13.4 The Nuclear-electronic Orbital (NEO) Approach: Integrating Electronic and Nuclear Quantum Effects in Quantum Chemistry

13.4.4 Job Control for the NEO-SCF methods

The NEO method is a natural extension of the Self-Consistent-Field methods and it inherits most of its functionalities. Thus, the keywords that are used in the SCF Job Control are used in the NEO-SCF methods with a few additional keywords. The NEO-SCF methods require definition of the nuclear basis sets (see Examples for more information). Refer to Ref. Culpitt:2019 for selection of the protonic basis sets. Only pure (Spherical) Gaussian basis sets are currently available. The following three $rem variables must be specified in order to run NEO-SCF calculations:

NEO
       Enable a NEO-SCF calculation.
TYPE:
       BOOLEAN
DEFAULT:
       FALSE
OPTIONS:
       TRUE Enable a NEO-SCF calculation. FALSE Disable a NEO-SCF calculation.
RECOMMENDATION:
       Set to TRUE if desired.

METHOD
       Specifies the exchange-correlation functional.
TYPE:
       STRING
DEFAULT:
       No default
OPTIONS:
       NAME Use METHOD = NAME, where NAME is one of the following: HF for Hartree-Fock theory; one of the DFT methods listed in Section 5.3.4.;
RECOMMENDATION:
       In general, consult the literature to guide your selection. Our recommendations for DFT are indicated in bold in Section 5.3.4.

BASIS
       Specifies the electronic basis sets to be used.
TYPE:
       STRING
DEFAULT:
       No default basis set
OPTIONS:
       General, Gen User defined ($basis keyword required). Symbol Use standard basis sets as per Chapter 8. Mixed Use a mixture of basis sets (see Chapter 8).
RECOMMENDATION:
       Consult literature and reviews to aid your selection.

In addition, the following $rem variables, that appear in the conventional SCF calculations can be used to customize the NEO-SCF calculation:

SCF_CONVERGENCE
       NEO-SCF is considered converged when the electronic wave function error is less that 10-SCF_CONVERGENCE. Adjust the value of THRESH at the same time. (Starting with Q-Chem 3.0, the DIIS error is measured by the maximum error rather than the RMS error as in earlier versions.)
TYPE:
       INTEGER
DEFAULT:
       5 For single point energy calculations. 8 For geometry optimizations.
OPTIONS:
       User-defined
RECOMMENDATION:
       None.

NEO_N_SCF_CONVERGENCE
       NEO-SCF is considered converged when the nuclear wave function error is less that 10-NEO_N_SCF_CONVERGENCE.
TYPE:
       INTEGER
DEFAULT:
       7
OPTIONS:
       User-defined
RECOMMENDATION:
       None.

UNRESTRICTED
       Controls the use of restricted or unrestricted orbitals.
TYPE:
       LOGICAL
DEFAULT:
       FALSE Closed-shell systems. TRUE Open-shell systems.
OPTIONS:
       FALSE Constrain the spatial part of the alpha and beta orbitals to be the same. TRUE Do not Constrain the spatial part of the alpha and beta orbitals.
RECOMMENDATION:
       The ROHF method is not available. Note that for unrestricted calculations on systems with an even number of electrons it is usually necessary to break α/β symmetry in the initial guess, by using SCF_GUESS_MIX or providing $occupied information (see Section 4.4 on initial guesses).

MAX_SCF_CYCLES
       Controls the maximum number of SCF iterations permitted.
TYPE:
       INTEGER
DEFAULT:
       50
OPTIONS:
       n n>0 User-selected.
RECOMMENDATION:
       Increase for slowly converging systems such as those containing transition metals.

SCF_ALGORITHM
       Algorithm used for converging the SCF.
TYPE:
       STRING
DEFAULT:
       DIIS Pulay DIIS.
OPTIONS:
       DIIS Pulay DIIS. DM Direct minimizer. DIIS_DM Uses DIIS initially, switching to direct minimizer for later iterations (See THRESH_DIIS_SWITCH, MAX_DIIS_CYCLES). DIIS_GDM Use DIIS and then later switch to geometric direct minimization (See THRESH_DIIS_SWITCH, MAX_DIIS_CYCLES). GDM Geometric Direct Minimization. RCA Relaxed constraint algorithm RCA_DIIS Use RCA initially, switching to DIIS for later iterations (see THRESH_RCA_SWITCH and MAX_RCA_CYCLES described later in this chapter) ROOTHAAN Roothaan repeated diagonalization.
RECOMMENDATION:
       In the NEO methods, the GDM procedure is recommended.

JOBTYPE
       Specifies the calculation.
TYPE:
       STRING
DEFAULT:
       Default is single-point, which should be changed to one of the following options.
OPTIONS:
       OPT Equilibrium structure optimization. TS Transition structure optimization is currently not available in NEO. RPATH Intrinsic reaction path following is currently not available in NEO.
RECOMMENDATION:
       Application-dependent. Always use SYM_IGNORE = 1 with geometry optimization.

XC_GRID
       Specifies the type of grid to use for DFT calculations.
TYPE:
       INTEGER
DEFAULT:
       Functional-dependent; see Table 5.3.
OPTIONS:
       0 Use SG-0 for H, C, N, and O; SG-1 for all other atoms. n Use SG-n for all atoms, n=1,2, or 3 XY A string of two six-digit integers X and Y, where X is the number of radial points and Y is the number of angular points where possible numbers of Lebedev angular points, which must be an allowed value from Table 5.2 in Section 5.5. -XY Similar format for Gauss-Legendre grids, with the six-digit integer X corresponding to the number of radial points and the six-digit integer Y providing the number of Gauss-Legendre angular points, Y=2N2.
RECOMMENDATION:
       Use the default unless numerical integration problems arise. Larger grids may be required for optimization and frequency calculations.

Additional NEO specific $rem variables can be used to customize the NEO-SCF calculation:

NEO_E_CONV
       Energy convergence criteria in the NEO-SCF calculations so that the difference in energy between electronic and protonic iterations is less than 10-NEO_E_CONV.
TYPE:
       INTEGER
DEFAULT:
       8
OPTIONS:
       User-defined
RECOMMENDATION:
       Tighter criteria for geometry optimization are recommended.

NEO_BASIS_LIN_DEP_THRESH
       This keyword is used to set the liner dependency threshold for nuclear basis sets. It is defined as 10-NEO_BASIS_LIN_DEP_THRESH.
TYPE:
       DOUBLE
DEFAULT:
       5.0
OPTIONS:
       User-defined
RECOMMENDATION:
       No recommendation.

NEO_PURECART
       This keyword is used to specify Cartesian or spherical Gaussians for nuclear basis functions.
TYPE:
       INTEGER
DEFAULT:
       2222
OPTIONS:
       User-defined
RECOMMENDATION:
       Default are Cartesian Gaussians. 1111 would define spherical Gaussians similar to keyword PURECART. Current NEO calculations do not support Cartesian electronic or nuclear basis sets with h angular momentum.

NEO_ISOTOPE
       Enable calculations of different types of isotopes. Only one type of isotope is allowed at present.
TYPE:
       INTEGER
DEFAULT:
       1 Default is the proton isotope.
OPTIONS:
       1 This NEO calculation is using proton isotope. 2 This NEO calculation is using deuterium isotope. 3 This NEO calculation is using tritium isotope.
RECOMMENDATION:
       Refer to the NEO literature for the best performance on the isotope effects calculations.

NEO_VPP
       Remove J-K terms from the nuclear Fock matrix and the corresponding kernel terms for NEO excited state methods for the case of one quantum proton.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       1 Enable this option. 0 Disable this option.
RECOMMENDATION:
       Use this only in the case of one quantum hydrogen.

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 following additional $rem variables can be used to customize the NEO excited states methods calculation to obtain excitation energies:

SET_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:
       n n>0 Looks for n NEO excited states.
RECOMMENDATION:
       None

SET_RPA
       Do a NEO-TDDFT or NEO-TDHF calculation.
TYPE:
       LOGICAL/INTEGER
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
       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.