Q-Chem 4.3 User’s Manual

B.11 More Efficient Hartree–Fock Gradient and Hessian Evaluations

Q-Chem combines the Head-Gordon–Pople (HGP) method [745] and the COLD prism method [180] 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$^ x$ P term in the gradient evaluation, and the P II$^{xy}$ 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.

Basis Set

AIX

Linux

 

Gradient Evaluation: P II$^{x}$ P Term

 

Old

New

New/Old

Old

New

New/Old

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$^{xy}$ P term

 

Old

New

New/Old

Old

New

New/Old

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  

Table B.1: AIX timings were obtained on an IBM RS/6000 workstation with AIX4 operating system, and Linux timings on an Opteron cluster where the Q-Chem executable was compiled with an Intel 32-bit compiler.