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:mod:`hessian` --- Analytical nuclear Hessian

The :mod:`hessian` module implements the analytical nuclear Hessian for mean-field methods. This module also provides functions for thermo-chemical corrections (entropic corrections) using the harmonic model obtained from the Hessian frequencies,

For example:

from pyscf import gto
mol = gto.M(
    atom = [
        ['O' , 0. , 0.     , 0],
        ['H' , 0. , -0.757 , 0.587],
        ['H' , 0. ,  0.757 , 0.587]],
    basis = '631g')

mf = mol.RHF().run()
h = mf.Hessian().kernel()

The resulting structure of the Hessian is ::h[Atom_1, Atom_2, Atom_1_XYZ, Atom_1_XYZ]:: in this case ::(3,3,3,3)::.

Examples

Relevant examples :file:`examples/hessian/01-scf_hessian.py` :file:`examples/hessian/10-thermochemistry.py`

Program reference

.. automodule:: pyscf.hessian

Spin-restricted Hartree-Fock

.. automodule:: pyscf.hessian.rhf
   :members:

Spin-unrestricted Hartree-Fock

.. automodule:: pyscf.hessian.uhf
   :members:

Spin-restricted DFT

.. automodule:: pyscf.hessian.rks
   :members:

Spin-unrestricted DFT

.. automodule:: pyscf.hessian.uks
   :members:

Thermo-chemistry analysis

.. automodule:: pyscf.hessian.thermo
   :members: