## Documentation for module eri_mme_error_control

Methods aiming for error estimate and automatic cutoff calibration. integrals.

source: eri_mme_error_control.F

#### public Subroutines/Functions:

Find optimal cutoff minimizing errors due to minimax approximation and due to finite cutoff using bisection on the difference of the errors
Compute upper bounds for the errors of 2-center ERI's (P|P) due to minimax approximation and due to finite cutoff, where P is a normalized Hermite Gaussian.

#### SUBROUTINEcalibrate_cutoff(hmat, h_inv, g_min, vol, zet_mm, l_mm, zet_c, l_c, n_minimax, cutoff_l, cutoff_r, tol, delta, cutoff, err_mm, err_c, c_mm, para_env, print_calib, unit_nr)^

Find optimal cutoff minimizing errors due to minimax approximation and due to finite cutoff using bisection on the difference of the errors

##### Arguments:
 REAL(dp), INTENT(in) :: hmat(3,3) ... REAL(dp), INTENT(in) :: h_inv(3,3) ... REAL(dp), INTENT(in) :: g_min ... REAL(dp) :: vol ... REAL(dp), INTENT(in) :: zet_mm Exponent to estimate minimax error INTEGER, INTENT(in) :: l_mm Total ang. mom. quantum number to estimate minimax error REAL(dp), INTENT(in) :: zet_c(:) Max. exponents to estimate cutoff error INTEGER, INTENT(in) :: l_c(:) Max. total ang. mom. quantum numbers to estimate cutoff error INTEGER, INTENT(in) :: n_minimax Number of terms in minimax approximation REAL(dp), INTENT(in) :: cutoff_l Initial guess of lower bound for cutoff REAL(dp), INTENT(in) :: cutoff_r Initial guess of upper bound for cutoff REAL(dp), INTENT(in) :: tol Tolerance (cutoff precision) REAL(dp), INTENT(in) :: delta to modify initial guess interval REAL(dp), INTENT(out) :: cutoff Best cutoff REAL(dp), INTENT(out) :: err_mm Minimax error REAL(dp), INTENT(out) :: err_c Cutoff error REAL(dp), INTENT(out) :: c_mm Scaling constant to generalize AM-GM upper bound estimate to minimax approx. TYPE(cp_para_env_type), INTENT(in), POINTER :: para_env ... LOGICAL, INTENT(in) :: print_calib ... INTEGER, INTENT(in) :: unit_nr ...

#### SUBROUTINEcutoff_minimax_error(cutoff, hmat, h_inv, vol, g_min, zet_mm, l_mm, zet_ctff, l_ctff, n_minimax, minimax_aw, err_mm, err_ctff, c_mm, para_env)^

Compute upper bounds for the errors of 2-center ERI's (P|P) due to minimax approximation and due to finite cutoff, where P is a normalized Hermite Gaussian.

##### Arguments:
 REAL(dp), INTENT(in) :: cutoff ... REAL(dp), INTENT(in) :: hmat(3,3) ... REAL(dp), INTENT(in) :: h_inv(3,3) ... REAL(dp), INTENT(in) :: vol ... REAL(dp), INTENT(in) :: g_min ... REAL(dp), INTENT(in) :: zet_mm Exponent of P to estimate minimax error INTEGER, INTENT(in) :: l_mm total ang. mom. quantum number of P to estimate minimax error REAL(dp), INTENT(in) :: zet_ctff(:) Max. exponents of P to estimate cutoff error INTEGER, INTENT(in) :: l_ctff(:) Max. total ang. mom. quantum numbers of P to estimate cutoff error INTEGER, INTENT(in) :: n_minimax Number of terms in minimax approximation REAL(dp), INTENT(out) :: minimax_aw(:) Minimax coefficients REAL(dp), INTENT(out) :: err_mm Minimax error REAL(dp), INTENT(out) :: err_ctff Cutoff error REAL(dp), INTENT(out) :: c_mm Scaling constant to generalize AM-GM upper bound estimate to minimax approx. TYPE(cp_para_env_type), INTENT(in), POINTER :: para_env ...