Class Scine::Sparrow::nddo::multipole::KlopmanParameter

class KlopmanParameter

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. \( U\left(\Theta^{\mu\nu}_t, \Theta^{\lambda\sigma}_s \right) = \sum^{C_t}_{c=1}\sum^{C_s}_{d=1} \frac{q_c^Iq_d^J}{\sqrt{|r_c^I - r_d^J|^2 + \left( \theta_c^I(\chi_\mu^I\chi_\nu^I) + \theta_d^J(\chi_\lambda^J\chi_\sigma^J) \right)}} \)

Public Functions

KlopmanParameter()

Constructor, calls the reset() function.

void reset()

Sets the values to zero.

void set(multipolePair_t type, double value)

stores the value of the KlopmanOhno parameter for a multipole type at the index given by the cast multipolePair_t.

double get(multipolePair_t type) const

returns the value correspoding to the multipolePair_t typed multipole

void generateUpToS(double gss)

generates the KlopmanOhno parameters up to the s orbitals

Return

The KlopmanOhno parameter for the s orbital

Parameters

  • gss: The one center repulsion parameter \(\gamma_{ss}\) parametrizing the \( \langle ss|ss \rangle\) integral

void generateUpToP(double gss, double hsp, double D1sp, double hpp, double D2pp)

generates the KlopmanOhno parameters up to the p orbitals

The parameter is calculated in an iterative fashion with the Newton’s method. The equation of which the root is searched are listed in T. Husch, A. C. Vaucher, M. Reiher, Semiempirical Molecular Orbital Models based on the Neglect of Diatomic Differential Overlap Approximation, doi: 1806.06147v2

Parameters

  • gss: the one center repulsion parameter \(\gamma_{ss}\) parametrizing the \( \langle ss|ss \rangle\) integral

  • hsp: the one center repulsion parameter \(\~{\gamma}_{sp}\) parametrizing the \( \langle sp|sp \rangle\) integral

  • D1sp: the charge separation parameter describing the charge distance on the dipoles formed by an s and a p orbitals

  • hpp: the one center repulsion parameter \( \gamma_{pp} \) parametrizing the \( \langle pp|pp \rangle \) integral

  • D2pp: the charge separation parameter describing the charge distance on the quadrupoles formed by two p orbitals

void generateUpToD(double gss, double hsp, double D1sp, double hpp, double D2pp, double F0dd, double G1pd, double D1pd, double G2sd, double D2sd, double F2dd, double D2dd)

generates the KlopmanOhno parameters up to the d orbitals

The parameter is calculated in an iterative fashion with the Newton’s method. The equation of which the root is searched are listed in T. Husch, A. C. Vaucher, M. Reiher, Semiempirical Molecular Orbital Models based on the Neglect of Diatomic Differential Overlap Approximation, doi: 1806.06147v2

Parameters

  • gss: the one center repulsion parameter \(\gamma_{ss}\) parametrizing the \( \langle ss|ss \rangle\) integral

  • hsp: the one center repulsion parameter \(\~{\gamma}_{sp}\) parametrizing the \( \langle sp|sp \rangle\) integral

  • D1sp: the charge separation parameter describing the charge distance on the dipoles formed by an s and a p orbitals

  • hpp: the one center repulsion parameter \( \gamma_{pp} \) parametrizing the \( \langle pp|pp \rangle \) integral

  • D2pp: the charge separation parameter describing the charge distance on the quadrupoles formed by two p orbitals

  • F0dd: the parametrized one-center radial integral corresponding to the zero-th term of equation 116 in the reference listed below between two d orbitals in the order given by equation 118 in the reference listed below.

  • G1pd: the parametrized one-center radial integral corresponding to the first term of equation 116 in the reference listed below between an s and a p orbital in the order given by equation 119.

  • D1pd: the charge separation parameter describing the charge distance on the quadrupoles formed by a p and a d orbital

  • G2sd: the parametrized one-center radial integral corresponding to the second term of equation 116 in the reference listed below between an s and a d orbital in the order given by equation 119

  • D2sd: the charge separation parameter describing the charge distance on the quadrupoles formed by an s and a d orbital

  • F2dd: the parametrized one-center radial integral corresponding to the second term of quation 116 in the reference listed below between two d orbitals in the order given by equation 118

  • D2dd: the charge separation parameter describing the charge distance on the quadrupoles formed by two d orbitals