tessl/pypi-pyscf

Python-based quantum chemistry framework providing electronic structure methods for molecular simulations

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AO2MO Transformations

Name: tessl/pypi-pyscf
Author: tessl

Atomic orbital to molecular orbital integral transformations essential for post-SCF methods, providing both in-core and out-of-core algorithms for different system sizes and memory requirements.

Capabilities

General Transformations

Core functions for transforming 2-electron integrals from atomic orbital to molecular orbital basis.

def kernel(eri_or_mol, mo_coeffs, erifile=None, dataname='eri_mo', intor='int2e', **kwargs):
    """
    General AO→MO integral transformation.
    
    Parameters:
    - eri_or_mol: ndarray or Mole, AO integrals or molecule object
    - mo_coeffs: ndarray or tuple, MO coefficients for transformation
    - erifile: str, output file for transformed integrals
    - dataname: str, dataset name in output file
    - intor: str, integral type ('int2e', 'int2e_spinor', etc.)
    
    Returns:
    ndarray or str, transformed integrals or filename
    """

def full(eri_or_mol, mo_coeff, erifile=None, dataname='eri_mo', intor='int2e', **kwargs):
    """
    Full 4-index (ij|kl) integral transformation.
    
    Transform all four indices using the same MO coefficients.
    Most common transformation for post-SCF methods.
    """

def general(eri_or_mol, mo_coeffs, erifile=None, dataname='eri_mo', intor='int2e', **kwargs):
    """
    General transformation with different orbital sets.
    
    Parameters:
    - mo_coeffs: tuple of 4 arrays, MO coefficients for each index
    
    Allows different orbital spaces for each integral index,
    useful for excited states and response properties.
    """

Specialized Transformations

def get_ao_eri(mol, aosym='s1', **kwargs):
    """
    Get atomic orbital 2-electron repulsion integrals.
    
    Parameters:
    - mol: Mole object
    - aosym: str, symmetry ('s1', 's4', 's8')
    
    Returns:
    ndarray, AO 2-electron integrals
    """

def restore(eri_mo, norb, tao):
    """
    Restore packed integral arrays to full format.
    
    Parameters:
    - eri_mo: ndarray, packed MO integrals
    - norb: int, number of orbitals
    - tao: ndarray, transformation coefficients
    
    Returns:
    ndarray, restored integrals
    """

Usage Examples

Basic Transformations

import pyscf

# Full transformation for post-SCF
mol = pyscf.M(atom='H2O', basis='6-31g')
mf = mol.RHF().run()

# Transform all integrals to MO basis
eri_mo = pyscf.ao2mo.full(mol, mf.mo_coeff)
print(f"MO integrals shape: {eri_mo.shape}")

# For large systems, use out-of-core
eri_file = pyscf.ao2mo.full(mol, mf.mo_coeff, erifile='h2o_mo.h5')

Different Orbital Spaces

# Separate occupied and virtual orbitals
nocc = mol.nelectron // 2
mo_occ = mf.mo_coeff[:, :nocc]
mo_vir = mf.mo_coeff[:, nocc:]

# (ov|ov) integrals for MP2
eri_ovov = pyscf.ao2mo.general(mol, [mo_occ, mo_vir, mo_occ, mo_vir])

# Mixed transformations for excited states
eri_mixed = pyscf.ao2mo.general(mol, [mo_occ, mo_occ, mo_vir, mo_vir])

Types

from typing import Union, Tuple
from typing_extensions import Literal
import numpy as np
ndarray = np.ndarray

# Orbital coefficient specifications
MOCoeffs = Union[ndarray, Tuple[ndarray, ...]]

# Symmetry specifications
AOSymmetry = Literal['s1', 's4', 's8']

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