ao_one_e_integrals

All the one-electron integrals in the AO basis are here.

The most important providers for usual quantum-chemistry calculation are:

  • ao_kinetic_integrals which are the kinetic operator integrals on the AO basis

  • ao_integrals_n_e which are the nuclear-elctron operator integrals on the AO basis

  • ao_one_e_integrals which are the the h_core operator integrals on the AO basis

EZFIO parameters

ao_integrals_e_n

Nucleus-electron integrals in AO basis set

io_ao_integrals_e_n

Read/Write AO nucleus-electron attraction integrals from/to disk [ Write | Read | None ]

Default: None

ao_integrals_kinetic

Kinetic energy integrals in AO basis set

io_ao_integrals_kinetic

Read/Write AO kinetic integrals from/to disk [ Write | Read | None ]

Default: None

ao_integrals_pseudo

Pseudopotential integrals in AO basis set

io_ao_integrals_pseudo

Read/Write AO pseudopotential integrals from/to disk [ Write | Read | None ]

Default: None

ao_integrals_overlap

Overlap integrals in AO basis set

io_ao_integrals_overlap

Read/Write AO overlap integrals from/to disk [ Write | Read | None ]

Default: None

ao_one_e_integrals

Combined integrals in AO basis set

io_ao_one_e_integrals

Read/Write AO one-electron integrals from/to disk [ Write | Read | None ]

Default: None

Providers

ao_cart_to_sphe_coef

File : ao_one_e_ints/ao_ortho_canonical.irp.f

double precision, allocatable   :: ao_cart_to_sphe_coef (ao_num,ao_num)
integer :: ao_cart_to_sphe_num

Coefficients to go from cartesian to spherical coordinates in the current basis set

Needs:

  • ao_l

  • ao_num

  • ao_power

  • cart_to_sphe_1

  • cart_to_sphe_2

  • cart_to_sphe_3

  • cart_to_sphe_4

  • cart_to_sphe_5

  • cart_to_sphe_6

  • cart_to_sphe_7

  • cart_to_sphe_8

  • cart_to_sphe_9

Needed by:

  • ao_cart_to_sphe_inv

  • ao_cart_to_sphe_overlap

  • ao_ortho_canonical_coef

ao_cart_to_sphe_inv

File : ao_one_e_ints/ao_ortho_canonical.irp.f

double precision, allocatable   :: ao_cart_to_sphe_inv  (ao_cart_to_sphe_num,ao_num)

Inverse of ao_cart_to_sphe_coef

Needs:

  • ao_cart_to_sphe_coef

  • ao_num

  • lin_dep_cutoff

ao_cart_to_sphe_num

File : ao_one_e_ints/ao_ortho_canonical.irp.f

double precision, allocatable   :: ao_cart_to_sphe_coef (ao_num,ao_num)
integer :: ao_cart_to_sphe_num

Coefficients to go from cartesian to spherical coordinates in the current basis set

Needs:

  • ao_l

  • ao_num

  • ao_power

  • cart_to_sphe_1

  • cart_to_sphe_2

  • cart_to_sphe_3

  • cart_to_sphe_4

  • cart_to_sphe_5

  • cart_to_sphe_6

  • cart_to_sphe_7

  • cart_to_sphe_8

  • cart_to_sphe_9

Needed by:

  • ao_cart_to_sphe_inv

  • ao_cart_to_sphe_overlap

  • ao_ortho_canonical_coef

ao_cart_to_sphe_overlap

File : ao_one_e_ints/ao_ortho_canonical.irp.f

double precision, allocatable   :: ao_cart_to_sphe_overlap      (ao_cart_to_sphe_num,ao_cart_to_sphe_num)

AO overlap matrix in the spherical basis set

Needs:

  • ao_cart_to_sphe_coef

  • ao_num

  • ao_overlap

Needed by:

  • ao_ortho_canonical_coef

ao_deriv2_x

File : ao_one_e_ints/kin_ao_ints.irp.f

double precision, allocatable   :: ao_deriv2_x  (ao_num,ao_num)
double precision, allocatable   :: ao_deriv2_y  (ao_num,ao_num)
double precision, allocatable   :: ao_deriv2_z  (ao_num,ao_num)

Second derivative matrix elements in the AO basis.

\[{\tt ao\_deriv2\_x} = \langle \chi_i(x,y,z) | \frac{\partial^2}{\partial x^2} |\chi_j (x,y,z) \rangle\]

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

Needed by:

  • ao_kinetic_integrals

ao_deriv2_y

File : ao_one_e_ints/kin_ao_ints.irp.f

double precision, allocatable   :: ao_deriv2_x  (ao_num,ao_num)
double precision, allocatable   :: ao_deriv2_y  (ao_num,ao_num)
double precision, allocatable   :: ao_deriv2_z  (ao_num,ao_num)

Second derivative matrix elements in the AO basis.

\[{\tt ao\_deriv2\_x} = \langle \chi_i(x,y,z) | \frac{\partial^2}{\partial x^2} |\chi_j (x,y,z) \rangle\]

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

Needed by:

  • ao_kinetic_integrals

ao_deriv2_z

File : ao_one_e_ints/kin_ao_ints.irp.f

double precision, allocatable   :: ao_deriv2_x  (ao_num,ao_num)
double precision, allocatable   :: ao_deriv2_y  (ao_num,ao_num)
double precision, allocatable   :: ao_deriv2_z  (ao_num,ao_num)

Second derivative matrix elements in the AO basis.

\[{\tt ao\_deriv2\_x} = \langle \chi_i(x,y,z) | \frac{\partial^2}{\partial x^2} |\chi_j (x,y,z) \rangle\]

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

Needed by:

  • ao_kinetic_integrals

ao_deriv_1_x

File : ao_one_e_ints/spread_dipole_ao.irp.f

double precision, allocatable   :: ao_deriv_1_x (ao_num,ao_num)
double precision, allocatable   :: ao_deriv_1_y (ao_num,ao_num)
double precision, allocatable   :: ao_deriv_1_z (ao_num,ao_num)

  • array of the integrals of AO_i * d/dx AO_j

  • array of the integrals of AO_i * d/dy AO_j

  • array of the integrals of AO_i * d/dz AO_j

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

ao_deriv_1_y

File : ao_one_e_ints/spread_dipole_ao.irp.f

double precision, allocatable   :: ao_deriv_1_x (ao_num,ao_num)
double precision, allocatable   :: ao_deriv_1_y (ao_num,ao_num)
double precision, allocatable   :: ao_deriv_1_z (ao_num,ao_num)

  • array of the integrals of AO_i * d/dx AO_j

  • array of the integrals of AO_i * d/dy AO_j

  • array of the integrals of AO_i * d/dz AO_j

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

ao_deriv_1_z

File : ao_one_e_ints/spread_dipole_ao.irp.f

double precision, allocatable   :: ao_deriv_1_x (ao_num,ao_num)
double precision, allocatable   :: ao_deriv_1_y (ao_num,ao_num)
double precision, allocatable   :: ao_deriv_1_z (ao_num,ao_num)

  • array of the integrals of AO_i * d/dx AO_j

  • array of the integrals of AO_i * d/dy AO_j

  • array of the integrals of AO_i * d/dz AO_j

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

ao_dipole_x

File : ao_one_e_ints/spread_dipole_ao.irp.f

double precision, allocatable   :: ao_dipole_x  (ao_num,ao_num)
double precision, allocatable   :: ao_dipole_y  (ao_num,ao_num)
double precision, allocatable   :: ao_dipole_z  (ao_num,ao_num)

  • array of the integrals of AO_i * x AO_j

  • array of the integrals of AO_i * y AO_j

  • array of the integrals of AO_i * z AO_j

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

Needed by:

  • mo_dipole_x

ao_dipole_y

File : ao_one_e_ints/spread_dipole_ao.irp.f

double precision, allocatable   :: ao_dipole_x  (ao_num,ao_num)
double precision, allocatable   :: ao_dipole_y  (ao_num,ao_num)
double precision, allocatable   :: ao_dipole_z  (ao_num,ao_num)

  • array of the integrals of AO_i * x AO_j

  • array of the integrals of AO_i * y AO_j

  • array of the integrals of AO_i * z AO_j

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

Needed by:

  • mo_dipole_x

ao_dipole_z

File : ao_one_e_ints/spread_dipole_ao.irp.f

double precision, allocatable   :: ao_dipole_x  (ao_num,ao_num)
double precision, allocatable   :: ao_dipole_y  (ao_num,ao_num)
double precision, allocatable   :: ao_dipole_z  (ao_num,ao_num)

  • array of the integrals of AO_i * x AO_j

  • array of the integrals of AO_i * y AO_j

  • array of the integrals of AO_i * z AO_j

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

Needed by:

  • mo_dipole_x

ao_integrals_n_e

File : ao_one_e_ints/pot_ao_ints.irp.f

double precision, allocatable   :: ao_integrals_n_e     (ao_num,ao_num)

Nucleus-electron interaction, in the AO basis set.

\(\langle \chi_i | -\sum_A \frac{1}{|r-R_A|} | \chi_j \rangle\)

These integrals also contain the pseudopotential integrals.

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • ao_pseudo_integrals

  • do_pseudo

  • n_pt_max_integrals

  • nucl_charge

  • nucl_coord

  • nucl_num

  • read_ao_integrals_n_e

Needed by:

  • ao_one_e_integrals

  • mo_integrals_n_e

ao_integrals_n_e_imag

File : ao_one_e_ints/pot_ao_ints.irp.f

double precision, allocatable   :: ao_integrals_n_e_imag        (ao_num,ao_num)

Nucleus-electron interaction, in the AO basis set.

\(\langle \chi_i | -\sum_A \frac{1}{|r-R_A|} | \chi_j \rangle\)

Needs:

  • ao_num

  • read_ao_integrals_n_e

ao_integrals_n_e_per_atom

File : ao_one_e_ints/pot_ao_ints.irp.f

double precision, allocatable   :: ao_integrals_n_e_per_atom    (ao_num,ao_num,nucl_num)

Nucleus-electron interaction in the AO basis set, per atom A.

\(\langle \chi_i | -\frac{1}{|r-R_A|} | \chi_j \rangle\)

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • n_pt_max_integrals

  • nucl_coord

  • nucl_num

Needed by:

  • mo_integrals_n_e_per_atom

ao_kinetic_integrals

File : ao_one_e_ints/kin_ao_ints.irp.f

double precision, allocatable   :: ao_kinetic_integrals (ao_num,ao_num)

Kinetic energy integrals in the AO basis.

\(\langle \chi_i |\hat{T}| \chi_j \rangle\)

Needs:

  • ao_deriv2_x

  • ao_num

  • read_ao_integrals_kinetic

Needed by:

  • ao_one_e_integrals

  • mo_kinetic_integrals

ao_kinetic_integrals_imag

File : ao_one_e_ints/kin_ao_ints.irp.f

double precision, allocatable   :: ao_kinetic_integrals_imag    (ao_num,ao_num)

Kinetic energy integrals in the AO basis.

\(\langle \chi_i |\hat{T}| \chi_j \rangle\)

Needs:

  • ao_num

  • read_ao_integrals_kinetic

ao_one_e_integrals

File : ao_one_e_ints/ao_one_e_ints.irp.f

double precision, allocatable   :: ao_one_e_integrals   (ao_num,ao_num)
double precision, allocatable   :: ao_one_e_integrals_diag      (ao_num)

One-electron Hamiltonian in the AO basis.

Needs:

  • ao_integrals_n_e

  • ao_kinetic_integrals

  • ao_num

  • read_ao_one_e_integrals

ao_one_e_integrals_diag

File : ao_one_e_ints/ao_one_e_ints.irp.f

double precision, allocatable   :: ao_one_e_integrals   (ao_num,ao_num)
double precision, allocatable   :: ao_one_e_integrals_diag      (ao_num)

One-electron Hamiltonian in the AO basis.

Needs:

  • ao_integrals_n_e

  • ao_kinetic_integrals

  • ao_num

  • read_ao_one_e_integrals

ao_one_e_integrals_imag

File : ao_one_e_ints/ao_one_e_ints.irp.f

double precision, allocatable   :: ao_one_e_integrals_imag      (ao_num,ao_num)

One-electron Hamiltonian in the AO basis.

Needs:

  • ao_num

  • read_ao_one_e_integrals

ao_ortho_canonical_coef

File : ao_one_e_ints/ao_ortho_canonical.irp.f

double precision, allocatable   :: ao_ortho_canonical_coef      (ao_num,ao_num)
integer :: ao_ortho_canonical_num

matrix of the coefficients of the mos generated by the orthonormalization by the S^{-1/2} canonical transformation of the aos ao_ortho_canonical_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital

Needs:

  • ao_cart_to_sphe_coef

  • ao_cart_to_sphe_overlap

  • ao_cartesian

  • ao_num

  • ao_overlap

  • lin_dep_cutoff

  • mpi_master

Needed by:

  • ao_ortho_canonical_coef_inv

  • ao_ortho_canonical_overlap

  • mo_coef

  • mo_num

ao_ortho_canonical_coef_inv

File : ao_one_e_ints/ao_ortho_canonical.irp.f

double precision, allocatable   :: ao_ortho_canonical_coef_inv  (ao_num,ao_num)

ao_ortho_canonical_coef^(-1)

Needs:

  • ao_num

  • ao_ortho_canonical_coef

Needed by:

  • mo_coef_in_ao_ortho_basis

ao_ortho_canonical_num

File : ao_one_e_ints/ao_ortho_canonical.irp.f

double precision, allocatable   :: ao_ortho_canonical_coef      (ao_num,ao_num)
integer :: ao_ortho_canonical_num

matrix of the coefficients of the mos generated by the orthonormalization by the S^{-1/2} canonical transformation of the aos ao_ortho_canonical_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital

Needs:

  • ao_cart_to_sphe_coef

  • ao_cart_to_sphe_overlap

  • ao_cartesian

  • ao_num

  • ao_overlap

  • lin_dep_cutoff

  • mpi_master

Needed by:

  • ao_ortho_canonical_coef_inv

  • ao_ortho_canonical_overlap

  • mo_coef

  • mo_num

ao_ortho_canonical_overlap

File : ao_one_e_ints/ao_ortho_canonical.irp.f

double precision, allocatable   :: ao_ortho_canonical_overlap   (ao_ortho_canonical_num,ao_ortho_canonical_num)

overlap matrix of the ao_ortho_canonical. Expected to be the Identity

Needs:

  • ao_num

  • ao_ortho_canonical_coef

  • ao_overlap

ao_overlap

File : ao_one_e_ints/ao_overlap.irp.f

double precision, allocatable   :: ao_overlap   (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_x (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_y (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_z (ao_num,ao_num)

Overlap between atomic basis functions:

\(\int \chi_i(r) \chi_j(r) dr\)

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

  • read_ao_integrals_overlap

Needed by:

  • ao_cart_to_sphe_overlap

  • ao_ortho_canonical_coef

  • ao_ortho_canonical_overlap

  • ao_overlap_complex

  • mo_overlap

  • s_half

  • s_half_inv

  • s_inv

  • s_mo_coef

ao_overlap_abs

File : ao_one_e_ints/ao_overlap.irp.f

double precision, allocatable   :: ao_overlap_abs       (ao_num,ao_num)

Overlap between absolute values of atomic basis functions:

\(\int |\chi_i(r)| |\chi_j(r)| dr\)

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_overlap_complex

  • ao_power

  • ao_prim_num

  • is_periodic

  • nucl_coord

ao_overlap_complex

File : ao_one_e_ints/ao_overlap.irp.f

complex*16, allocatable :: ao_overlap_complex   (ao_num,ao_num)

Overlap for complex AOs

Needs:

  • ao_num

  • ao_overlap

  • ao_overlap_imag

Needed by:

  • ao_overlap_abs

  • s_inv_complex

ao_overlap_imag

File : ao_one_e_ints/ao_overlap.irp.f

double precision, allocatable   :: ao_overlap_imag      (ao_num,ao_num)

Imaginary part of the overlap

Needs:

  • ao_num

Needed by:

  • ao_overlap_complex

ao_overlap_x

File : ao_one_e_ints/ao_overlap.irp.f

double precision, allocatable   :: ao_overlap   (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_x (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_y (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_z (ao_num,ao_num)

Overlap between atomic basis functions:

\(\int \chi_i(r) \chi_j(r) dr\)

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

  • read_ao_integrals_overlap

Needed by:

  • ao_cart_to_sphe_overlap

  • ao_ortho_canonical_coef

  • ao_ortho_canonical_overlap

  • ao_overlap_complex

  • mo_overlap

  • s_half

  • s_half_inv

  • s_inv

  • s_mo_coef

ao_overlap_y

File : ao_one_e_ints/ao_overlap.irp.f

double precision, allocatable   :: ao_overlap   (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_x (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_y (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_z (ao_num,ao_num)

Overlap between atomic basis functions:

\(\int \chi_i(r) \chi_j(r) dr\)

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

  • read_ao_integrals_overlap

Needed by:

  • ao_cart_to_sphe_overlap

  • ao_ortho_canonical_coef

  • ao_ortho_canonical_overlap

  • ao_overlap_complex

  • mo_overlap

  • s_half

  • s_half_inv

  • s_inv

  • s_mo_coef

ao_overlap_z

File : ao_one_e_ints/ao_overlap.irp.f

double precision, allocatable   :: ao_overlap   (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_x (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_y (ao_num,ao_num)
double precision, allocatable   :: ao_overlap_z (ao_num,ao_num)

Overlap between atomic basis functions:

\(\int \chi_i(r) \chi_j(r) dr\)

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

  • read_ao_integrals_overlap

Needed by:

  • ao_cart_to_sphe_overlap

  • ao_ortho_canonical_coef

  • ao_ortho_canonical_overlap

  • ao_overlap_complex

  • mo_overlap

  • s_half

  • s_half_inv

  • s_inv

  • s_mo_coef

ao_pseudo_integrals

File : ao_one_e_ints/pot_ao_pseudo_ints.irp.f

double precision, allocatable   :: ao_pseudo_integrals  (ao_num,ao_num)

Pseudo-potential integrals in the AO basis set.

Needs:

  • ao_num

  • ao_pseudo_integrals_local

  • ao_pseudo_integrals_non_local

  • do_pseudo

  • pseudo_klocmax

  • pseudo_kmax

  • read_ao_integrals_pseudo

Needed by:

  • ao_integrals_n_e

  • mo_pseudo_integrals

ao_pseudo_integrals_local

File : ao_one_e_ints/pot_ao_pseudo_ints.irp.f

double precision, allocatable   :: ao_pseudo_integrals_local    (ao_num,ao_num)

Local pseudo-potential

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_charge

  • nucl_coord

  • nucl_num

  • pseudo_klocmax

  • pseudo_v_k_transp

Needed by:

  • ao_pseudo_integrals

ao_pseudo_integrals_non_local

File : ao_one_e_ints/pot_ao_pseudo_ints.irp.f

double precision, allocatable   :: ao_pseudo_integrals_non_local        (ao_num,ao_num)

Non-local pseudo-potential

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_charge

  • nucl_coord

  • nucl_num

  • pseudo_kmax

  • pseudo_lmax

  • pseudo_v_kl_transp

Needed by:

  • ao_pseudo_integrals

ao_spread_x

File : ao_one_e_ints/spread_dipole_ao.irp.f

double precision, allocatable   :: ao_spread_x  (ao_num,ao_num)
double precision, allocatable   :: ao_spread_y  (ao_num,ao_num)
double precision, allocatable   :: ao_spread_z  (ao_num,ao_num)

  • array of the integrals of AO_i * x^2 AO_j

  • array of the integrals of AO_i * y^2 AO_j

  • array of the integrals of AO_i * z^2 AO_j

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

Needed by:

  • mo_spread_x

ao_spread_y

File : ao_one_e_ints/spread_dipole_ao.irp.f

double precision, allocatable   :: ao_spread_x  (ao_num,ao_num)
double precision, allocatable   :: ao_spread_y  (ao_num,ao_num)
double precision, allocatable   :: ao_spread_z  (ao_num,ao_num)

  • array of the integrals of AO_i * x^2 AO_j

  • array of the integrals of AO_i * y^2 AO_j

  • array of the integrals of AO_i * z^2 AO_j

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

Needed by:

  • mo_spread_x

ao_spread_z

File : ao_one_e_ints/spread_dipole_ao.irp.f

double precision, allocatable   :: ao_spread_x  (ao_num,ao_num)
double precision, allocatable   :: ao_spread_y  (ao_num,ao_num)
double precision, allocatable   :: ao_spread_z  (ao_num,ao_num)

  • array of the integrals of AO_i * x^2 AO_j

  • array of the integrals of AO_i * y^2 AO_j

  • array of the integrals of AO_i * z^2 AO_j

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_num

  • ao_power

  • ao_prim_num

  • nucl_coord

Needed by:

  • mo_spread_x

give_polynomial_mult_center_one_e_erf:

File : ao_one_e_ints/pot_ao_erf_ints.irp.f

  subroutine give_polynomial_mult_center_one_e_erf(A_center,B_center,alpha,beta,&
power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in)

Returns the explicit polynomial in terms of the $t$ variable of the following polynomial:

$I_{x1}(a_x, d_x,p,q) times I_{x1}(a_y, d_y,p,q) times I_{x1}(a_z, d_z,p,q)$.

Calls:

  • i_x1_pol_mult_one_e()

  • multiply_poly()

give_polynomial_mult_center_one_e_erf_opt:

File : ao_one_e_ints/pot_ao_erf_ints.irp.f

  subroutine give_polynomial_mult_center_one_e_erf_opt(A_center,B_center,alpha,beta,&
power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in,p,p_inv,p_inv_2,p_new,P_center)

Returns the explicit polynomial in terms of the $t$ variable of the following polynomial:

$I_{x1}(a_x, d_x,p,q) times I_{x1}(a_y, d_y,p,q) times I_{x1}(a_z, d_z,p,q)$.

Called by:

  • nai_pol_mult_erf()

Calls:

  • i_x1_pol_mult_one_e()

  • multiply_poly()

i_x1_pol_mult_one_e:

File : ao_one_e_ints/pot_ao_ints.irp.f

recursive subroutine I_x1_pol_mult_one_e(a,c,R1x,R1xp,R2x,d,nd,n_pt_in)

Recursive routine involved in the electron-nucleus potential

Called by:

  • give_polynomial_mult_center_one_e()

  • give_polynomial_mult_center_one_e_erf()

  • give_polynomial_mult_center_one_e_erf_opt()

  • i_x1_pol_mult_one_e()

  • i_x2_pol_mult_one_e()

Calls:

  • i_x1_pol_mult_one_e()

  • i_x2_pol_mult_one_e()

  • multiply_poly()

i_x2_pol_mult_one_e:

File : ao_one_e_ints/pot_ao_ints.irp.f

recursive subroutine I_x2_pol_mult_one_e(c,R1x,R1xp,R2x,d,nd,dim)

Recursive routine involved in the electron-nucleus potential

Called by:

  • i_x1_pol_mult_one_e()

Calls:

  • i_x1_pol_mult_one_e()

  • multiply_poly()

pseudo_dz_k_transp

File : ao_one_e_ints/pot_ao_pseudo_ints.irp.f

double precision, allocatable   :: pseudo_v_k_transp    (pseudo_klocmax,nucl_num)
integer, allocatable    :: pseudo_n_k_transp    (pseudo_klocmax,nucl_num)
double precision, allocatable   :: pseudo_dz_k_transp   (pseudo_klocmax,nucl_num)

Transposed arrays for pseudopotentials

Needs:

  • nucl_num

  • pseudo_dz_k

  • pseudo_klocmax

  • pseudo_n_k

  • pseudo_v_k

Needed by:

  • ao_pseudo_integrals_local

pseudo_dz_kl_transp

File : ao_one_e_ints/pot_ao_pseudo_ints.irp.f

double precision, allocatable   :: pseudo_v_kl_transp   (pseudo_kmax,0:pseudo_lmax,nucl_num)
integer, allocatable    :: pseudo_n_kl_transp   (pseudo_kmax,0:pseudo_lmax,nucl_num)
double precision, allocatable   :: pseudo_dz_kl_transp  (pseudo_kmax,0:pseudo_lmax,nucl_num)

Transposed arrays for pseudopotentials

Needs:

  • nucl_num

  • pseudo_dz_kl

  • pseudo_kmax

  • pseudo_lmax

  • pseudo_n_kl

  • pseudo_v_kl

Needed by:

  • ao_pseudo_integrals_non_local

pseudo_n_k_transp

File : ao_one_e_ints/pot_ao_pseudo_ints.irp.f

double precision, allocatable   :: pseudo_v_k_transp    (pseudo_klocmax,nucl_num)
integer, allocatable    :: pseudo_n_k_transp    (pseudo_klocmax,nucl_num)
double precision, allocatable   :: pseudo_dz_k_transp   (pseudo_klocmax,nucl_num)

Transposed arrays for pseudopotentials

Needs:

  • nucl_num

  • pseudo_dz_k

  • pseudo_klocmax

  • pseudo_n_k

  • pseudo_v_k

Needed by:

  • ao_pseudo_integrals_local

pseudo_n_kl_transp

File : ao_one_e_ints/pot_ao_pseudo_ints.irp.f

double precision, allocatable   :: pseudo_v_kl_transp   (pseudo_kmax,0:pseudo_lmax,nucl_num)
integer, allocatable    :: pseudo_n_kl_transp   (pseudo_kmax,0:pseudo_lmax,nucl_num)
double precision, allocatable   :: pseudo_dz_kl_transp  (pseudo_kmax,0:pseudo_lmax,nucl_num)

Transposed arrays for pseudopotentials

Needs:

  • nucl_num

  • pseudo_dz_kl

  • pseudo_kmax

  • pseudo_lmax

  • pseudo_n_kl

  • pseudo_v_kl

Needed by:

  • ao_pseudo_integrals_non_local

pseudo_v_k_transp

File : ao_one_e_ints/pot_ao_pseudo_ints.irp.f

double precision, allocatable   :: pseudo_v_k_transp    (pseudo_klocmax,nucl_num)
integer, allocatable    :: pseudo_n_k_transp    (pseudo_klocmax,nucl_num)
double precision, allocatable   :: pseudo_dz_k_transp   (pseudo_klocmax,nucl_num)

Transposed arrays for pseudopotentials

Needs:

  • nucl_num

  • pseudo_dz_k

  • pseudo_klocmax

  • pseudo_n_k

  • pseudo_v_k

Needed by:

  • ao_pseudo_integrals_local

pseudo_v_kl_transp

File : ao_one_e_ints/pot_ao_pseudo_ints.irp.f

double precision, allocatable   :: pseudo_v_kl_transp   (pseudo_kmax,0:pseudo_lmax,nucl_num)
integer, allocatable    :: pseudo_n_kl_transp   (pseudo_kmax,0:pseudo_lmax,nucl_num)
double precision, allocatable   :: pseudo_dz_kl_transp  (pseudo_kmax,0:pseudo_lmax,nucl_num)

Transposed arrays for pseudopotentials

Needs:

  • nucl_num

  • pseudo_dz_kl

  • pseudo_kmax

  • pseudo_lmax

  • pseudo_n_kl

  • pseudo_v_kl

Needed by:

  • ao_pseudo_integrals_non_local

s_half

File : ao_one_e_ints/ao_overlap.irp.f

double precision, allocatable   :: s_half       (ao_num,ao_num)

\(S^{1/2}\)

Needs:

  • ao_num

  • ao_overlap

s_half_inv

File : ao_one_e_ints/ao_overlap.irp.f

double precision, allocatable   :: s_half_inv   (AO_num,AO_num)

\(X = S^{-1/2}\) obtained by SVD

Needs:

  • ao_num

  • ao_overlap

s_inv

File : ao_one_e_ints/ao_overlap.irp.f

double precision, allocatable   :: s_inv        (ao_num,ao_num)

Inverse of the overlap matrix

Needs:

  • ao_num

  • ao_overlap

  • lin_dep_cutoff

s_inv_complex

File : ao_one_e_ints/ao_overlap.irp.f

complex*16, allocatable :: s_inv_complex        (ao_num,ao_num)

Inverse of the overlap matrix

Needs:

  • ao_num

  • ao_overlap_complex

  • lin_dep_cutoff

Subroutines / functions

ao_one_e_integral_zero:

File : ao_one_e_ints/screening.irp.f

logical function ao_one_e_integral_zero(i,k)

Needs:

  • ao_integrals_threshold

  • ao_overlap_abs

  • io_ao_integrals_overlap

  • is_periodic

give_all_erf_kl_ao:

File : ao_one_e_ints/pot_ao_erf_ints.irp.f

subroutine give_all_erf_kl_ao(integrals_ao,mu_in,C_center)

Subroutine that returns all integrals over $r$ of type $frac{ erf(mu * | r - R_C | ) }{ | r - R_C | }$

Needs:

  • ao_num

give_polynomial_mult_center_one_e:

File : ao_one_e_ints/pot_ao_ints.irp.f

subroutine give_polynomial_mult_center_one_e(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out)

Returns the explicit polynomial in terms of the “t” variable of the following

$I_{x1}(a_x, d_x,p,q) times I_{x1}(a_y, d_y,p,q) times I_{x1}(a_z, d_z,p,q)$.

Called by:

  • nai_pol_mult()

Calls:

  • i_x1_pol_mult_one_e()

  • multiply_poly()

int_gaus_pol:

File : ao_one_e_ints/pot_ao_ints.irp.f

double precision function int_gaus_pol(alpha,n)

Computes the integral:

$int_{-infty}^{infty} x^n exp(-alpha x^2) dx$.

nai_pol_mult:

File : ao_one_e_ints/pot_ao_ints.irp.f

double precision function NAI_pol_mult(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in)

Computes the electron-nucleus attraction with two primitves.

\(\langle g_i | \frac{1}{|r-R_c|} | g_j \rangle\)

Calls:

  • give_polynomial_mult_center_one_e()

nai_pol_mult_erf:

File : ao_one_e_ints/pot_ao_erf_ints.irp.f

double precision function NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in)

Computes the following integral :

\[\int dr (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 ) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.\]

Calls:

  • give_polynomial_mult_center_one_e_erf_opt()

nai_pol_mult_erf_ao:

File : ao_one_e_ints/pot_ao_erf_ints.irp.f

double precision function NAI_pol_mult_erf_ao(i_ao,j_ao,mu_in,C_center)

Computes the following integral : $int_{-infty}^{infty} dr chi_i(r) chi_j(r) frac{erf(mu | r - R_C | )}{ | r - R_C | }$.

Needs:

  • ao_coef_normalized_ordered_transp

  • ao_expo_ordered_transp

  • ao_nucl

  • ao_power

  • ao_prim_num

  • n_pt_max_integrals

  • nucl_coord

overlap_bourrin_deriv_x:

File : ao_one_e_ints/spread_dipole_ao.irp.f

subroutine overlap_bourrin_deriv_x(i_component,A_center,B_center,alpha,beta,power_A,power_B,dx,lower_exp_val,overlap_x,nx)

Called by:

  • ao_deriv_1_x

Calls:

  • overlap_bourrin_x()

overlap_bourrin_dipole:

File : ao_one_e_ints/spread_dipole_ao.irp.f

subroutine overlap_bourrin_dipole(A_center,B_center,alpha,beta,power_A,power_B,overlap_x,lower_exp_val,dx,nx)

Called by:

  • ao_dipole_x

overlap_bourrin_spread:

File : ao_one_e_ints/spread_dipole_ao.irp.f

subroutine overlap_bourrin_spread(A_center,B_center,alpha,beta,power_A,power_B,overlap_x,lower_exp_val,dx,nx)
Computes the following integral :

int [-infty ; +infty] of [(x-A_center)^(power_A) * (x-B_center)^power_B * exp(-alpha(x-A_center)^2) * exp(-beta(x-B_center)^2) * x ] needed for the dipole and those things

Called by:

  • ao_spread_x

overlap_bourrin_x:

File : ao_one_e_ints/spread_dipole_ao.irp.f

subroutine overlap_bourrin_x(A_center,B_center,alpha,beta,power_A,power_B,overlap_x,lower_exp_val,dx,nx)

Called by:

  • overlap_bourrin_deriv_x()

v_n_e:

File : ao_one_e_ints/pot_ao_ints.irp.f

double precision function V_n_e(a_x,a_y,a_z,b_x,b_y,b_z,alpha,beta)

Primitve nuclear attraction between the two primitves centered on the same atom.

$p_1 = x^{a_x} y^{a_y} z^{a_z} exp(-alpha r^2)$

$p_2 = x^{b_x} y^{b_y} z^{b_z} exp(-beta r^2)$

v_phi:

File : ao_one_e_ints/pot_ao_ints.irp.f

double precision function V_phi(n,m)

Computes the angular $phi$ part of the nuclear attraction integral:

$int_{0}^{2 pi} cos(phi)^n sin(phi)^m dphi$.

v_r:

File : ao_one_e_ints/pot_ao_ints.irp.f

double precision function V_r(n,alpha)

Computes the radial part of the nuclear attraction integral:

$int_{0}^{infty} r^n exp(-alpha r^2) dr$

v_theta:

File : ao_one_e_ints/pot_ao_ints.irp.f

double precision function V_theta(n,m)

Computes the angular $theta$ part of the nuclear attraction integral:

$int_{0}^{pi} cos(theta)^n sin(theta)^m dtheta$

wallis:

File : ao_one_e_ints/pot_ao_ints.irp.f

double precision function Wallis(n)

Wallis integral:

$int_{0}^{pi} cos(theta)^n dtheta$.