用前面得到的計算勒讓德多項式系數(shù)的新方法改寫了計算重疊積分的程序，這次驗證這個程序的性能，主要參考了

1.Approximate Molecular Orbital Theory by Pople John A., Beveridge David L. ?

2.Calculation of the One-Electron Two-Center Integrals Over Slater-Type Orbitals by Means of the Ellipsoidal Coordinates Method by SIDI MOHAMED MEKELLECHE, ABDELLATIF BABA-AHMED（1996）

3.Evaluation of Two-center One- and Two-electron Integrals over Slater Type Orbitals by YAKAR, Yusuf , ?ZMEN, Ayhan，ATAV, ülfet （2006）

計算得到的表格

	n	l	n'	l'	λ	ζ	ζ'	R	YAKAR, Yusuf	計算值	計算值/參照值
	2	1	3	2	1	4.2	4.4	2.5	-0.012921364533705600	-0.012921364533721100	1.000000000001200000	double d= Sab ( 2.5, 4.2, 4.4 ,??? 2, 1 , 1 ,3 ,2 );
	3	2	2	1	0	2.3	2.3	2.5	-0.225219666538108000	-0.225219666538093000	0.999999999999933000	double d= Sab ( 2.5, 2.3, 2.3,??? 3, 2, 0, 2, 1? );
	3	2	3	2	2	5.8	4.5	0.2	0.878358705056473000	0.878358707428179000	1.000000002700160000	double d= Sab ( 0.2, 5.8, 4.5,??? 3, 2, 2, 3, 2? );
	3	2	3	2	1	2	4.4	8.7	-0.000006314661261245	-0.000006315678534335	1.000161097016560000	double d= Sab ( 8.7, 2.0, 4.4,??? 3, 2, 1, 3, 2? );
	4	3	5	2	1	1.5	0.5	15	-0.012890231001724500	-0.012890230947022000	0.999999995756282000	double d= Sab ( 15, 1.5, 0.5,??? 4, 3, 1, 5, 2? );
	5	3	6	4	3	1.5	1	0.1	-0.025946449868473100	0.000000000000000000	0.000000000000000000	double d= Sab ( 0.1, 1.5, 1,??? 5, 3, 3, 6, 4? );
	4	3	8	5	2	3.6	3.7	0.1	0.008313612868317390	1551313174102550000.0	186599159556070000000	double d= Sab ( 0.1, 3.6, 3.7,??? 4, 3, 2, 8, 5? );
	6	4	12	4	4	3.5	0.5	20	0.000011906964150515		0.000000000000000000
	5	3	8	5	3	2.5	2	2.2	0.414308041044988000		0.000000000000000000
	10	5	5	4	2	0.3	0.1	10	0.244313116241577000		0.000000000000000000
	15	12	10	8	3	4	2.5	1.5	0.145246101309526000		0.000000000000000000
	22	20	24	18	15	1.5	3.5	0.8	0.009891139692046750		0.000000000000000000
									John A. Pople
1-6	1	0	1	0	0	8.7	1	1.733	0.054800000000000000	0.054840104000444100	1.000731824825620000	double d= Sab (1.733, 8.7,1,?? 1, 0 , 0 ,1 ,0 );
2-6	2	0	1	0	0	2.6	1	1.733	0.471700000000000000	0.471700639846316000	1.000001356468760000	double d= Sab ( 1.733,2.6,1,?? 2, 0 , 0 ,1 ,0 );
3-6	2	1	1	0	0	2.6	1	1.733	0.298900000000000000	0.298911819595470000	1.000039543644930000	double d= Sab (1.733, 2.6,1,?? 2, 1 , 0 ,1 ,0 );
									SIDI MOHAMED MEKELLECHE
<1s|1s>	1	0	1	0	0	2.2	1.5	2	0.231371105832753000	0.231371105832752000	0.999999999999996000	double d= Sab (2, 2.2 , 1.5 ,??? 1, 0 , 0 ,1 ,0 );
<1s|1s>	1	0	1	0	0	5.5	1.5	2	0.059125938608933700	0.059125938608931800	0.999999999999968000	double d= Sab (2, 5.5 , 1.5 ,??? 1, 0 , 0 ,1 ,0 );
<1s|1s>	1	0	1	0	0	7.7	1.5	2	0.035054800488251800	0.035054800488252500	1.000000000000020000	double d= Sab (2, 7.7 , 1.5 ,??? 1, 0 , 0 ,1 ,0 );
<1s|1s>	1	0	1	0	0	9.9	1.5	2	0.023836349699891400	0.023836349699889800	0.999999999999933000	double d= Sab (2, 9.9 , 1.5 ,??? 1, 0 , 0 ,1 ,0 );
<1s|1s>	1	0	1	0	0	10	10	1.4	0.000066799473767987	0.000066799473773200	1.000000000078040000	double d= Sab (1.4, 10 , 10 ,??? 1, 0 , 0 ,1 ,0 );
<5s|5s>	5	0	5	0	0	0.1	0.1	1.4	0.999637189410387000	0.999637189410387000	1.000000000000000000	double d= Sab (1.4, 0.1 , 0.1 ,??? 5, 0 , 0 ,5 ,0 );
<1s|2p0>	1	0	2	1	0	10	2	1.4	-0.117413789686628000	-0.117413789686631000	1.000000000000030000	double d= Sab (1.4, 10 , 2 ,??? 1, 0 , 0 ,2 ,1 );
<4s|4p0>	4	0	4	1	0	0.5	0.4	1.4	-0.123035213531177000	-0.123035185362651000	0.999999771053138000	double d= Sab (1.4, 0.5 , 0.4 ,??? 4, 0 , 0 ,4 ,1 );
<2p0|2p0>	2	1	2	1	0	2	2	1.4	-0.100740382147441000	-0.100740382147440000	0.999999999999990000	double d= Sab (1.4, 2, 2 ,??? 2, 1 , 0 ,2 ,1 );
<1s|1s>	1	0	1	0	0	7.7	1.5	1.4	0.084173621969720800	0.084173621969731700	1.000000000000130000	double d= Sab (1.4, 7.7, 1.5 ,??? 1, 0 , 0 ,1 ,0 );
<3d1|3d1>	3	2	3	2	1	6.5	2	1.4	-0.095957753440884500	-0.095957753440886700	1.000000000000020000	double d= Sab (1.4, 6.5, 2 ,??? 3, 2 , 1 ,3 ,2 );
<4s|4p1>	4	0	4	1	0	1.5	0.3	1.4	-0.047652956826569900	-0.047652956826569600	0.999999999999994000	double d= Sab (1.4, 1.5, 0.3 ,??? 4, 0 , 0 ,4 ,1 );

實測結(jié)果表明，這個程序n和n’取值范圍只能小于等于5，

Java程序

package udp;import java.io.DataInputStream; import java.io.FileWriter; import java.io.IOException; import java.io.InputStream; import java.text.ParseException;public class HFoverlapC {public static double calc2( String stra ) throws IOException, ParseException, InterruptedException {FileWriter fileWriter5 = new FileWriter("d:/工業(yè)/hk/python/表達式.csv");//stra="hin( fx1,fx1)";//stra="jin( rj1,rj2)";stra=stra.replaceAll(",","#");fileWriter5.write( stra + "\r\n");fileWriter5.flush();String exe = "python";String command = "D:/Download/cal.py"; String[] cmdArr = new String[] {exe ,command };Process process = Runtime.getRuntime().exec(cmdArr);InputStream is = process.getInputStream();DataInputStream dis = new DataInputStream(is);String str = dis.readLine();process.waitFor();System.out.println(str); double df= Double.parseDouble(str.trim()); return df;}public static double overLap( int n1,int n2 ,int c, int d, int m ,double α1 ,double β1) throws IOException, ParseException, InterruptedException {String f1= "sympy.exp(-0.5*("+α1+"+"+β1+")*μ-0.5*("+α1+"-"+β1+")*v )";String f2="(μ*μ-1)**"+m+"*(1-v*v)**"+m+"*(1+μ*v)**"+c+"*(1-μ*v)**"+d+"*(μ+v)**("+n1+"-"+m+"-"+c+")*(μ-v)**("+n2+"-"+m+"-"+d+")"; String d2 ="(integrate(integrate("+f1+" *"+ f2+" , (μ, 1, float('inf'))),(v, -1, 1)))";System.out.println( d2+" ** " );double ds=calc2( d2 );return ds; }public static double FACT( double n ) throws IOException, ParseException {double prodt=1.0;for(int a=1 ;a<n+1 ;a++){prodt=prodt*a;}return prodt;}//9.6-21 574public static double D( int L1,int L2,int m ) throws IOException, ParseException {double ss1=0;ss1 = (FACT(m + 1) / 8) * (FACT(m + 1) / 8) * Math.pow( ( (2 * L1 + 1) * FACT(L1 - m) * (2 * L2 + 1) * FACT(L2 - m) / (4.0 * FACT(L1 + m) * FACT(L2 + m))) ,0.5 );// ss1 = Math.pow( ( (2 * L1 + 1) * FACT(L1 - m) * (2 * L2 + 1) * FACT(L2 - m) / (4.0 * FACT(L1 + m) * FACT(L2 + m))) ,0.5 );System.out.println( ss1+" ** ss1" );return ss1; }//9.6-24public static double SS( int n1,int L1 ,int m ,int n2 ,int L2 ,double α1 ,double β1 ) throws IOException, ParseException, InterruptedException {double d1=D(L1,L2,m);double[] cL1= chcL1( L1 ,m ); double[] cL2= chcL1( L2 ,m ); double d2=0;for(int c=0 ;c<L1-m+1;c++){for(int d=0;d<L2-m+1;d++){d2 =d2+ cL1[c]*cL2[d]* overLap( n1, n2 , c, d, m , α1 , β1);//System.out.println( cL1[c]+" "+ cL2[d]+" "+ d2+" "+d1+" ** d2"+" "+c+" "+d );}}System.out.println( d2+" ** **d2" );return d2*d1; }public static double[] chcL1( int L ,int m ) throws IOException, ParseException, InterruptedException {double[] a1= new double[L-m+1];double f1=0; for(int u=0 ;u<L-m+1 ;u++){double d1=Math.pow( -1 ,(L-m-u)/2);double d2=1+Math.pow( -1 ,(L-m-u));double d3=FACT(L+m+u);double d4=Math.pow( 2 , L+1);double d5=FACT ( (L-m-u)/2 );double d6=FACT ( (L+m+u)/2 );f1=(8/FACT(m + 1) ) * d1*d2*d3/(d4*FACT(u)*d5*d6);//System.out.println( f1+" ** **f1 "+d1+" "+(L-m-u)/2+" "+(L-m-u) );//System.out.println( L+" "+m+" "+u +" "+(L-m-u)/2);a1[u]=f1;}return a1; }public static double Sab(double R,double za,double zb, int n1,int L1 ,int m ,int n2 ,int L2 ) throws IOException, ParseException, InterruptedException {double α1 =za*R;double β1 = zb*R;double f1=0;double d1= Math.pow((2*za),(n1+0.5))* Math.pow((2*zb) ,(n2+0.5) )/ Math.pow( ( FACT(2*n1)*FACT(2*n2) ),0.5) * Math.pow( (R/2),(n1+n2+1)) ;double d2=SS(n1,L1,m,n2,L2,α1 ,β1);f1=Math.pow(-1 , L2+m )*d1*d2;System.out.println( f1+" "+d1+" "+d2+" Sab "+Math.pow(-1 , L2+m ) );// System.out.println( f1+" f1 Sab " );return f1;}public static void so( ) throws IOException, ParseException, InterruptedException {//double d= Sab (1.733, 8.7,1, 1, 0 , 0 ,1 ,0 ); //1-6 0.05484010400044412//double d= Sab ( 1.733,2.6,1, 2, 0 , 0 ,1 ,0 ); //2-6 0.471700639846316//double d= Sab (1.733, 2.6,1, 2, 1 , 0 ,1 ,0 ); //3-6 0.29891181959547//double d= Sab ( 1.733,8.7,2.6, 1, 0 , 0 ,2 ,0 ); //1-2 0.237710896136317//double d= Sab (2, 2.2 , 1.5 , 1, 0 , 0 ,1 ,0 ); // 0.23137110583275272//double d= Sab (2, 5.5 , 1.5 , 1, 0 , 0 ,1 ,0 ); //0.05912593860893186//double d= Sab (2, 7.7 , 1.5 , 1, 0 , 0 ,1 ,0 ); //0.035054800488252554//double d= Sab (2, 9.9 , 1.5 , 1, 0 , 0 ,1 ,0 ); //0.023836349699889875//double d= Sab (1.4, 10 , 10 , 1, 0 , 0 ,1 ,0 ); //6.679947377319999E-5//double d= Sab (1.4, 0.1 , 0.1 , 5, 0 , 0 ,5 ,0 ); //0.9996371894103874//double d= Sab (1.4, 10 , 2 , 1, 0 , 0 ,2 ,1 ); //-0.11741378968663181//double d= Sab (1.4, 0.5 , 0.4 , 4, 0 , 0 ,4 ,1 ); // 4s0 4p0 -0.12303518536265186double d= Sab (1.4, 2, 2 , 2, 1 , 0 ,2 ,1 ); //-0.10074038214744//double d= Sab (1.4, 7.7, 1.5 , 1, 0 , 0 ,1 ,0 ); // 0.0841736219697317//double d= Sab (1.4, 6.5, 2 , 3, 2 , 1 ,3 ,2 ); // 3d1 -0.09595775344088678//double d= Sab (1.4, 1.5, 0.3 , 4, 0 , 0 ,4 ,1 ); //-0.04765295682656969//R=2.5;//double d= Sab ( 2.5, 4.2, 4.4 , 2, 1 , 1 ,3 ,2 ); //-0.012921364533721143//double d= Sab ( 2.5, 2.3, 2.3, 3, 2, 0, 2, 1 ); //-0.2252196665380932//double d= Sab ( 0.2, 5.8, 4.5, 3, 2, 2, 3, 2 ); //0.8783587074281796//double d= Sab ( 8.7, 2.0, 4.4, 3, 2, 1, 3, 2 ); //-6.315678534334961E-6//double d= Sab ( 15, 1.5, 0.5, 4, 3, 1, 5, 2 ); //-0.012890230947022028//double d= Sab ( 0.1, 1.5, 1, 5, 3, 3, 6, 4 ); //0//double d= Sab ( 0.1, 3.6, 3.7, 4, 3, 2, 8, 5 ); //1.55131317410255283E18System.out.println( d+" Sab " );}public static void main(String[] args) throws IOException, ParseException, InterruptedException {so( );}}

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