pyscf.hessian package

Submodules

pyscf.hessian.dispersion module

Hessian of dispersion correction for HF and DFT

pyscf.hessian.dispersion.get_dispersion(hessobj, disp=None, with_3body=None)

pyscf.hessian.rhf module

Non-relativistic RHF analytical Hessian

class pyscf.hessian.rhf.Hessian(scf_method)

Bases: HessianBase

hess_elec(mo_energy=None, mo_coeff=None, mo_occ=None, mo1=None, mo_e1=None, h1ao=None, atmlst=None, max_memory=4000, verbose=None)

make_h1(mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=None)

partial_hess_elec(mo_energy=None, mo_coeff=None, mo_occ=None, atmlst=None, max_memory=4000, verbose=None)

Partial derivative

class pyscf.hessian.rhf.HessianBase(scf_method)

Bases: StreamObject

Non-relativistic restricted Hartree-Fock hessian

gen_hop(mo_energy=None, mo_coeff=None, mo_occ=None, verbose=None)

get_dispersion(disp=None, with_3body=None)

get_hcore(mol=None)

hcore_generator(mol=None)

hess(mo_energy=None, mo_coeff=None, mo_occ=None, atmlst=None)

Kernel function is the main driver of a method. Every method should define the kernel function as the entry of the calculation. Note the return value of kernel function is not strictly defined. It can be anything related to the method (such as the energy, the wave-function, the DFT mesh grids etc.).

hess_elec(*args, **kwargs)

hess_nuc(mol=None, atmlst=None)

kernel(mo_energy=None, mo_coeff=None, mo_occ=None, atmlst=None)

Kernel function is the main driver of a method. Every method should define the kernel function as the entry of the calculation. Note the return value of kernel function is not strictly defined. It can be anything related to the method (such as the energy, the wave-function, the DFT mesh grids etc.).

level_shift = 0

make_h1(*args, **kwargs)

max_cycle = 50

solve_mo1(mo_energy, mo_coeff, mo_occ, h1ao, fx=None, atmlst=None, max_memory=4000, verbose=None)

to_gpu()

pyscf.hessian.rhf.gen_hop(hobj, mo_energy=None, mo_coeff=None, mo_occ=None, verbose=None)

pyscf.hessian.rhf.gen_vind(mf, mo_coeff, mo_occ)

pyscf.hessian.rhf.get_hcore(mol)

Part of the second derivatives of core Hamiltonian

pyscf.hessian.rhf.get_ovlp(mol)

pyscf.hessian.rhf.hess_elec(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None, mo1=None, mo_e1=None, h1ao=None, atmlst=None, max_memory=4000, verbose=None)

pyscf.hessian.rhf.hess_nuc(mol, atmlst=None)

pyscf.hessian.rhf.make_h1(hessobj, mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=None)

pyscf.hessian.rhf.partial_hess_elec(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None, atmlst=None, max_memory=4000, verbose=None)

Partial derivative

pyscf.hessian.rhf.solve_mo1(mf, mo_energy, mo_coeff, mo_occ, h1ao, fx=None, atmlst=None, max_memory=4000, verbose=None, max_cycle=50, level_shift=0)

Solve the first order equation

Kwargs:

fxfunction(dm_mo) => v1_mo

A function to generate the induced potential. See also the function gen_vind.

pyscf.hessian.rks module

Non-relativistic RKS analytical Hessian

class pyscf.hessian.rks.Hessian(mf)

Bases: HessianBase

Non-relativistic RKS hessian

hess_elec(mo_energy=None, mo_coeff=None, mo_occ=None, mo1=None, mo_e1=None, h1ao=None, atmlst=None, max_memory=4000, verbose=None)

make_h1(mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=None)

partial_hess_elec(mo_energy=None, mo_coeff=None, mo_occ=None, atmlst=None, max_memory=4000, verbose=None)

pyscf.hessian.rks.contract_d2rhodAdB_d2gammadAdB(d3mu_dr3, d2mu_dr2, dmu_dr, mu, drho_dr, dm0, aoslices, fw_rho, fw_gamma)

pyscf.hessian.rks.get_d2mu_dr2(ao)

pyscf.hessian.rks.get_d2rho_dAdr_grid_response(d2mu_dr2, dmu_dr, mu, dm0, atom_to_grid_index_map=None, i_atom=None)

pyscf.hessian.rks.get_d2rho_dAdr_orbital_response(d2mu_dr2, dmu_dr, mu, dm0, aoslices)

pyscf.hessian.rks.get_d2rhodAdB_d2gammadAdB(mol, grids_coords, dm0)

This function should never be used in practice. It requires crazy amount of memory, and it’s left for debug purpose only. Use the contract function instead.

pyscf.hessian.rks.get_d3mu_dr3(ao)

pyscf.hessian.rks.get_drhodA_dgammadA_grid_response(d2mu_dr2, dmu_dr, mu, drho_dr, dm0, atom_to_grid_index_map=None, i_atom=None)

pyscf.hessian.rks.get_drhodA_dgammadA_orbital_response(d2mu_dr2, dmu_dr, mu, drho_dr, dm0, aoslices)

pyscf.hessian.rks.get_dweight_dA(mol, grids)

pyscf.hessian.rks.get_vnlc_resp(mf, mol, mo_coeff, mo_occ, dm1s, max_memory)

Equation notation follows: Liang J, Feng X, Liu X, Head-Gordon M. Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments. J Chem Phys. 2023 May 28;158(20):204109. doi: 10.1063/5.0152838.

mo_coeff, mo_occ are 0-th order dm1s is first order

TODO: check the effect of different grid, using mf.nlcgrids right now

pyscf.hessian.rks.make_h1(hessobj, mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=None)

pyscf.hessian.rks.partial_hess_elec(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None, atmlst=None, max_memory=4000, verbose=None)

pyscf.hessian.thermo module

Thermochemistry analysis.

Ref:

psi4/psi4/driver/qcdb/vib.py http://gaussian.com/vib/

pyscf.hessian.thermo.dump_normal_mode(mol, results)

pyscf.hessian.thermo.dump_thermo(mol, results)

pyscf.hessian.thermo.harmonic_analysis(mol, hess, exclude_trans=True, exclude_rot=True, imaginary_freq=True, mass=None)

Each column is one mode

imaginary_freq (boolean): save imaginary_freq as complex number (if True) or negative real number (if False)

pyscf.hessian.thermo.rotation_const(mass, atom_coords, unit='GHz')

Rotational constants to characterize rotational spectra

Kwargs:

unit (string) : One of GHz, wavenumber

pyscf.hessian.thermo.rotational_symmetry_number(mol)

Number of unique orientations of the rigid molecule that only interchange identical atoms.

Source http://cccbdb.nist.gov/thermo.asp (search “symmetry number”)

pyscf.hessian.thermo.thermo(model, freq, temperature=298.15, pressure=101325)

pyscf.hessian.uhf module

Non-relativistic UHF analytical Hessian

class pyscf.hessian.uhf.Hessian(scf_method)

Bases: HessianBase

Non-relativistic UHF hessian

gen_hop(mo_energy=None, mo_coeff=None, mo_occ=None, verbose=None)

hess_elec(mo_energy=None, mo_coeff=None, mo_occ=None, mo1=None, mo_e1=None, h1ao=None, atmlst=None, max_memory=4000, verbose=None)

make_h1(mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=None)

partial_hess_elec(mo_energy=None, mo_coeff=None, mo_occ=None, atmlst=None, max_memory=4000, verbose=None)

solve_mo1(mo_energy, mo_coeff, mo_occ, h1ao, fx=None, atmlst=None, max_memory=4000, verbose=None)

pyscf.hessian.uhf.gen_hop(hobj, mo_energy=None, mo_coeff=None, mo_occ=None, verbose=None)

pyscf.hessian.uhf.gen_vind(mf, mo_coeff, mo_occ)

pyscf.hessian.uhf.hess_elec(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None, mo1=None, mo_e1=None, h1ao=None, atmlst=None, max_memory=4000, verbose=None)

pyscf.hessian.uhf.make_h1(hessobj, mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=None)

pyscf.hessian.uhf.partial_hess_elec(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None, atmlst=None, max_memory=4000, verbose=None)

pyscf.hessian.uhf.solve_mo1(mf, mo_energy, mo_coeff, mo_occ, h1ao, fx=None, atmlst=None, max_memory=4000, verbose=None, max_cycle=50, level_shift=0)

pyscf.hessian.uks module

Non-relativistic UKS analytical Hessian

class pyscf.hessian.uks.Hessian(mf)

Bases: HessianBase

Non-relativistic UKS hessian

gen_hop(mo_energy=None, mo_coeff=None, mo_occ=None, verbose=None)

hess_elec(mo_energy=None, mo_coeff=None, mo_occ=None, mo1=None, mo_e1=None, h1ao=None, atmlst=None, max_memory=4000, verbose=None)

make_h1(mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=None)

partial_hess_elec(mo_energy=None, mo_coeff=None, mo_occ=None, atmlst=None, max_memory=4000, verbose=None)

solve_mo1(mo_energy, mo_coeff, mo_occ, h1ao, fx=None, atmlst=None, max_memory=4000, verbose=None)

pyscf.hessian.uks.make_h1(hessobj, mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=None)

pyscf.hessian.uks.partial_hess_elec(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None, atmlst=None, max_memory=4000, verbose=None)

Module contents