Q-Chem combines the Head-Gordon–Pople (HGP) method355 and the COLD prism method24 for Hartree-Fock gradient and Hessian evaluations. All two-electron four-center integrals are classified according to their angular momentum types and degrees of contraction. For each type of integrals, the program chooses one with a lower cost. In practice, the HGP method is chosen for most integral classes in a gradient or Hessian calculation, and thus it dominates the total CPU time.
Recently the HGP codes within Q-Chem were completely rewritten for the evaluation of the P II P term in the gradient evaluation, and the P II P term in the Hessian evaluation. Our emphasis is to improve code efficiency by reducing cache misses rather than by reducing FLOP counts. Some timing results from a Hartree-Fock calculation on azt are shown below.
|Gradient Evaluation: P II P Term|
|3-21G||34 s||20 s||0.58||25 s||14 s||0.56|
|6-31G**||259 s||147 s||0.57||212 s||120 s||0.57|
|DZ||128 s||118 s||0.92||72 s||62 s||0.86|
|cc-pVDZ||398 s||274 s||0.69||308 s||185 s||0.60|
|Hessian Evaluation: P II P term|
|3-21G||294 s||136 s||0.46||238 s||100 s||0.42|
|6-31G**||2520 s||976 s||0.39||2065 s||828 s||0.40|
|DZ||631 s||332 s||0.53||600 s||230 s||0.38|
|cc-pVDZ||3202 s||1192 s||0.37||2715 s||866 s||0.32|