Empirical Performance Analysis

The CO path is designed for large systems. Therefore the test `molecule' is C₃₄₀ arranged as a 4x85 rectangular lattice in which adjacent atoms are 1.25 Å apart. The basis set used is 6-31G*, which gives 5100 basis functions. The timings were carried out on an IBM model 43P Power PC workstation.

Table 5.3 presents the timings data for a selection of typical classes that arise. The actual timings are of little interest; instead, the ratios between the CO and OC times are presented.

  

Table 5.3: Timing ratios for the CO and OC Paths

Class	(KBra,KKet)	OC/CO Ratio
(ss|ss)	(12,12)	2.83
(ss|ss)	(6,6)	1.52
(ps|ss)	(8,12)	2.48
(ps|ss)	(8,6)	1.64
(pp|ss)	(8,12)	2.26
(pp|ss)	(8,6)	1.44
(ds|ss)	(6,12)	2.07
(ds|ss)	(6,6)	1.38
(dp|ss)	(3,12)	1.07
(dp|ss)	(3,6)	1.00
(dd|ss)	(1,12)	1.00
(dd|ss)	(1,6)	0.98
(ps|ps)	(8,8)	2.03
(pp|ps)	(8,8)	1.76
(pp|pp)	(8,8)	1.76
(ds|ps)	(6,8)	1.85
(ds|pp)	(6,8)	1.08
(dp|ps)	(3,8)	0.96
(ds|ds)	(6,6)	1.01

The timings confirm most of the trends seen in the flop-counts. CO is obviously faster for integrals of high contraction and low momentum. For (ss|ss) with K_Bra=K_Ket=12 it is nearly three times faster. However, as the momentum increases and the contraction decreases, the CO advantage diminishes, until, by (dd|ss) with K_Bra=1 and K_Ket=6, CO is slightly slower. The timings overall show a slight improvement over that predicted by flop-counts.