Atomic Orbitals

1. Gaussian basis
2. Basis

"Atomic basis set"

1 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_Ai and the Gaussian part are both centered on nucleus $A$.

1.1 Type

Gaussian_basis.t

open Common
open Particles
open Linear_algebra
open Gaussian_integrals
open Operators

type t

1.2 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

1.3 Computation

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

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

1.4 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

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

1.5 Printers

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

2 Basis

Data structure for Atomic Orbitals.

2.1 Dimensions noexports

2.2 Polymorphic types

type t =
  | Unknown
  | Gaussian of Basis_gaussian.t

2.3 Types

type t
type ao = Ao_dim.t 

open Common
open Particles
open Operators
open Linear_algebra

2.4 Conversions

val of_nuclei_and_basis_filename :
  ?kind:[> `Gaussian ] -> ?operators:Operator.t list -> ?cartesian:bool ->
  nuclei:Nuclei.t -> string -> t

of_nuclei_and_basis_filename Creates the data structure for the atomic orbitals basis from a molecule Nuclei.t and the name of the basis-set file