Specialized Methods

class X2C:
    """
    Exact two-component relativistic method.
    
    Provides scalar relativistic effects through exact decoupling
    of positive/negative energy states with 2-component efficiency.
    """
    
    def __init__(self, mol):
        """Initialize X2C method."""
    
    def RHF(self):
        """X2C enhanced restricted Hartree-Fock."""

def sfx2c1e(mf):
    """
    Spin-free X2C with 1-electron X-matrix approximation.
    
    Efficient scalar relativistic treatment including effects
    only in 1-electron integrals.
    """

class PCM:
    """
    Polarizable Continuum Model.
    
    Treats solvent as continuous dielectric medium with
    molecular-shaped cavity for solute.
    
    Attributes:
    - eps: float, solvent dielectric constant
    - method: str, PCM variant ('IEF-PCM', 'SS(V)PE', 'C-PCM')
    """

class COSMO:
    """
    Conductor-like Screening Model.
    
    Approximates solvent as conductor with dielectric scaling
    for realistic solvent response.
    """

class ddCOSMO:
    """
    Domain decomposition COSMO with linear scaling.
    
    Efficient COSMO implementation with linear scaling
    for large molecular systems.
    """

class QMMMole:
    """
    QM/MM molecule combining quantum and classical regions.
    
    Partitions system into QM (high accuracy) and MM (efficiency)
    regions with proper boundary treatment.
    
    Attributes:
    - qm_atoms: list, atoms in QM region
    - mm_atoms: list, atoms in MM region  
    - qm_charge: float, total charge of QM region
    """

class QMMM:
    """
    QM/MM method interface.
    
    Handles coupling between quantum mechanical and molecular
    mechanical descriptions including electrostatic embedding.
    """

def density_fit(mf, auxbasis=None, with_df=None, only_dfj=False):
    """
    Add density fitting acceleration to SCF method.
    
    Parameters:
    - mf: SCF object to enhance
    - auxbasis: str, auxiliary basis set name
    - with_df: DF object for custom fitting
    - only_dfj: bool, fit only Coulomb integrals
    
    Returns:
    density-fitted SCF object with reduced computational scaling
    """

class DF:
    """
    Density fitting base class.
    
    Implements 3-center integral approximation (μν|P) for
    efficient 4-center integral evaluation.
    """

class GDF:
    """
    Gaussian density fitting.
    
    Specialized DF implementation for Gaussian basis sets
    with optimal auxiliary basis selection.
    """

def sgx_fit(mol, auxbasis=None):
    """
    Semi-numerical exchange fitting procedure.
    
    Reduces computational cost of exact exchange evaluation
    through numerical fitting techniques.
    """

def make_sgx(mf):
    """
    Create semi-numerical exchange object.
    
    Transforms SCF method to use semi-numerical exchange
    for improved efficiency in large systems.
    """

class GW:
    """
    GW approximation for quasi-particle energies.
    
    Calculates ionization potentials and electron affinities
    through self-energy corrections to mean-field results.
    """

class AGF2:
    """
    Auxiliary second-order Green's function method.
    
    Efficient implementation of self-consistent GF(2)
    for accurate ionization and excitation energies.
    """

class ADC:
    """
    Algebraic Diagrammatic Construction.
    
    Systematic approach to excited states through
    Green's function pole analysis.
    """

import pyscf

# X2C for heavy elements
mol_au = pyscf.M(atom='Au 0 0 0; H 0 0 1.5', basis='cc-pvdz-pp')
mf_x2c = pyscf.scf.X2C(mol_au).RHF()
mf_x2c.run()
print(f"X2C energy: {mf_x2c.e_tot}")

# Spin-free X2C approximation
mf_sfx2c = pyscf.scf.sfx2c1e(mol_au.RHF())
mf_sfx2c.run()

# PCM solvation in water
mol = pyscf.M(atom='H2CO', basis='6-31g')
mf = mol.RHF()

# Add PCM solvent
mf_pcm = pyscf.solvent.PCM(mf)
mf_pcm.eps = 78.4  # water dielectric constant
mf_pcm.run()
print(f"Solvation energy: {mf_pcm.e_tot - mf.run().e_tot}")

# ddCOSMO for large systems
mf_cosmo = pyscf.solvent.ddCOSMO(mf)
mf_cosmo.run()

# Density fitting for large molecules
mol_big = pyscf.M(atom='protein.xyz', basis='6-31g')
mf = mol_big.RHF()

# Add density fitting
mf_df = pyscf.scf.density_fit(mf, auxbasis='cc-pvdz-jkfit')
mf_df.run()

# DF for post-SCF methods
mp2_df = pyscf.mp.DFMP2(mf_df)
mp2_df.run()

# QM/MM setup
mol_system = pyscf.M(atom='large_system.xyz', basis='6-31g')

# Define QM region (first 10 atoms)
qmmm = pyscf.qmmm.QMMM(mol_system, qm_atoms=list(range(10)))
mf_qmmm = qmmm.RHF()
mf_qmmm.run()

from typing import List, TypedDict
from typing_extensions import Literal

# Relativistic method types
RelativisticMethod = Literal['X2C', 'DKH', 'ZORA']

# Solvation parameters
SolvationParams = TypedDict('SolvationParams', {
    'eps': float,
    'eps_inf': float,
    'method': str
})

# QM/MM region specification
QMRegion = List[int]  # atom indices
MMRegion = List[int]  # atom indices