
No recommendation.
FIELD_PEAK
The peak position (in atomic units of time) for the Gaussian impulse field.
INPUT SECTION: $tdks
TYPE:
DOUBLE
DEFAULT:
0.0
OPTIONS:
NONE
RECOMMENDATION:
No recommendation.
FIELD_TAU
The value of (in atomic units of time) for the Gaussian impulse field.
INPUT SECTION: $tdks
TYPE:
DOUBLE
DEFAULT:
800.0
OPTIONS:
NONE
RECOMMENDATION:
No recommendation.
FIELD_FREQUENCY
The frequency of the external field, in eV units.
INPUT SECTION: $tdks
TYPE:
DOUBLE
DEFAULT:
6.0
OPTIONS:
NONE
RECOMMENDATION:
No recommendation.
FIELD_DIRECTION
The direction of the external applied field vector.
INPUT SECTION: $tdks
TYPE:
STRING
DEFAULT:
NONE
OPTIONS:
XYZ
Pulse along the direction {1, 1, 1}
X
Pulse along the direction {1, 0, 0}
Y
Pulse along the direction {0, 1, 0}
Z
Pulse along the direction {0, 0, 1}
NONE
RECOMMENDATION:
No recommendation.
FIELD_PARTICLE
The subsystem on which to apply the external field perturbation.
INPUT SECTION: $tdks
TYPE:
STRING
DEFAULT:
NONE
OPTIONS:
BOTH
Electrons and quantized protons
ELECTRONS
PROTONS
RECOMMENDATION:
No recommendation.
By quantizing select nuclei, NEO gives rise to a potential energy surface with fewer nuclear degrees of freedom, which prevents a direct
calculation of the vibrational frequencies of the entire molecule. Consequently, diagonalization of a coordinate Hessian in the NEO framework yields
vibrational frequencies and accompanying normal modes of only the classical nuclei, with the quantum nuclei responding instantaneously to the motion
of the classical nuclei.
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J. Chem. Phys.
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Although the fundamental anharmonic vibrational frequencies of the quantum nuclei can be accurately
obtained through LR-NEO-TDDFT,
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J. Chem. Phys.
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the couplings between the vibrations of the classical and quantum nuclei are missing.
To obtain the fully coupled molecular vibrations, an effective strategy denoted NEO-DFT(V) was developed.
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(2019),
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pp. 1167.
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,
282
J. Chem. Theory Comput.
(2019),
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The NEO-DFT(V) method has been shown to incorporate key anharmonic effects in full molecular vibrational analyses and to produce accurate
molecular vibrational frequencies compared to experiments.
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(2019),
10,
pp. 1167.
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,
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J. Chem. Theory Comput.
(2019),
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The NEO-DFT(V) method involves diagonalization of an extended NEO Hessian composed of partial second derivatives of the coordinates of the classical nuclei () and the expectation values of the quantum nuclei (). This extended Hessian matrix is composed of three sub-matrices: , , and , where in each case, all other coordinates of the classical nuclei and expectation values of the quantum nuclei are fixed. The extended Hessian has the following structure:
(13.65) |
where
(13.66a) | ||||
(13.66b) | ||||
(13.66c) |
The quantity and the NEO Hessian matrix is
(without the constraint that the expectation values of the quantum nuclei are fixed).
In the expression for the matrix, is the diagonal mass matrix, and is the diagonal matrix with elements corresponding to the squares of the LR-NEO-TDDFT fundamental vibrational frequencies.
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J. Phys. Chem. Lett.
(2019),
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is a unitary matrix that transforms to the target coordinate system and is approximated with the transition dipole moment vectors afforded by a LR-NEO-TDDFT calculation.
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Diagonalization of produces the fully coupled molecular vibrational frequencies including anharmonic effects associated with the quantum protons. NEO-SCF(V) calculations can be invoked by setting NEO_SCFV = TRUE:
NEO_SCFV
NEO_SCFV
Enable a NEO-SCFV calculation
TYPE:
INTEGER
DEFAULT:
0 No NEO-SCFV calculation.
OPTIONS:
1 Enable a NEO-SCFV calculation.
0 Disable a NEO-SCFV calculation.
RECOMMENDATION:
None.
In addition, the variables for NEO-HF 13.5.2.1 (or NEO-DFT 13.5.2.2) should be included, and JOBTYPE should be set to FREQ. Furthermore, the NEO-HF(V) method involves building the extended NEO-Hessian based on the NEO-HF Hessian and inputs from NEO-TDHF, and therefore the variables specific to LR-NEO-TDHF (TDDFT) ( 13.5.2.6) can be also be used to tune the calculation.
An alternative route for inclusion of correlation effects between quantum particles (i.e., electrons and protons) is with wave functions methods that
are systematically improvable and parameter-free.
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J. Chem. Phys.
(2002),
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pp. 4106.
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,
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Chem. Rev.
(2020),
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pp. 4222.
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Among the various developed multicomponent wave function methods, the NEO coupled cluster (NEO-CC) methods have been particularly
successful.
1002
J. Chem. Theory Comput.
(2018),
15,
pp. 338.
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,
1004
J. Chem. Phys.
(2019),
151,
pp. 074104.
Link
,
1005
J. Phys. Chem. Lett.
(2020),
11,
pp. 1578.
Link
,
1006
J. Phys. Chem. Lett.
(2021),
12,
pp. 1631.
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The NEO-CC wave function is given by
(13.67) |
where is the cluster operator that incorporates the correlation effects between quantum particles, and is the NEO-HF reference wave function. In the NEO-CCSD method,
1002
J. Chem. Theory Comput.
(2018),
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pp. 338.
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the cluster operator is given by
(13.68) |
where are the excitation operators expressed in terms of
creation/annihilation () fermionic operators, and is the excitation rank. Here, the indices denote occupied
electronic orbitals, the indices denote unoccupied electronic orbitals, and the indices denote general electronic orbitals.
The protonic orbitals are denoted analogously using the capitalized indices. The unknown wave function parameters (amplitudes) are
determined by solving the set of nonlinear equations for each :
1002
J. Chem. Theory Comput.
(2018),
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pp. 338.
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(13.69) |
In this equation, is the second-quantized NEO Hamiltonian, where and are conventional electronic core Hamiltonian and two-electron integrals, respectively. The remaining protonic ( and ) and electron-proton () integrals are defined analogously. Lastly, the NEO-CCSD energy is calculated from
(13.70) |
To increase the computational efficiency and reduce the memory requirements for the NEO-CCSD method, the two-particle integrals can be approximated with the density fitting (DF) approximation,
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(2021),
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in which the two-particle four-center integrals are factorized into a sum of products of three-center and two-center two-particle integrals.
In particular, the four-center two-electron integrals are approximated by
(13.71) |
where and are three-center and two-center two-electron integrals, respectively. In this equation, and indices denote electronic and auxiliary electronic basis functions, respectively. The four-center two-proton integrals are approximated analogously by
(13.72) |
where primed indices denote protonic basis functions and and are three-center and two-center two-proton integrals, respectively. Finally, the four-center electron-proton integrals are approximated as
(13.73) |
By employing the DF approximation, the memory requirements for storing four-center two-particle
integrals are reduced from to , where and are the number of electronic or protonic basis functions and auxiliary basis functions, respectively.
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(2021),
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Currently only JOBTYPE = SP is supported. NEO-CC is activated by the following keyword in addition to the variables for NEO-HF (NEO = TRUE and METHOD = HF):
NEO_RICCSD
NEO_RICCSD
Enable a NEO-RICCSD calculation.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
1
Enable this option.
0
Disable this option.
RECOMMENDATION:
Both electronic and protonic auxiliary basis sets must be specified.
The following additional $rem variables can also be used to customize the NEO-RICCSD calculation (also see the examples in Section 13.5.6):
NEO_CCSD_MAX_CYCLES
NEO_CCSD_MAX_CYCLES
Controls the maximum number of CC iterations permitted.
TYPE:
INTEGER
DEFAULT:
5000
OPTIONS:
Set the maximum number of iterations to .
RECOMMENDATION:
None
NEO_CCSD_CONVERGENCE
NEO_CCSD_CONVERGENCE
NEO-RICCSD is considered converged when the energy error is less than
.
TYPE:
INTEGER
DEFAULT:
8
OPTIONS:
User-defined
RECOMMENDATION:
None
Second-order Møller-Plesset perturbation theory provides a useful framework for wave function based correlation effects with lower cost than NEO-CC
1275
Chem. Phys. Lett.
(2005),
404,
pp. 394.
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. The NEO-MP2 correlation energy is composed of the electron-electron, proton-proton and electron-proton contributions:
(13.74) |
where
(13.75a) | ||||
(13.75b) | ||||
(13.75c) |
Here, and are occupied electronic spin orbitals with energies and , and are virtual (unoccupied) electronic spin orbitals with energies and , and uppercase indices indicate the analogous protonic spin orbitals and energies.
To provide accuracy that is competitive with NEO-CCSD, NEO-MP2 has been extended to include orbital optimization and empirical spin-component and electron-proton correlation scaling.
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J. Phys. Chem. Lett.
(2020),
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,
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J. Phys. Chem. Lett.
(2021),
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This leads to the NEO equivalents of SOS-OOMP2 (O2)
823
J. Chem. Phys.
(2007),
126,
pp. 164101.
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and SOS-MP2
471
J. Chem. Phys.
(2003),
118,
pp. 9095.
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,
637
J. Chem. Phys.
(2004),
121,
pp. 9793.
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(Sections 6.6.5 and 6.6.6). The NEO equivalents are referred to as NEO-SOS-OOMP2 and NEO-SOS-MP2 to indicate the inclusion of an electron-proton correlation scaling factor:
(13.76) |
where and are the same- and opposite-spin parts of the electron-electron correlation energy, which are scaled by and , respectively, and is the electron-proton scaling factor.
Orbital optimization is performed by minimizing the NEO-MP2 energy with respect to the unitary operator formed from the rotation operator , with being the set of unknown electronic and protonic orbital rotation parameters. Optimal orbital rotation parameters are solved for by finding the stationary points of electronic and protonic orbital gradients and , which have elements
(13.77a) | |||
and | |||
(13.77b) |
and are solved in an alternating fashion until self-consistency is achieved. For computational efficiency, all NEO-MP2 methods are implemented with the density fitting approximation for two-particle integrals,
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as described in more detail in Section 13.5.2.9.
Currently only JOBTYPE = SP is supported. NEO-MP2 methods are invoked with NEO_RIMP2 = 1 to run without orbital optimization and NEO_RIMP2 = 2 to run with orbital optimization. Additionally, the variables for NEO-HF (NEO = TRUE and METHOD = HF) should be included:
NEO_RIMP2
NEO_RIMP2
Enable a NEO-MP2 or NEO-OOMP2 calculation.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
2
Perform a NEO-OOMP2 calclulation.
1
Perform a NEO-MP2 calculation.
0
Disable this option.
RECOMMENDATION:
Both electronic and protonic auxiliary basis sets must be specified.
Spin-component scaling settings are controlled with the SCS variable. Custom and can be set with SSS_FACTOR and SOS_FACTOR, respectively, when SCS = 3 is set (arbitrary scaling). By default, is set to the same value as , but a custom electron-proton scaling factor can be input with the EP_FACTOR variable, which will always override the default set by SCS. These settings are as follows (also see the examples in Section 13.5.6):
SCS
SCS
Set the type of spin-component scaling.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
1
Turns on spin-component scaling with SCS (, ).
2
Turns on spin-component scaling with SOS (, for MP2, for OOMP2).
3
arbitrary SCS (set with SSS_FACTOR and SOS_FACTOR).
0
no spin-component scaling.
RECOMMENDATION:
NONE
SSS_FACTOR
SSS_FACTOR
Controls the strength of the same-spin component of the MP2 electron-electron correlation energy.
TYPE:
INTEGER
DEFAULT:
1000000
OPTIONS:
Corresponding to .
RECOMMENDATION:
NONE
SOS_FACTOR
SOS_FACTOR
Controls the strength of the opposite-spin component of the MP2 electron-electron correlation energy.
TYPE:
INTEGER
DEFAULT:
1000000
OPTIONS:
Corresponding to .
RECOMMENDATION:
NONE
EP_FACTOR
EP_FACTOR
Controls the strength of the electron-proton component of the NEO-MP2 correlation energy.
TYPE:
INTEGER
DEFAULT:
1000000
OPTIONS:
Corresponding to .
RECOMMENDATION:
NONE
The NEO Configuration Interaction (NEO-CI) wavefunction is a linear combination of NEO configurations:
(13.78) |
where is electronic determinant and is nuclear determinant .
The electronic determinant is composed of electronic orbitals and the nuclear determinant is composed of protonic orbitals.
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J. Chem. Theory Comput.
(2025),
21,
pp. 3968.
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The NEO-CI wavefunction is almost always truncated to include only single, or single and double excitations into the virtual orbital space. In the single-reference case, the electronic and nuclear determinants use the NEO-HF electronic and nuclear orbitals, respectively. In the multi-reference case, the electronic and nuclear orbitals are optimized via NEO-MCSCF. The orbitals can be optimized for multiple states with state-averaging.
Available models include:
NEO-MCSCF(CASSCF,RASSCF)
NEO-CI
NEO-MR-CI
NEO-OOMRCI
In addition to setting NEO = TRUE, METHOD = HF, and JOBTYPE = SP, the job settings for these available models are controlled by the following $rem variables:
Note: Wavefunction Keywords
NEO_WF_N_ELECS
NEO_WF_N_ELECS
Total number of electrons in wavefunction.
TYPE:
INTEGER
DEFAULT:
(Read from $molecule input.)
OPTIONS:
User-defined
RECOMMENDATION:
NONE
NEO_WF_E_FROZEN_CORE
NEO_WF_E_FROZEN_CORE
Number of electronic frozen core orbitals. Orbitals are doubly occupied in all configurations.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
Generally, 1s orbitals can be treated as frozen core orbitals.
NEO_WF_E_FROZEN_VIRT
NEO_WF_E_FROZEN_VIRT
Number of electronic frozen virtual orbitals. These orbitals are unoccupied in all configurations.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
Virtual orbitals contribute to the dynamic correlation recovered by CI calculations,
so it is not recommended that this value is set, except in special cases.
NEO_WF_E_DOCC
NEO_WF_E_DOCC
Number of electronic reference doubly-occupied orbitals minus the
CI frozen core orbitals. There are NEO_WF_E_XLEVEL excitations out of
these orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
NONE
NEO_WF_E_RAS
NEO_WF_E_RAS
Number of electronic reference restricted active space orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
NONE
NEO_WF_E_RAS_NHOLES
NEO_WF_E_RAS_NHOLES
Maximum Number of electronic reference excitations out of the RAS orbitals
and into the CAS and AUX orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
NONE
NEO_WF_E_CAS
NEO_WF_E_CAS
Number of electronic reference complete active space orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
NONE
NEO_WF_E_AUX
NEO_WF_E_AUX
Number of electronic reference auxilliary space orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
NONE
NEO_WF_E_AUX_NELECS
NEO_WF_E_AUX_NELECS
Maximum number of electronic reference excitations into the AUX orbitals
from the RAS and AUX orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
NONE
NEO_WF_E_XLEVEL
NEO_WF_E_XLEVEL
Electronic excitation level of NEO-CI expansion: 1 = single, 2 = single and double, etc.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
NONE
NEO_WF_N_FROZEN_VIRT
NEO_WF_N_FROZEN_VIRT
Number of nuclear frozen virtual orbitals. These orbitals are unoccupied in all configurations.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
Virtual orbitals contribute to the dynamic correlation recovered by CI calculations,
so it is not recommended that this value is set, except in special cases.
NEO_WF_N_DOCC
NEO_WF_N_DOCC
Number of nuclear reference doubly-occupied orbitals.
There are NEO_WF_N_XLEVEL excitations out of these orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
NONE
NEO_WF_N_CAS
NEO_WF_N_CAS
Number of nuclear reference complete active space orbitals.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
NONE
NEO_WF_N_XLEVEL
NEO_WF_N_XLEVEL
Nuclear excitation level of NEO-CI expansion: 1 = single, 2 = single and double, etc.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
NONE
Note: NEO-MRCI Keywords
NEO_MRCI
NEO_MRCI
Perform NEO Multireference Configuration Interaction
TYPE:
BOOLEAN
DEFAULT:
FALSE
OPTIONS:
TRUE
Run a NEO-MRCI Calculation.
FALSE
Do not run a NEO-MRCI Calculation.
RECOMMENDATION:
NONE
NEO_MRCI_MAX_ITER
NEO_MRCI_MAX_ITER
Maximum NEO CI iterations.
TYPE:
INTEGER
DEFAULT:
100
OPTIONS:
User-defined
RECOMMENDATION:
NONE
NEO_MRCI_NUM_ROOTS
NEO_MRCI_NUM_ROOTS
Number of NEO CI states to converge.
TYPE:
INTEGER
DEFAULT:
1
OPTIONS:
User-defined
RECOMMENDATION:
Due to the spectrum and structure of the NEO CI Hamiltonian, it is advisable
to set NEO_MRCI_NUM_ROOTS to be greater than the number of desired roots.
NEO_MRCI_KSPACE_MIN
NEO_MRCI_KSPACE_MIN
Minimum size of Krylov subspace.
TYPE:
INTEGER
DEFAULT:
NEO_MRCI_NUM_ROOTS + 1
OPTIONS:
User-defined
RECOMMENDATION:
Increasing the number of guess vectors improves CI convergence but has increased
memory costs.
NEO_MRCI_KSPACE_MAX
NEO_MRCI_KSPACE_MAX
Maximum size of Krylov subspace.
TYPE:
INTEGER
DEFAULT:
NEO_MRCI_KSPACE_MIN + 5
OPTIONS:
User-defined
RECOMMENDATION:
Increasing the number of guess vectors before contraction improves CI convergence
but has increased memory costs.
NEO_MRCI_PREDIAG_ROUTINE
NEO_MRCI_PREDIAG_ROUTINE
Choose how initial guess vectors are created.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0
Linear combination of lowest NEO_MRCI_PREDIAG_DIM NEO-CI diagonal elements.
1
Eigenvectors of NEO_MRCI_PREDIAG_DIM x NEO_MRCI_PREDIAG_DIM block of NEO-CI Hamiltonian.
2
MCSCF vectors are used for initial guess.
RECOMMENDATION:
0
NEO_MRCI_PREDIAG_DIM
NEO_MRCI_PREDIAG_DIM
Dimension for NEO_MRCI_PREDIAG_ROUTINE
TYPE:
INTEGER
DEFAULT:
1000
OPTIONS:
User-defined
RECOMMENDATION:
The larger the size, the better the initial guess.
NEO_MRCI_CONV_THRESH
NEO_MRCI_CONV_THRESH
Convergence tolerance for roots of NEO-CI. It is defined as
TYPE:
INTEGER
DEFAULT:
5
OPTIONS:
4
Sufficient for energies.
5
Gradients and couplings.
RECOMMENDATION:
4
NEO_MRCI_PRINT_CIVECS
NEO_MRCI_PRINT_CIVECS
Print the final NEO CI vectors to civec.dat.
TYPE:
BOOLEAN
DEFAULT:
TRUE
OPTIONS:
User-defined
RECOMMENDATION:
None
NEO_MRCI_READ_CIVECS
NEO_MRCI_READ_CIVECS
Read in NEO CI vectors from civec.dat.
TYPE:
BOOLEAN
DEFAULT:
FALSE
OPTIONS:
User-defined
RECOMMENDATION:
This can be used to restart from a previously unconverged CI calculation.
NEO_MRCI_READ_MOS
NEO_MRCI_READ_MOS
Read in MO coefficients from mocoefs.electronic and mocoefs.protonic.
TYPE:
BOOLEAN
DEFAULT:
FALSE
OPTIONS:
User-defined
RECOMMENDATION:
None
NEO_MRCI_PRINT_LEVEL
NEO_MRCI_PRINT_LEVEL
Determines print level for NEO CI calculation.
TYPE:
INTEGER
DEFAULT:
1
OPTIONS:
0
No convergence information is printed. Only iteration number and timings.
1
Convergence information is printed.
1
Detailed printing for debugging.
RECOMMENDATION:
1
NEO_MRCI_CIVEC_ANALYSIS
NEO_MRCI_CIVEC_ANALYSIS
Perform brief analysis for CI vectors, largest contributing configurations.
TYPE:
BOOLEAN
DEFAULT:
FALSE
OPTIONS:
FALSE
No analysis is performed.
TRUE
Analysis is performed.
RECOMMENDATION:
FALSE
NEO_MRCI_CIDEN_PRINT
NEO_MRCI_CIDEN_PRINT
Print the NEO CI protonic densities of the converged roots to .cube files
TYPE:
BOOLEAN
DEFAULT:
FALSE
OPTIONS:
FALSE
Do not print protonic densities.
TRUE
Print protonic densities.
RECOMMENDATION:
None
Note: NEO-MCSCF Keywords
NEO_MCSCF
NEO_MCSCF
Run a NEO-MCSCF calculation.
TYPE:
BOOLEAN
DEFAULT:
FALSE
OPTIONS:
FALSE
Do not run a NEO-MCSCF.
TRUE
Run a NEO-MCSCF.
RECOMMENDATION:
None
NEO_MCSCF_DEBUG
NEO_MCSCF_DEBUG
Run NEO-MCSCF in debug mode.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
0
Do not debug NEO-MCSCF.
1
Debug NEO-MCSCF
RECOMMENDATION:
0
NEO_MCSCF_MACRO_MAX_ITER
NEO_MCSCF_MACRO_MAX_ITER
Maximum number of NEO-MCSCF macroiterations.
TYPE:
INTEGER
DEFAULT:
50
OPTIONS:
User-defined
RECOMMENDATION:
Most CAS calculations should require few macroiterations. More complex RASSCF wavefunctions
may require more iterations as convergence can be slow.
NEO_MCSCF_MACRO_CONV_THRESH
NEO_MCSCF_MACRO_CONV_THRESH
Orbital gradient convergence tolerance for NEO-MCSCF. Defined as .
TYPE:
INTEGER
DEFAULT:
5
OPTIONS:
User-defined
RECOMMENDATION:
5
NEO_MCSCF_MICRO_MAX_ITER
NEO_MCSCF_MICRO_MAX_ITER
Maximum NEO-CI iterations.
TYPE:
INTEGER
DEFAULT:
1000
OPTIONS:
User-defined
RECOMMENDATION:
Set as high as necessary to converge all roots required.
1000
NEO_MCSCF_MICRO_OPT_MAX_ITER
NEO_MCSCF_MICRO_OPT_MAX_ITER
Maximum number of orbital optimizations per macroiteration.
TYPE:
INTEGER
DEFAULT:
5
OPTIONS:
User-defined
RECOMMENDATION:
5
NEO_MCSCF_EMC_CONV_THRESH
NEO_MCSCF_EMC_CONV_THRESH
Convergence threshold for NEO-MCSCF energy. Defined as .
TYPE:
INTEGER
DEFAULT:
8
OPTIONS:
User-defined
RECOMMENDATION:
8
NEO_MCSCF_NSTATES
NEO_MCSCF_NSTATES
Number of NEO-CI roots to compute during microiterations.
TYPE:
INTEGER
DEFAULT:
1
OPTIONS:
User-defined
RECOMMENDATION:
None
NEO_MCSCF_SA
NEO_MCSCF_SA
Perform state-averaged NEO-MCSCF.
TYPE:
BOOLEAN
DEFAULT:
FALSE
OPTIONS:
FALSE
Perform CASSCF.
TRUE
Perform SA-MCSCF
RECOMMENDATION:
None
NEO_MCSCF_SA_NSTATES
NEO_MCSCF_SA_NSTATES
Number of states to include in state-averaging.
TYPE:
INTEGER
DEFAULT:
0
OPTIONS:
User-defined
RECOMMENDATION:
None
NEO_MCSCF_PRINT_CIVECS
NEO_MCSCF_PRINT_CIVECS
Print the NEO-MCSCF CI vectors to mcvec.dat.
TYPE:
BOOLEAN
DEFAULT:
FALSE
OPTIONS:
FALSE
No printing.
TRUE
MCSCF CI vectors are printed to mcvec.dat and wavefunction is printed to mcwf.dat.
RECOMMENDATION:
None
NEO_MCSCF_READ_MOS
NEO_MCSCF_READ_MOS
Read MCSCF MO coefficients from mocoefs.electronic and mocoefs.protonic.
TYPE:
BOOLEAN
DEFAULT:
FALSE
OPTIONS:
FALSE
NEO-HF MO coefficients used for initial guess.
TRUE
MO coefficients from files used as initial guess.
RECOMMENDATION:
None
NEO_MCSCF_PRINT_MOS
NEO_MCSCF_PRINT_MOS
Print MCSCF MO coefficients to mocoefs.electronic.new and mocoefs.protonic.new.
TYPE:
BOOLEAN
DEFAULT:
TRUE
OPTIONS:
TRUE
Print MO coefficients.
FALSE
MO coefficients are not printed.
RECOMMENDATION:
TRUE
NEO_MCSCF_PRINT_LEVEL
NEO_MCSCF_PRINT_LEVEL
Print level for NEO-MCSCF.
TYPE:
INTEGER
DEFAULT:
1
OPTIONS:
0
Only convergence information is printed.
1
Macro and micro iteration information is printed.
2
Detailed printing.
RECOMMENDATION:
1
NEO_MCSCF_OPT_METHOD
NEO_MCSCF_OPT_METHOD
Orbital optimization method for NEO-MCSCF.
TYPE:
INTEGER
DEFAULT:
2
OPTIONS:
0
GDM macroiterations. No microiterations.
1
Augmented Hessian macroiterations. Augmented Hessian microiterations.
2
Augmented Hessian macroiterations. GDM microiterations.
RECOMMENDATION:
2
NEO_MCSCF_KSPACE_MIN
NEO_MCSCF_KSPACE_MIN
Minimum size of the Krylov subspace for NEO-CI microiterations.
TYPE:
INTEGER
DEFAULT:
NEO_MCSCF_NSTATES + 2
OPTIONS:
User-defined
RECOMMENDATION:
None
NEO_MCSCF_KSPACE_MAX
NEO_MCSCF_KSPACE_MAX
Maximum size of the Krylov subspace for NEO-CI microiterations.
TYPE:
INTEGER
DEFAULT:
NEO_MCSCF_KSPACE_MIN + 10
OPTIONS:
User-defined
RECOMMENDATION:
None
NEO_MCSCF_CIDEN_PRINT
NEO_MCSCF_CIDEN_PRINT
Print the CI protonic density for MCSCF states to *.cube files.
TYPE:
BOOLEAN
DEFAULT:
FALSE
OPTIONS:
FALSE
Do not print density.
TRUE
Print density.
RECOMMENDATION:
None
NEO_MCSCF_REORDER_MOS
NEO_MCSCF_REORDER_MOS
Reorder initial guess molecular orbitals. Requires reorder_mo.txt and reorder_nuc_mo.txt.
TYPE:
BOOLEAN
DEFAULT:
FALSE
OPTIONS:
FALSE
Orbitals are not reordered.
TRUE
Orbitals are reordered.
RECOMMENDATION:
None