occ::qm::HessianEvaluator< Proc > Class Template Reference

Evaluates molecular Hessian matrices (second derivatives of energy). More...

#include <hessians.h>

Public Types
enum class	Method { FiniteDifferences , Analytical }
	Method for Hessian calculation. More...

Public Member Functions
	HessianEvaluator (Proc &p)
	Construct a HessianEvaluator for the given procedure.
void	set_method (Method method)
	Set the method for Hessian calculation.
void	set_cphf_settings (const cphf::Settings &settings)
	CPHF settings used by the analytical method.
void	set_step_size (double h)
	Set the finite differences step size.
void	set_use_acoustic_sum_rule (bool use)
	Enable/disable acoustic sum rule optimization.
double	step_size () const
	Get the current step size for finite differences.
bool	use_acoustic_sum_rule () const
	Check if acoustic sum rule is enabled.
Method	method () const
	Get the current calculation method.
void	set_scf_convergence_settings (const SCFConvergenceSettings &settings)
	Set the SCF convergence settings for displaced calculations.
const SCFConvergenceSettings &	scf_convergence_settings () const
	Get the current SCF convergence settings.
HessianMatrix	nuclear_repulsion () const
	Compute the nuclear repulsion contribution to the Hessian.
const HessianMatrix &	operator() (const Wavefunction &wfn)
	Compute the full molecular Hessian.
HessianMatrix	compute_analytical (const MolecularOrbitals &mo)
	Analytic Hessian at converged orbitals.

Detailed Description

template<typename Proc>
class occ::qm::HessianEvaluator< Proc >

Evaluates molecular Hessian matrices (second derivatives of energy).

The HessianEvaluator class computes the Hessian matrix, which contains second derivatives of the energy with respect to nuclear coordinates: H_ij = d2E/dR_i dR_j

Methods:

• Finite differences of analytic gradients, with configurable step size and the acoustic sum rule to skip one atom's displacements
• Analytic second derivatives via coupled-perturbed SCF, for procedures satisfying AnalyticHessianProcedure

Template Parameters

Proc	The quantum chemical procedure type (e.g., HartreeFock, DFT)

Usage example:

HessianEvaluator<HartreeFock> hess_eval(hf);
hess_eval.set_step_size(0.005);  // 0.005 Bohr
hess_eval.set_use_acoustic_sum_rule(true);  // Use optimization
auto hessian = hess_eval(mo);

Member Enumeration Documentation

Method

template<typename Proc>

enum class occ::qm::HessianEvaluator::Method

strong

Method for Hessian calculation.

Enumerator
FiniteDifferences	Central finite differences of gradients.
Analytical	Analytic second derivatives via CPHF.

Constructor & Destructor Documentation

HessianEvaluator()

template<typename Proc>

occ::qm::HessianEvaluator< Proc >::HessianEvaluator ( Proc & p )

inlineexplicit

Construct a HessianEvaluator for the given procedure.

Parameters

p	The quantum chemical procedure (HF, DFT, etc.)

Member Function Documentation

compute_analytical()

template<typename Proc>

HessianMatrix occ::qm::HessianEvaluator< Proc >::compute_analytical ( const MolecularOrbitals & mo )

inline

Analytic Hessian at converged orbitals.

H = H_nn + sum P h^{xy} + E2^{xy}[Gamma] - sum Q S^{xy} (skeleton)

• n sum_s [ 2 sum_{p,i} F^{(x)}_{pi} U^y_{pi}
  • 2 sum_{p,i} S^{(x)}_{pi} U^y_{pi} e_i
  • sum_{ij} S^{(x)}_{ij} e1^y_{ij} ] (response)

summed over the spin channels s (one restricted, two unrestricted) with n electrons per orbital (2 restricted, 1 unrestricted). P, Q total density and energy-weighted density; F^{(x)} = h^{(x)} + skeleton two-electron Fock derivative of the channel; U^y_ij = -S^{(y)}_ij / 2 on the occupied block and the CPHF solution on the virtual-occupied block; e1^y = F^{(y)}_oo - S^{(y)}_oo (e_i + e_j)/2 + G[D^y]_oo.

method()

template<typename Proc>

Method occ::qm::HessianEvaluator< Proc >::method ( ) const

inline

Get the current calculation method.

Returns

The Hessian calculation method

nuclear_repulsion()

template<typename Proc>

HessianMatrix occ::qm::HessianEvaluator< Proc >::nuclear_repulsion ( ) const

inline

Compute the nuclear repulsion contribution to the Hessian.

Returns

Nuclear repulsion Hessian matrix (3N×3N)

Computes d²V_nn/dR_A dR_B where V_nn is the nuclear-nuclear repulsion. This is the only part of the Hessian that can be computed analytically without significant computational cost.

operator()()

template<typename Proc>

const HessianMatrix & occ::qm::HessianEvaluator< Proc >::operator() ( const Wavefunction & wfn )

inline

Compute the full molecular Hessian.

Parameters

wfn	Wavefunction from converged SCF calculation

Returns

Complete Hessian matrix including nuclear and electronic contributions

This is the main interface for computing the Hessian. The method used depends on the configuration (set_method, set_step_size, etc.). The wavefunction provides both the molecular orbitals for the reference calculation and the charge/multiplicity for displaced calculations.

scf_convergence_settings()

template<typename Proc>

const SCFConvergenceSettings & occ::qm::HessianEvaluator< Proc >::scf_convergence_settings ( ) const

inline

Get the current SCF convergence settings.

Returns

The SCF convergence settings used for displaced calculations

set_cphf_settings()

template<typename Proc>

void occ::qm::HessianEvaluator< Proc >::set_cphf_settings ( const cphf::Settings & settings )

inline

CPHF settings used by the analytical method.

set_method()

template<typename Proc>

void occ::qm::HessianEvaluator< Proc >::set_method ( Method method )

inline

Set the method for Hessian calculation.

Parameters

method

The method to use

set_scf_convergence_settings()

template<typename Proc>

void occ::qm::HessianEvaluator< Proc >::set_scf_convergence_settings ( const SCFConvergenceSettings & settings )

inline

Set the SCF convergence settings for displaced calculations.

Parameters

settings

SCF convergence settings to use

By default, Hessian calculations use tighter convergence criteria (energy_threshold=1e-10, commutator_threshold=1e-8) for improved accuracy.

set_step_size()

template<typename Proc>

void occ::qm::HessianEvaluator< Proc >::set_step_size ( double h )

inline

Set the finite differences step size.

Parameters

h	Step size in Bohr (typical: 0.001 to 0.01)

Smaller step sizes reduce truncation error but increase numerical error. Default: 0.005 Bohr (matches ORCA default)

set_use_acoustic_sum_rule()

template<typename Proc>

void occ::qm::HessianEvaluator< Proc >::set_use_acoustic_sum_rule ( bool use )

inline

Enable/disable acoustic sum rule optimization.

Parameters

use	If true, use acoustic sum rule to reduce computations

The acoustic sum rule (translational invariance) reduces the number of required displacements from 3N to 3(N-1), saving some computation for a 3-atom system. Based on: d2E/dR_i dR_j = -Σ_k≠j d2E/dR_i dR_k

step_size()

template<typename Proc>

double occ::qm::HessianEvaluator< Proc >::step_size ( ) const

inline

Get the current step size for finite differences.

Returns

Step size in Bohr

use_acoustic_sum_rule()

template<typename Proc>

bool occ::qm::HessianEvaluator< Proc >::use_acoustic_sum_rule ( ) const

inline

Check if acoustic sum rule is enabled.

Returns

True if acoustic sum rule optimization is enabled

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The documentation for this class was generated from the following file:

• /home/runner/work/occ/occ/include/occ/qm/hessians.h