Documentation for module eri_mme_error_control

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

source: eri_mme_error_control.F
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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.
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(inout)
:: 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(inout)
:: 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.
INTENT(in),
POINTER
:: para_env ...