Namespace Scine::Sparrow::nddo::multipole

namespace multipole

Enums

enum ChargeDistance

Values:

d0
dp1
dm1
dp2
dm2
dps2
dms2
enum ChargeDistanceSeparation

Values:

d00
d01
d10
d02
d20
d0s2
ds20
p11
m11
p12
p21
m12
m21
p1s2
ps21
m1s2
ms21
p22
m22
p2s2
ps22
m2s2
ms22
ps2s2
ms2s2
enum multipolePair_t

enum listing the possible charge configurations of a multipole.

It is possible i.e. to infer the charge separation D_{sp1} from it. They are separated in monopole (l = 0), dipole (l = 1) and quadrupole (l = 2).

Values:

sp1
pd1
pp2
sd2
dd2
ss0
pp0
dd0
enum multipole_t

Multipole types used in the calculation of the ERI with the multipole expansion approximation.

Confusion might arise by the use of two merged formalisms: the one for just s and p orbitals and the one for s, p and d orbitals.

l: orbital quantum number m: magnetic quantum number \( M00 = M_{0,0} = q^I\) a monopole with l = 0, m = 0 \( M1m1 = M_{1,-1} = \mu_y \) a dipole in y direction with l = 1, m = -1 \( M10 = M_{1,0} = \mu_z \) a dipole in z direction with l = 1, m = 0 \( M11 = M_{1,1} = \mu_x \) a dipole in x direction with l = 1, m = 1 \( Qxx = Q_{x,x} \) a linear quadrupole in x direction with l = 2, m = 0 \( Qyy = Q_{y,y} \) a linear quadrupole in y direction with l = 2, m = 0 \( Qzz = Q_{z,z} \) a linear quadrupole in z direction with l = 2, m = 0 \( M2m2 = M_{2,-2} = Q_{x,y} \) a x,y square quadrupole with l = 2, m = -2 \( M2m1 = M_{2,-1} = Q_{y,z} \) a y,z square quadrupole with l = 2, m = -1 \( M20 = M_{2,0} = -\~{Q}_{x,z} - \frac{1}{2}\~{Q}_{x,y} \) a quadrupole with charges along each axis at \( \sqrt{2} \) distance from the origin with l = 2, m = 0 \( M21 = M_{2,1} = Q_{x,z}\) a x,z square quadrupole with l = 2, m = 1 \( M22 = M_{2,2} = \~{Q}_{x,y} \) a square quadrupole with charges along the x,y axes at \( \sqrt{2} \) distance from the origin with l = 2, m = 2 \( Qzx = \~{Q}_{z,x} = -\~{Q}_{x,z} \) a square quadrupole with charges along the x,z axes at \( \sqrt{2} \) distance from the origin with l = 2, m = 2

Values:

M00
Qxx
Qyy
Qzz
M1m1
M10
M11
M2m2
M2m1
M20
M21
M22
Qzx

Functions

template<>
Utils::AutomaticDifferentiation::DerivativeType<Utils::derivativeType::first> getDerivative<Utils::derivativeType::first>(orbPair_index_t op1, orbPair_index_t op2) const
template<>
Utils::AutomaticDifferentiation::DerivativeType<Utils::derivativeType::second_atomic> getDerivative<Utils::derivativeType::second_atomic>(orbPair_index_t op1, orbPair_index_t op2) const
template<>
Utils::AutomaticDifferentiation::DerivativeType<Utils::derivativeType::second_full> getDerivative<Utils::derivativeType::second_full>(orbPair_index_t op1, orbPair_index_t op2) const
template<>
Utils::AutomaticDifferentiation::Value1DType<Utils::derivOrder::zero> expr<Utils::derivOrder::zero>(double f, double, double invsqrt) const
template<>
Utils::AutomaticDifferentiation::Value1DType<Utils::derivOrder::one> expr<Utils::derivOrder::one>(double f, double dz, double invsqrt) const
template<>
Utils::AutomaticDifferentiation::Value1DType<Utils::derivOrder::two> expr<Utils::derivOrder::two>(double f, double dz, double invsqrt) const
GeneralTypes::rotationOrbitalPair getRotPairType(GeneralTypes::orb_t o1, GeneralTypes::orb_t o2)

Given 2 orbitals, gives the corresponding orbital pair.

Throws InvalidOrbitalPairException() if the orbital types given are invalid. Order matters.

Return

a GeneralTypes::rotationOrbitalPair corresponding to the input orbitals

Parameters

  • o1: first orbital

  • o2: second orbital

int MQuantumNumber(multipole_t m)

Returns the magnetic quantum number m of a multipole, i.e.

-1 for a dipole in y direction, 0 for a dipole in z direction and 1 for a dipole in x direction. Throws InvalidMultipoleException() if the multipole is not valid.

int LQuantumNumber(multipole_t m)

Returns the orbital quantum number l of an orbital, i.e.

0 for s, 1 for p and 2 for d type orbitals. Throws InvalidMultipoleException() if the multipole is not a valid one.

multipolePair_t pairType(int l1, int l2, int l)

Function to infer the charge configuration of a multipole.

Return

throws InvalidQuantumNumbersException() if the quantum number is invalid. Otherwise returns a multipolePair_t.

Parameters

  • l1: the orbital quantum number of the first orbital

  • l2: the orbital quantum number of the second orbital

  • l: the multipole orbital quantum number

class ChargesInMultipoles
#include <ChargesInMultipoles.h>

This class defines the point charges of the different multipole.

class Global2c2eMatrix
#include <Global2c2eMatrix.h>

This class calculates the two-center two-electron integrals in the global coordinate system.

class Local2c2eIntegralCalculator
#include <Local2c2eIntegralCalculator.h>

This class is responsible for the calculation of the 2-center-2-electron integrals in the local coordinate system.

template<Utils::derivOrder O>
class Local2c2eMatrix
#include <Local2c2eMatrix.h>

This class creates the local two-center two-electron matrix for an atom pair.

class MultipoleCharge
#include <MultipoleCharge.h>

This class defines an object containing the position and charge of a point charge.

class MultipoleChargePair
#include <MultipoleChargePair.h>

This class stores the information about the distance between two point charges and about the product of their charges

class MultipoleMultipoleInteraction
#include <MultipoleMultipoleInteraction.h>

This header-only class performs the actual calculation of the multipole-multipole interaction.

First all the charge-charge configurations between two multipoles (MultipoleMultipoleTerm) are inferred and stored in a list, then they are calculated by calling MultipoleMultipoleTerm::calculate(…)

class MultipoleMultipoleInteractionContainer
#include <MultipoleMultipoleInteractionContainer.h>

This class keeps a list of terms of charge-charge-interactions for a pair of multipoles.

All the possible interactions can be stored in a 13x13 matrix, as there are 13 multipole types: 1 monopole, 3 dipoles, 3 linear quadrupoles, 3 square quadrupoles with charges between the axis, 3 square quadrupoles with charges along the axis.

class MultipoleMultipoleTerm
#include <MultipoleMultipoleTerm.h>

This header-only class defines an object for the calculation of an interaction between two charges in a multipole.

The total interaction between two electrons is approximated by a classical multipole expansion. This class defines an object that calculates the interaction between two charges of said multipoles. The charge interaction is calculated within the Klopman approximation to retrieve the correct 1-center, 2-electrons interaction in the limit of vanishing distance between the charges. The template functions allow for the analytical calculation of all the values up to the second derivative of the repulsion energy.

class VuvB
#include <VuvB.h>

This class returns the \(V_{\mu\nu,B}\) terms needed in semi-empirical methods.

class ZeroLocal2c2eIntegrals
#include <zeroLocal2c2eIntegrals.h>

Class that specifies which local two-center two-electron integrals are equal to zero in the semi-empirical approximation.

class ChargeSeparationParameter
#include <ChargeSeparationParameter.h>

Charge separation D of semi-empirical models. It describes the separation between two charges of opposite sign in a multipole.

The calculation of the charge separation is described in Thiel, Voityuk, Theor Chim Acta, 1992, 81, 391. The charge separation are stored ad a static c-array of size 5. The charge separations are ordered as in the nddo::multipole::multipolePair_t enum, i.e. sp1, pd1, pp2, sd2, dd2. ss0, pp0, dd0 are not present as there is no charge separation for them (they are monopoles).

class KlopmanParameter
#include <KlopmanParameter.h>

This class is the container for the Klopman-Ohno parameters used for the evaluation of the multipoles.

The Klopman-Ohno are used in the calculation of the two-center ERIs in the NDDO formalism. \( U\left(\Theta^{\mu\nu}_t, \Theta^{\lambda\sigma}_s \right) = \sum^{C_t}_{c=1}\sum^{C_s}_{d=1} \frac{q_c^Iq_d^J}{\sqrt{|r_c^I - r_d^J|^2 + \left( \theta_c^I(\chi_\mu^I\chi_\nu^I) + \theta_d^J(\chi_\lambda^J\chi_\sigma^J) \right)}} \)