Nuclear gradient and derivative coupling¶
Description¶
The force section can be used to compute the analytical gradient (force), the numerical gradient by finite difference, or the non-adiabatic coupling matrix elements (NACME). Analytical gradients are implemented for unrestricted Hartree–Fock (UHF), restricted open-shell Hartree–Fock (ROHF), restricted Hartree–Fock (RHF), Dirac–Hartree–Fock (DHF), Møller–Plesset perturbation theory (MP2), complete active space self consistent field (CASSCF), and multireference perturbation theory (CASPT2). For CASSCF and CASPT2, it is also possible to perform multiple evaluations of the gradients without repeating the energy calculations. In addition, the relaxed density in MP2, SA-CASSCF, and CASPT2 calculations can be printed in the Gaussian Cube format.
Keywords¶
Required Keywords¶
title
force: Calculates the gradient (force)nacme: Calculates the non-adiabatic coupling matrix elementsdgrad: Difference gradient (only available for CASSCF)forces: Calculates many gradients [available for multi-state methods, such as SA-CASSCF and (X)MS-CASPT2]method
grads
title, target, target2, nacmtype, maxziter can be specified for each gradient evaluation. See below for example.nacmtype
full: Full non-adiabatic couplinginterstate: Interstate couplingetf: Non-adiabtic coupling with built-in electronic translational factor (ETF)noweight: Interstate coupling without weighting it by energy gapOptional Keywords¶
numerical
true: Uses finite differencefalse : Uses analytical gradientdx
target
int: ground state = 0target2
int: first exited state = 1dipole
ciderivative
export
export_single
maxziter
nproc
density_print
moprint block (see below for example and here for the keywords).Example¶
The benzophenone molecule
The benzophenone molecule with carbon atoms in grey, oxygen in red, and hydrogen in white.¶
Sample input: force¶
{ "bagel" : [
{
"title" : "molecule",
"basis" : "cc-pvdz",
"df_basis" : "cc-pvdz-jkfit",
"angstrom" : false,
"geometry" : [
{ "atom" : "C", "xyz" : [ -2.002493, -2.027773, 0.004882 ] },
{ "atom" : "C", "xyz" : [ -2.506057, -4.613700, 0.009896 ] },
{ "atom" : "C", "xyz" : [ 0.536515, -1.276360, 0.003515 ] },
{ "atom" : "C", "xyz" : [ -0.558724, -6.375134, 0.013503 ] },
{ "atom" : "H", "xyz" : [ -4.396140, -5.341490, 0.011057 ] },
{ "atom" : "C", "xyz" : [ 2.478233, -3.024614, 0.007049 ] },
{ "atom" : "H", "xyz" : [ 0.959539, 0.714937, -0.000292 ] },
{ "atom" : "C", "xyz" : [ 1.936441, -5.592475, 0.012127 ] },
{ "atom" : "H", "xyz" : [ -1.012481, -8.367883, 0.017419 ] },
{ "atom" : "H", "xyz" : [ 4.418042, -2.380738, 0.005919 ] },
{ "atom" : "H", "xyz" : [ 3.448750, -6.968581, 0.014980 ] },
{ "atom" : "C", "xyz" : [ -6.758666, -0.057378, 0.001157 ] },
{ "atom" : "C", "xyz" : [ -8.231109, -2.241648, 0.000224 ] },
{ "atom" : "C", "xyz" : [ -8.022986, 2.269249, 0.001194 ] },
{ "atom" : "C", "xyz" : [ -10.853532, -2.110536, -0.000769 ] },
{ "atom" : "H", "xyz" : [ -7.410047, -4.093049, 0.000224 ] },
{ "atom" : "C", "xyz" : [ -10.632155, 2.405932, 0.000369 ] },
{ "atom" : "H", "xyz" : [ -6.913797, 3.976253, 0.001805 ] },
{ "atom" : "C", "xyz" : [ -12.064741, 0.207004, -0.000695 ] },
{ "atom" : "H", "xyz" : [ -11.941318, -3.840822, -0.001614 ] },
{ "atom" : "H", "xyz" : [ -11.548963, 4.232744, 0.000447 ] },
{ "atom" : "H", "xyz" : [ -14.107194, 0.302907, -0.001460 ] },
{ "atom" : "C", "xyz" : [ -3.892311, 0.136360, 0.001267 ] },
{ "atom" : "O", "xyz" : [ -3.026383, 2.227189, -0.001563 ] }
]
},
{
"title" : "force",
"method" : [ {
"title" : "hf",
"thresh" : 1.0e-12
} ]
}
]}
Using the same molecule block, a XMS-CASPT2 analytical gradient calculation can be performed. In this particular example as is often the case, the active keyword is used to select the orbitals for the active space that includes 4 electrons and 3 orbitals. Three sets of \(\pi\) and \(\pi^*\) orbitals localized on the phenyl rings are included along with one non-bonding orbital (oxygen lone pair). The CASSCF orbitals are state-averaged over two states.
{
"title" : "casscf",
"nstate" : 2,
"nclosed" : 46,
"nact" : 3,
"active" : [37, 44, 49]
},
{
"title" : "force",
"target" : 0,
"method" : [ {
"title" : "caspt2",
"smith" : {
"method" : "caspt2",
"ms" : "true",
"xms" : "true",
"sssr" : "true",
"shift" : 0.2,
"frozen" : true
},
"nstate" : 2,
"nact" : 3,
"nclosed" : 46
} ]
}
Sample input: NACME and DGRAD¶
{
"title" : "nacme",
"target" : 0,
"target2" : 1,
"method" : [ {
"title" : "caspt2",
"smith" : {
"method" : "caspt2",
"ms" : "true",
"xms" : "true",
"sssr" : "true",
"shift" : 0.2,
"frozen" : true
},
"nstate" : 3,
"nact" : 7,
"nclosed" : 44
} ]
}
Using the keyword forces, you can run multiple gradient or derivative coupling calculations without repeating the energy calculations. The example below evaluates the nuclear gradient of the energy of the ground state, the first excited state, and the interstate coupling vector (nacmtype is interstate) between these two states.
{
"title" : "forces",
"grads" : [
{ "title" : "force", "target" : 0 },
{ "title" : "force", "target" : 1 },
{ "title" : "nacme", "target" : 0, "target2" : 1, "nacmtype" : "interstate" }
],
"method" : [ {
"title" : "caspt2",
"smith" : {
"method" : "caspt2",
"ms" : "true",
"xms" : "true",
"sssr" : "true",
"shift" : 0.2,
"frozen" : true
},
"nstate" : 3,
"nact" : 7,
"nclosed" : 44
} ]
}
Sample input: Printing dipole moments¶
You can use the keyword dipole to compute the dipole moments for all the states, the transition dipole moments and oscillator strengths of all possible pairs of electronic states.
{
"title" : "forces",
"dipole" : "true",
"method" : [ {
"title" : "caspt2",
"smith" : {
"method" : "caspt2",
"ms" : "true",
"xms" : "true",
"sssr" : "true",
"shift" : 0.2,
"frozen" : true
},
"nstate" : 3,
"nact" : 7,
"nclosed" : 44
} ]
}
Alternatively, for CASPT2, you can use the keyword "ciderivative" : "false" to evaluate the dipole moments, transition dipole moments and oscillator strengths of selected states,
without computing the CI derivative term and gradient.
The example below evaluates the dipole moments of state 0, state 1, and transition dipole moment of the state 0 – state 1 transition.
{
"title" : "forces",
"grads" : [
{ "title" : "force", "target" : 0, "ciderivative" : "false" },
{ "title" : "force", "target" : 1, "ciderivative" : "false" },
{ "title" : "nacme", "target" : 0, "target2" : 1, "nacmtype" : "interstate", "ciderivative" : "false" }
],
"method" : [ {
"title" : "caspt2",
"smith" : {
"method" : "caspt2",
"ms" : "true",
"xms" : "true",
"sssr" : "true",
"shift" : 0.2,
"frozen" : true
},
"nstate" : 3,
"nact" : 7,
"nclosed" : 44
} ]
}
Sample input: Printing relaxed density¶
The relaxed density in MP2, SA-CASSCF, and CASPT2 gradient calculations can be printed in the Gaussian Cube format (density.cub file) by setting the keyword density_print to true
(see the example below).
{ "bagel" : [
{
"title" : "molecule",
"basis" : "svp",
"df_basis" : "svp-jkfit",
"geometry" : [
{ "atom" : "Li", "xyz" : [ 0.000000, 0.000000, 6.000000] },
{ "atom" : "F", "xyz" : [ 0.000000, 0.000000, 0.000000] }
]
},
{
"title" : "force",
"target" : 0,
"density_print" : true,
"moprint" : {
"inc_size" : [ 0.20, 0.20, 0.20]
},
"method" : [ {
"title" : "caspt2",
"smith" : {
"method" : "caspt2",
"shift" : 0.2,
"frozen" : true
},
"nstate" : 4,
"nact" : 4,
"nclosed" : 3
} ]
}
]}
Using the keyword forces, you can print multiple relaxed densities without repeating the energy calculations.
The example below prints all the XMS-CASPT2 relaxed densities.
{
"title" : "forces",
"grads" : [
{ "title" : "force", "target" : 0, "density_print" : true, "moprint" : { "density_filename" : "density_0" } },
{ "title" : "force", "target" : 1, "density_print" : true, "moprint" : { "density_filename" : "density_1" } },
{ "title" : "force", "target" : 2, "density_print" : true, "moprint" : { "density_filename" : "density_2" } },
{ "title" : "force", "target" : 3, "density_print" : true, "moprint" : { "density_filename" : "density_3" } }
],
"method" : [ {
"title" : "caspt2",
"smith" : {
"method" : "caspt2",
"ms" : "true",
"xms" : "true",
"sssr" : "true",
"shift" : 0.2,
"frozen" : true
},
"nstate" : 4,
"nact" : 4,
"nclosed" : 3
} ]
}
References¶
BAGEL References¶
Description of Reference |
Reference |
|---|---|
SS-CASPT2 gradient |
M. K. MacLeod and T. Shiozaki, J. Chem. Phys. 142, 051103 (2015). |
(X)MS-CASPT2 gradient |
B. Vlaisavljevich and T. Shiozaki, J. Chem. Theory Comput. 12, 3781 (2016). |
(X)MS-CASPT2 derivative coupling |
J. W. Park and T. Shiozaki, J. Chem. Theory Comput. 13, 2561 (2017). |
Current (X)MS-CASPT2 gradient algorithm |
J. W. Park and T. Shiozaki, J. Chem. Theory Comput. 13, 3676 (2017). |
General References¶
Description of Reference |
Reference |
|---|---|
General review of gradient methods |
P. Pulay, WIREs Comput. Mol. Sci. 4, 169-181 (2014). |