basis_func Module

BASIS_FUNC module to define basis-set functions from atomic orbitals represented on multicenter molecular grids written by Son, Sang-Kil and Hao, Yajiang in Mar. 2014

USAGE: type(Basis) :: B

Ref) Becke, J. Chem. Phys. 88, 2547 (1988) Becke & Dickson, J. Chem. Phys. 89, 2993 (1988) Becke & Dickson, J. Chem. Phys. 92, 3610 (1990) Dickson & Becke, J. Chem. Phys. 99, 3898 (1993)


Uses


Variables

Type Visibility Attributes Name Initial
integer, public, parameter :: n_symop = 8
integer, public, parameter :: symop_e = 1

1 E
integer, public, parameter :: symop_c2x = 2

2 C2X
integer, public, parameter :: symop_c2y = 3

3 C2Y
integer, public, parameter :: symop_c2z = 4

4 C2Z
integer, public, parameter :: symop_i = 5

5 i
integer, public, parameter :: symop_sigxy = 6

6 SIGXY
integer, public, parameter :: symop_sigxz = 7

7 SIGXZ
integer, public, parameter :: symop_sigyz = 8

8 SIGYZ
character(len=5), public, parameter :: sym_op_name(8) = (/'E    ', 'C2X  ', 'C2Y  ', 'C2Z  ', 'i    ', 'SIGXY', 'SIGXZ', 'SIGYZ'/)

Derived Types

type, public ::  basis

basis information

Components

Type Visibility Attributes Name Initial
logical, public :: yes_initialized = .false.
integer, public :: n_basis

total # of basis functions
integer, public :: nr_basis

total # of basis functions projected out
real(kind=long), public, allocatable :: func(:,:)

(1:N_grid,1:N_basis)
real(kind=long), public, allocatable :: dfdr(:,:,:)

(1:N_grid,1:N_basis,3)
real(kind=long), public, allocatable :: d2f(:,:)

(1:N_grid,1:N_basis)
logical, public, allocatable :: yes_skip(:,:)

(1:N_nuc,1:N_basis) skip if all basis functions (and its deriv.) are zero for a given atom A it helps to speed up because we know that B%func are zero if r > A%rmax and we don't need to evaluate anything beyond A%rmax --> initialized in place_AO_on_Grid3D()
integer, public, allocatable :: info(:,:)

basis function info B%info(i,1) : atomic index for the i-th basis B%info(i,2) : nuclear charge for the i-th basis B%info(i,3) : n of AO for the i-th basis B%info(i,4) : l of AO for the i-th basis B%info(i,5) : m of AO for the i-th basis
character(len=10), public, allocatable :: label(:)
real(kind=long), public, allocatable :: s(:,:)

overlap matrix
real(kind=long), public, allocatable :: ssqrt(:,:)

sqrt overlap matrix
real(kind=long), public, allocatable :: sinvsqrt(:,:)

sqrt of inverse overlap matrix
real(kind=long), public, allocatable :: sinv(:,:)

inverse overlap matrix
real(kind=long), public, allocatable :: x(:,:)
real(kind=long), public, allocatable :: xxts(:,:)
real(kind=long), public, allocatable :: hkin(:,:)

Kinetic operator matrix, (1:N_basis,1:N_basis)
real(kind=long), public, allocatable :: vext(:,:)

Nuclear potential (1:N_basis,1:N_basis)
real(kind=long), public, allocatable :: h0(:,:)

Kinetic + nuclear potential
real(kind=long), public, allocatable :: teint(:)

Two-Electron integrals
logical, public, allocatable :: yes_overlap(:,:)

yes_overlap(k_nuc,ij): whether a multiplication of two basis functions (i and j) contributes to the k_nuc-th atomic sphere [k_nuc=1...N_nuc] If this variable is yes, then the k_nuc-th atom will be included in multicenter integration involving the i-th and j-th basis functions. If no, then it is not included, which means "save the CPU time!"

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real(kind=long), public, allocatable :: overlap(:,:)
real(kind=long), public :: eps_overlap
real(kind=long), public :: eps_overlap_single
real(kind=long), public :: r_max_overlap
real(kind=long), public :: error_single

numerical accuracy for single-center and multicenter integration and integration optimization by truncation
real(kind=long), public :: error_multi

numerical accuracy for single-center and multicenter integration and integration optimization by truncation
real(kind=long), public :: error_trunc

numerical accuracy for single-center and multicenter integration and integration optimization by truncation
integer, public, allocatable :: first_bf_on_atom(:)
integer, public, allocatable :: num_bf_on_atom(:)
logical, public :: yes_symmetry(n_symop)
integer, public, allocatable :: irrep_prod(:,:)
real(kind=long), public, allocatable :: sym_bf(:,:)

conversion matrix from symmetric bf to atomic orbitals
integer, public, allocatable :: irrep_sym_bf(:)

index of irreducible representation per sym bf
integer, public, allocatable :: irrep_sym_bfr(:)

index of irreducible representation per sym bf
character(len=5), public :: sym_label

Schoenflies symbol
integer, public :: nirrep

number of irrep
character(len=4), public, allocatable :: irrep_name(:)

name of irrep
real(kind=long), public :: minimal_s_eigenvalue

minimal overlap matrix eigenvalue
real(kind=long), public :: minimal_s_remaining_eigenvalue

minimal overlap matrix eigenval that is not projected out
real(kind=long), public, allocatable :: env(:)
integer, public, allocatable :: atm(:,:)
integer, public, allocatable :: bas(:,:)
integer, public, allocatable :: first_bf_of_shell(:)

Functions

public function braket(g, b, i, j, f) result(value)

braket(): where i, j indicate i-th and j-th basis function braket_Laplacian():

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Arguments

Type IntentOptional Attributes Name
type(grid3d), intent(in) :: g
type(basis), intent(in) :: b
integer, intent(in) :: i
integer, intent(in) :: j
real(kind=long), intent(in) :: f(:)

Return Value real(kind=long)


Subroutines

public subroutine construct_basis(a, g, b, eps_overlap, eps_overlap_single, yes_sym, gto_file_path, yes_gradient, basissetoverlaplim)

construct (or reconstruct) B from A and G all necessary informations are obtained from - A : atomic orbitals of individual atoms - G : molecular grids

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Arguments

Type IntentOptional Attributes Name
type(atom_set), intent(in) :: a(:)

atom set
type(grid3d), intent(in) :: g

grid
type(basis), intent(out) :: b

basis
real(kind=long), intent(in), optional :: eps_overlap

truncation parameters
real(kind=long), intent(in), optional :: eps_overlap_single

truncation parameters
logical, intent(in), optional :: yes_sym

use symmetry?
character(len=*), intent(in), optional :: gto_file_path

path to file with gto informations
logical, intent(in), optional :: yes_gradient

prepare for calculating gradients?
real(kind=long), intent(in), optional :: basissetoverlaplim

truncation parameters

public subroutine purge_basis(b)

deallocate basis structure

Arguments

Type IntentOptional Attributes Name
type(basis), intent(inout) :: b

public subroutine precalculate_twoel_gto(p, b)

subroutine to precalculate all 2el matrix elements

Arguments

Type IntentOptional Attributes Name
type(param), intent(in) :: p
type(basis), intent(inout) :: b

public subroutine print_calc_info(p, a, g, b)

print grid parameters and basis function (numerical atomic orbital) info it is supposed to be in read_param.f90, but it requires A(:) and G wait a minute... even it doesn't contain F!!! why should it be here? it has beend moved to basis_func

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Arguments

Type IntentOptional Attributes Name
type(param), intent(in) :: p
type(atom_set), intent(in) :: a(:)
type(grid3d), intent(in) :: g
type(basis), intent(in) :: b

public subroutine calc_trans_dipole_moment_bf(p, b, g, tdipole_bf)

calculates the transition dipole matrix elements between basisfunctions and stores them in tdipole_bf( mu, nu, p)

Arguments

Type IntentOptional Attributes Name
type(param), intent(in) :: p
type(basis), intent(in) :: b
type(grid3d), intent(in) :: g
real(kind=long), intent(out), dimension(p%n_basis, p%n_basis, 3) :: tdipole_bf

public subroutine orthonormalizeorbitals(b, c, irrep_mo)

Do a Gram-Schmidt orthogonalization for the coefficients given by C according to the metric given by the overlap matrix B%S, i.e. such that < C(:,i) S(:,:) C(:,j) > = delta_i,j B are the basis set parameters

Arguments

Type IntentOptional Attributes Name
type(basis), intent(in) :: b
real(kind=long), intent(inout), dimension(:, :) :: c
integer, intent(in), optional :: irrep_mo(:)