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13.5 Nuclear–Electronic Orbital Method

13.5.9 Examples

(April 13, 2024)

Example 13.7  Input for the NEO-HF calculation on H2O molecule with the second proton treated quantum-mechanically. The electronic basis set is cc-pVDZ and the protonic is an uncontracted 2s2p2d basis set with exponents 4.0 and 8.0.

$molecule
   0 1
   H   -3.5008791    1.2736107    0.7596000
   O   -3.9840791    1.3301107   -0.0574000
   H   -4.9109791    1.2967107    0.1521000
$end

$rem
   METHOD   hf
   BASIS    cc-pvdz
   NEO      true
$end

$neo_basis
H    3
S    1    1.000000
   4.0 1.0
S    1    1.000000
   8.0 1.0
P    1    1.000000
   4.0 1.0
P    1    1.000000
   8.0 1.0
D    1    1.000000
   4.0 1.0
D    1    1.000000
   8.0 1.0
****
$end

Example 13.8  Input for the NEO-DFT-epc172 geometry optimization calculation of all centers on CH2O molecule with both protons treated quantum-mechanically. The electronic exchange-correlation functional is PBE0. The electronic basis set is STO-3G and the protonic is an uncontracted 1s1p basis set with exponents 4.0. This calculation utilizes DFT grid with 99 radial and 302 spherical quadrature points along with the DIIS algorithm.

$molecule
   0 1
   C     0.000000    0.000000    0.000000
   O     0.000000    0.000000    1.220000
   H     0.935307    0.000000   -0.540000
   H    -0.935307    0.000000   -0.540000
$end

$rem
   JOBTYPE           OPT
   METHOD            pbe0
   BASIS             sto-3g
   NEO               true
   NEO_EPC           epc172
point_group_symmetry False
   SCF_CONVERGENCE   11
   MAX_SCF_CYCLES    100
   SCF_ALGORITHM     diis
   XC_GRID           000099000302
$end

$neo_basis
H    3
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
H    4
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
$end

Example 13.9  Input for the NEO-DFT-epc19 geometry optimization calculation of the NEO center only on open-shell OH radical molecule with a proton treated quantum-mechanically. The electronic exchange-correlation functional is PBE0. The electronic basis set is 6-31G and the protonic is an uncontracted 1s1p basis set with exponents 4.0. This calculation utilizes DFT grid with 99 radial and 230 spherical quadrature points along with the DIIS algorithm.

$molecule
   0 2
   O    -4.511414   1.264878   0.000000
   H    -2.739325   1.866123   0.000000
$end

$rem
   JOBTYPE           OPT
   METHOD            pbe0
   BASIS             6-31g
   UNRESTRICTED      true
   INPUT_BOHR        true
   NEO               true
point_group_symmetry False
   SCF_CONVERGENCE   6
   MAX_SCF_CYCLES    100
   SCF_ALGORITHM     diis
   NEO_EPC           epc19
   XC_GRID           000099000230
$end

$opt
   FIXED
   1 XYZ
   ENDFIXED
$end

$neo_basis
H    2
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
$end

Example 13.10  Input for the NEO-DFT-epc172 geometry optimization calculation of a CH2O molecule in C-PCM water. A van der Waals surface is constructed around the fixed, classical nuclear point charge positions and the nuclear basis function center positions of the two quantum hydrogens. Here, the Bondi radii for hydrogen is used in the construction of the spherical cavity surrounding the delocalized proton densities, but the user has the option to specify a custom-defined atomic radii in a $van_der_waals input section. The entire cavity is scaled by a factor of αvdW=1.2, and is then discretized via the SwiG approach.

$molecule
0 1
  C        0.000000    0.000000    0.000000
  O        0.000000    0.000000    1.220000
  H        0.935307    0.0000000  -0.5400000
  H       -0.935307    0.000000   -0.540000
$end

$rem
point_group_symmetry False
   JOBTYPE              OPT
   INPUT_BOHR           FALSE
   BASIS                sto-3g
   NEO                  TRUE
   METHOD               pbe0
   xc_grid = 000099000302
   NEO_EPC              epc172
   SCF_CONVERGENCE = 8
   NEO_E_CONV = 8
   SCF_ALGORITHM        GDM
   SOLVENT_METHOD       PCM
$end

$neo_basis
H    3
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
H    4
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
$end

$pcm
   Theory               CPCM
   Method               SWIG
   Solver               INVERSION
   HeavyPoints          194
   HPoints              194
   Radii                Bondi
   vdwScale             1.2
$end

$solvent
  Dielectric   78.39
$end

Example 13.11  Input for NEO-HF analytic Hessian calculation on HCN molecule with a proton treated quantum mechanically. The electronic basis set is STO-3G and the protonic basis is 1s1p with exponents 4.0.

$molecule
0 1
  C         0.0000000000    0.0000000000    0.9684140792
  N         0.0000000000    0.0000000000   -1.2085828830
  H         0.0000000000    0.0000000000    2.9046475823
$end

$rem
jobtyp = freq
input_bohr = true
point_group_symmetry = False
method = hf
basis = sto-3g
neo = true
SCF_ALGORITHM = gdm
$end

$neo_basis
H    3
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
$end

Example 13.12  Input for NEO-HF(V) on HCN molecule with a proton treated quantum mechanically. The electronic basis set is STO-3G and the protonic basis is 1s1p with exponents 4.0.

$molecule
0 1
  C         0.0000000000    0.0000000000    0.9684140792
  N         0.0000000000    0.0000000000   -1.2085828830
  H         0.0000000000    0.0000000000    2.9046475823
$end

$rem
jobtyp = freq
input_bohr = true
point_group_symmetry = False
method = hf
SCF_ALGORITHM = gdm
basis = sto-3g
neo = true
neo_scfv = 1
$end

$neo_basis
H    3
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
$end

Example 13.13  Input for the NEO-TDDFT-epc19 calculation on CH2O molecule (both protons treated quantum-mechanically) of the first five roots obtained with the Davidson algorithm. The electronic exchange-correlation functional is PBE0. The electronic basis set is STO-3G and the protonic is an uncontracted 1s1p basis set with exponents 4.0. This calculation utilizes DFT grid with 99 radial and 302 spherical quadrature points.

$molecule
   0 1
   C     0.000000    0.000000    0.000000
   O     0.000000    0.000000    1.220000
   H     0.935307    0.000000   -0.540000
   H    -0.935307    0.000000   -0.540000
$end

$rem
   METHOD            pbe0
   BASIS             sto-3g
   THRESH            14
   XC_GRID           000099000302
   S2THRESH          12
   NEO               true
   NEO_EPC           epc172
   SET_ROOTS         5
   RPA               true
   SCF_CONVERGENCE   12
   NEO_E_CONV        12
$end

$neo_basis
H    3
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
H    4
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
$end

Example 13.14  Input for the NEO-TDHF calculation on the FDF- molecule treating quantum nuclei as deuterium and employing NO_VPP option. The electronic basis set is cc-pVDZ and the protonic is an uncontracted even-tempered 8s8p basis set.

$molecule
   -1 1
   F   0.000000   0.000000   -1.122987
   F   0.000000   0.000000    1.122987
   H   0.000000   0.000000    0.000000
$end

$rem
   METHOD            hf
   BASIS             cc-pvdz
   NEO               true
   SCF_ALGORITHM     GDM
   RPA               true
   CIS_N_ROOTS       100
   THRESH            14
   S2THRESH          12
   SCF_CONVERGENCE   11
   MAX_SCF_CYCLES    300
   NEO_VPP           0
   NEO_ISOTOPE       2
   NEO_E_CONV        11
$end

$neo_basis
H    3
S    1    1.000000
   2.828400 1.0
S    1    1.000000
   4.0 1.0
S    1    1.000000
   5.6569 1.0
S    1    1.000000
   8.0 1.0
S    1    1.000000
   11.3137 1.0
S    1    1.000000
   16.0 1.0
S    1    1.000000
   22.6274 1.0
S    1    1.000000
   32.0 1.0
P    1    1.000000
   2.828400 1.0
P    1    1.000000
   4.0 1.0
P    1    1.000000
   5.6569 1.0
P    1    1.000000
   8.0 1.0
P    1    1.000000
   11.3137 1.0
P    1    1.000000
   16.0 1.0
P    1    1.000000
   22.6274 1.0
P    1    1.000000
   32.0 1.0
****
$end

Example 13.15  Input for the analytic NEO-TDDFT gradient calculation on the CH2 molecule with both protons treated quantum mechanically. A total of four excited states are requested and the gradient is computed for the 3rd excited state. The electronic exchange-correlation functional is CAM-B3LYP, and electron-proton correlation functional epc17-2 is used. The electronic basis set is STO-3G and the protonic basis is 1s1p with exponents 4.0. This calculation utilizes DFT grid with 99 radial and 302 spherical quadrature points along with the GDM algorithm.

$molecule
0 3
C  0.00000000000000e+00  0.00000000000000e+00 -5.63654429543699e-02
H  1.81800983405161e+00  0.00000000000000e+00 -9.92269386019353e-01
H -1.81800983405161e+00  0.00000000000000e+00 -9.92269386019353e-01
$end

$rem
point_group_symmetry = False
input_bohr = true
method = cam-b3lyp
basis = sto-3g
thresh = 14
s2thresh = 12
neo = true
SET_ROOTS = 4
RPA = true
xc_grid = 000099000302
unrestricted = 1
neo_epc = epc172
SCF_ALGORITHM = gdm
SET_STATE_DERIV = 3
$end

$neo_basis
H    2
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
H    3
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
$end

Example 13.16  Input for NEO-TDDFT geometry optimization on the C2H2 molecule with both protons treated quantum mechanically. A total of three excited states are requested and the geometry optimization is computed for the 1st excited state. The electronic exchange-correlation functional is B3LYP, and electron-proton correlation functional epc17-2 is used. The electronic basis set is STO-3G and the protonic basis is 1s1p with exponents 4.0. This calculation utilizes DFT grid with 99 radial and 302 spherical quadrature points along with the GDM algorithm.

$molecule
0 1
        C       0.4142076725     1.0563578037     0.0000000223
        C      -0.4142118956    -1.0563667882     0.0000000223
        H       1.1661939287     2.9673893099     0.0000000246
        H      -1.1661909474    -2.9673788285     0.0000000246
$end

$rem
point_group_symmetry = False
NEO_SET_OPT = 1
neo_epc = epc172
SET_STATE_DERIV = 1
jobtype = opt
input_bohr = true
method = b3lyp
neo = true
SCF_ALGORITHM = gdm
thresh = 14
s2thresh = 12
basis = sto-3g
rpa = true
SET_ROOTS = 3
xc_grid = 000099000302
$end

$neo_basis
H    3
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
H    4
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
$end

Example 13.17  Input for NEO-TDDFT on the C2H2 molecule with both protons treated quantum mechanically. A total of 12 excited states are requested. Ground-state protonic and electronic densities are printed in the cube files. Protonic and electronic transition densities of the first and the second vibronic excitations with electronic dominant characters are also printed in the cube files. The electronic exchange-correlation functional is B3LYP, and electron-proton correlation functional epc17-2 is used. The electronic basis set is STO-3G and the protonic basis is 1s1p with exponents 4.0. This calculation utilizes DFT grid with 99 radial and 302 spherical quadrature points along with the GDM algorithm.

$molecule
0 1
       C        -0.2315710674    1.2702261467    0.0000001295
       C         0.2315702809   -1.2702255666    0.0000001295
       H         1.2946585350    2.6676952886   -0.0000000923
       H        -1.2946589903   -2.6676943717   -0.0000000923
$end

$rem
point_group_symmetry = False
input_bohr = true
method = b3lyp
neo = true
NEO_SET_ESTATE = 1
SCF_ALGORITHM = gdm
thresh = 14
s2thresh = 12
basis = sto-3g
GEOM_OPT_MAX_CYCLES = 500
rpa = true
SET_ROOTS = 12
xc_grid = 000099000302
MAKE_CUBE_FILES = true
plots = true
$end

$neo_basis
H    3
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
H    4
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
$end

$plots
grid information to plot protonic and electronic ground state densities and transition densities for two eletronic dominant transitions
   100  -4.0 6.0
   100  -5.0 4.0
   100  -4.0 4.0
   0 1 2 0
   0
   0 1
$end

Example 13.18  Input for the NEO-RICCSD calculation on H2O molecule with the second proton treated quantum-mechanically. The electronic basis set is STO-3G and the protonic is an uncontracted 1s1p basis set with exponents 4.0. The electronic auxiliary basis set is RIMP2-aug-cc-pVDZ and the protonic auxiliary basis set is an uncontracted even-tempered 8s8p basis set.

$molecule
0 1
O          0.00000       -0.07579        0.00000
H          0.86681        0.60144        0.00000
H         -0.86681        0.60144        0.00000
$end

$rem
neo = true
basis = sto-3g
aux_basis = rimp2-aug-cc-pVDZ
NEO_RICCSD 1
$end

$neo_basis
H    3
S    1    1.000000
   4.0 1.0
P    1    1.000000
   4.0 1.0
****
$end

$neo_aux_basis
H   3
S    1    1.000000
   2.8284 1.0
S    1    1.000000
   4.0 1.0
S    1    1.000000
   5.6569 1.0
S    1    1.000000
   8.0 1.0
S    1    1.000000
   11.3137 1.0
S    1    1.000000
   16.0 1.0
S    1    1.000000
   22.6274 1.0
S    1    1.000000
   32.0 1.0
P    1    1.000000
   2.8284 1.0
P    1    1.000000
   4.0 1.0
P    1    1.000000
   5.6569 1.0
P    1    1.000000
   8.0 1.0
P    1    1.000000
   11.3137 1.0
P    1    1.000000
   16.0 1.0
P    1    1.000000
   22.6274 1.0
P    1    1.000000
   32.0 1.0
****
$end