QCaml/ao/basis_gaussian.org

• Gaussian basis
  • Type
  • Access
  • Computation
  • Creation
  • Printers

Gaussian basis

Data structure for Gaussian Atomic Orbitals:

\[ \chi_i(\mathbf{r}) = P_i(\mathbf{r}) \sum_k c_k \exp\left( -\alpha_k (\mathbf{r-R_A})^2 \right) \]

where the polynomial $P_i$ and the Gaussian part are both centered on nucleus $A$.

Type

<<<~Gaussian_basis.t~>>>

open Common
open Particles
open Linear_algebra
open Gaussian_integrals
open Operators

type t

Access

val basis             : t -> Gaussian.Basis.t
val cartesian         : t -> bool
val ee_ints           : t -> Eri.t
val ee_lr_ints        : t -> Eri_long_range.t
val eN_ints           : t -> Electron_nucleus.t
val f12_ints          : t -> F12.t
val f12_over_r12_ints : t -> Screened_eri.t
val kin_ints          : t -> Kinetic.t
val multipole         : t -> Multipole.t
val ortho             : t -> Orthonormalization.t
val overlap           : t -> Overlap.t
val size              : t -> int

basis	One-electron basis set
cartesian	If true, use cartesian Gaussians (6d, 10f, …)
ee_ints	Electron-electron potential integrals
ee_lr_ints	Electron-electron long-range potential integrals
eN_ints	Electron-nucleus potential integrals
f12_ints	Electron-electron potential integrals
f12_over_r12_ints	Electron-electron potential integrals
kin_ints	Kinetic energy integrals
multipole	Multipole matrices
ortho	Orthonormalization matrix of the overlap
overlap	Overlap matrix
size	Number of atomic orbitals

Computation

val values : t ->
          Coordinate.t ->
          Gaussian.Basis.t Vector.t

values

Returns the values of all the AOs evaluated at a given point

Creation

val make : basis:Gaussian.Basis.t ->
        ?operators:Operator.t list ->
        ?cartesian:bool ->
        Nuclei.t ->
        t

Creates the data structure for atomic orbitals from a Gaussian basis and the molecular geometry Nuclei.t.

Defaults:

• operators : []
• cartesian : false

Example:

let b = Ao.Basis_gaussian.make ~basis nuclei ;;
val b : Ao.Basis_gaussian.t = Gaussian Basis, spherical, 15 AOs

Printers

val pp : Format.formatter -> t -> unit