The general form of the integrals tested is .
The analytical
evaluation of this integral is given in analytical4.doc
.htm. The main code is in testing\rijtest.for which has includes to setup.for, random.for, hfuns.for, xnfind.for, and xnefin.for. The
main code contains the various parameters that are changed in the tests. The codes setup, random, xnfind
and xnefin are the
The initial testing on the normalization integral yields.
Method |
electrons # |
a |
b |
Analytical |
configurations |
Numerical estimate |
Residual |
BAR |
3 |
1 |
1 |
0.503362 |
1048576 |
0.494202 +- 0.0064 |
-1.4 |
M 0.7 |
3 |
1 |
1 |
0.5033618 |
1048576 |
0.494123 +-0.006235 |
-1.5 |
M 0.7 |
2 |
1 |
1 |
2.7732 |
1048576 |
2.801653 +-0.01323 |
+2.2 |
M 0.7 |
3 |
1 |
4 |
1.105 E-2 |
1048576 |
1.098 E-2 +-0.0049 E-2 |
-1.4 |
The final testing involves calculating the normalization integral, the integral times the sum of 1/rI, times the sum 1/ri2, times the double sum of 1/rij, and finally times the double sum of 1/rij2. These tests were run by selecting the first electron with respect to the nucleus, and the next with respect to the nucleus (30% probability) and also with respect to one of the electrons already selected (70% probability).
NUP=6
beta=4
alpha=1
CALL RSEED(123,451)
CALL SETUP(NGUIDE,GCON)
C ** zero all sums
DO IMC=1,NMC
C PICK FIRST ELECTRON BIASED AS RANDOM
CALL XNFIND(X,WXT,1)
DO I=2,NUP
C PICK ELECTRONS 2 TO NUP WITH RESPECT TO NUCLEUS AND
ELECTRONS
CALL XNEFIN(X,WNXT,I-1,I)
wxt=wxt*wnxt
ENDDO
In each table space the first number is the Monte-Carlo estimate of the integral,
The second is the Monte-Carlo error estimate. The third is the analytical value of the
integral. The fourth is Res =
(Monte-Carlo – Analytical)/(
NMC= 1048576
N a b |
ò Gaussian |
òGå1/rI |
òGå1/rI2 |
òGå1/rIJ |
òGå1/rIJ2 |
|
2 1
4 |
0.4448+-
0.0016 0.44236 R
1.46 |
1.3765+-
0.0039 1.3720 R
1.13 |
3.3453+-
0.0071 |
1.4585+-0.0035 |
7.5235+-0.0103 |
|
|
6 1
4 |
6.1953E-9+- 0.0952 |
9.77
E-8+- 0.14 |
4.065E-7 +- 0.055 |
5.197E-7+- 0.074 5.260E-7 R –0.85 |
4.569E-6 +- 0.051 4.615E-6 R –0.90 |
|
6 1 -0.03 |
842224+- 121893 847225
R -0.04 |
4862637+-593633 4732944 R
0.22 |
7232194 +- 590436 6922013 R 0.53 |
8209386 +- 1041249 8111858 R 0.09 |
8192845 +- 727167 |