1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
|
SUBROUTINE REPP(NI,NJ,RIJ,RI,CORE)
C***********************************************************************
C
C..VECTOR VERSION WRITTEN BY ERNEST R. DAVIDSON, INDIANA UNIVERSITY
C
C
C REPP CALCULATES THE TWO-ELECTRON REPULSION INTEGRALS AND THE
C NUCLEAR ATTRACTION INTEGRALS.
C
C ON INPUT RIJ = INTERATOMIC DISTANCE
C NI = ATOM NUMBER OF FIRST ATOM
C NJ = ATOM NUMBER OF SECOND ATOM
C (REF) ADD = ARRAY OF GAMMA, OR TWO-ELECTRON ONE-CENTER,
C INTEGRALS.
C (REF) TORE = ARRAY OF NUCLEAR CHARGES OF THE ELEMENTS
C (REF) DD = ARRAY OF DIPOLE CHARGE SEPARATIONS
C (REF) QQ = ARRAY OF QUADRUPOLE CHARGE SEPARATIONS
C
C THE COMMON BLOCKS ARE INITIALIZED IN BLOCK-DATA, AND NEVER CHANGED
C
C ON OUTPUT RI = ARRAY OF TWO-ELECTRON REPULSION INTEGRALS
C CORE = 4 X 2 ARRAY OF ELECTRON-CORE ATTRACTION
C INTEGRALS
C
C
C *** THIS ROUTINE COMPUTES THE TWO-CENTRE REPULSION INTEGRALS AND THE
C *** NUCLEAR ATTRACTION INTEGRALS.
C *** THE TWO-CENTRE REPULSION INTEGRALS (OVER LOCAL COORDINATES) ARE
C *** STORED AS FOLLOWS (WHERE P-SIGMA = O, AND P-PI = P AND P* )
C (SS/SS)=1, (SO/SS)=2, (OO/SS)=3, (PP/SS)=4, (SS/OS)=5,
C (SO/SO)=6, (SP/SP)=7, (OO/SO)=8, (PP/SO)=9, (PO/SP)=10,
C (SS/OO)=11, (SS/PP)=12, (SO/OO)=13, (SO/PP)=14, (SP/OP)=15,
C (OO/OO)=16, (PP/OO)=17, (OO/PP)=18, (PP/PP)=19, (PO/PO)=20,
C (PP/P*P*)=21, (P*P/P*P)=22.
C *** THE STORAGE OF THE NUCLEAR ATTRACTION INTEGRALS CORE(KL/IJ) IS
C (SS/)=1, (SO/)=2, (OO/)=3, (PP/)=4
C WHERE IJ=1 IF THE ORBITALS CENTRED ON ATOM I, =2 IF ON ATOM J.
C *** NI AND NJ ARE THE ATOMIC NUMBERS OF THE TWO ELEMENTS.
C
C***********************************************************************
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
LOGICAL SI,SJ
COMMON /MULTIP/ DD(107),QQ(107),ADD(107,3)
COMMON /CORE/ TORE(107)
COMMON /NATORB/ NATORB(107)
DIMENSION RI(22),CORE(4,2)
DIMENSION ARG(72),SQR(72)
DATA TD/2.D00/
DATA PP/0.5D00/
DATA A0/0.529167D0/ ,EV/27.21D0/, EV1/13.605D0/, EV2/6.8025D0/,
1 EV3/3.40125D0/, EV4/1.700625D0/
C
C ATOMIC UNITS ARE USED IN THE CALCULATION,
C FINAL RESULTS ARE CONVERTED TO EV
C
R=RIJ/A0
C
SI = (NATORB(NI).GE.3)
SJ = (NATORB(NJ).GE.3)
C
IF ((.NOT.SI) .AND. (.NOT.SJ)) THEN
C
C HYDROGEN - HYDROGEN (SS/SS)
C
AEE = PP/ADD(NI,1) + PP/ADD(NJ,1)
AEE = AEE * AEE
RI(1) = EV/SQRT(R*R+AEE)
CORE(1,1 )= TORE(NJ)*RI(1)
CORE(1,2) = TORE(NI)*RI(1)
C
ELSE IF (SI .AND. (.NOT.SJ)) THEN
C
C HEAVY ATOM - HYDROGEN
C
AEE = PP/ADD(NI,1) + PP/ADD(NJ,1)
AEE = AEE * AEE
DA=DD(NI)
QA=QQ(NI) * TD
ADE = PP/ADD(NI,2) + PP/ADD(NJ,1)
ADE = ADE * ADE
AQE = PP/ADD(NI,3) + PP/ADD(NJ,1)
AQE = AQE * AQE
RSQ = R*R
ARG(1) = RSQ + AEE
XXX = R+DA
ARG(2) = XXX*XXX + ADE
XXX = R-DA
ARG(3) = XXX*XXX + ADE
XXX = R+QA
ARG(4) = XXX*XXX + AQE
XXX = R-QA
ARG(5) = XXX*XXX + AQE
ARG(6) = RSQ + AQE
ARG(7) = ARG(6) + QA*QA
C$DOIT ASIS
DO 10 I = 1,7
SQR(I) = SQRT(ARG(I))
10 CONTINUE
EE = EV/SQR(1)
RI(1) = EE
RI(2) = EV1/SQR(2) - EV1/SQR(3)
RI(3) = EE + EV2/SQR(4) + EV2/SQR(5) - EV1/SQR(6)
RI(4) = EE + EV1/SQR(7) - EV1/SQR(6)
CORE(1,1) = TORE(NJ)*RI(1)
CORE(1,2) = TORE(NI)*RI(1)
CORE(2,1) = TORE(NJ)*RI(2)
CORE(3,1) = TORE(NJ)*RI(3)
CORE(4,1) = TORE(NJ)*RI(4)
C
ELSE IF ((.NOT.SI).AND.SJ) THEN
C
C HYDROGEN - HEAVY ATOM
C
AEE = PP/ADD(NI,1) + PP/ADD(NJ,1)
AEE = AEE * AEE
DB=DD(NJ)
QB=QQ(NJ) * TD
AED = PP/ADD(NI,1) + PP/ADD(NJ,2)
AED = AED * AED
AEQ = PP/ADD(NI,1) + PP/ADD(NJ,3)
AEQ = AEQ * AEQ
RSQ = R*R
ARG(1) = RSQ + AEE
XXX = R-DB
ARG(2) = XXX*XXX + AED
XXX = R+DB
ARG(3) = XXX*XXX + AED
XXX = R-QB
ARG(4) = XXX*XXX + AEQ
XXX = R+QB
ARG(5) = XXX*XXX + AEQ
ARG(6) = RSQ + AEQ
ARG(7) = ARG(6) + QB*QB
C$DOIT ASIS
DO 20 I = 1,7
SQR(I) = SQRT(ARG(I))
20 CONTINUE
EE = EV/SQR(1)
RI(1) = EE
RI(5) = EV1/SQR(2) - EV1/SQR(3)
RI(11) = EE + EV2/SQR(4) + EV2/SQR(5) - EV1/SQR(6)
RI(12) = EE + EV1/SQR(7) - EV1/SQR(6)
CORE(1,1) = TORE(NJ)*RI(1)
CORE(1,2) = TORE(NI)*RI(1)
CORE(2,2) = TORE(NI)*RI(5)
CORE(3,2) = TORE(NI)*RI(11)
CORE(4,2) = TORE(NI)*RI(12)
C
ELSE
C
C HEAVY ATOM - HEAVY ATOM
C
C DEFINE CHARGE SEPARATIONS.
DA=DD(NI)
DB=DD(NJ)
QA=QQ(NI) * TD
QB=QQ(NJ) * TD
C
AEE = PP/ADD(NI,1) + PP/ADD(NJ,1)
AEE = AEE * AEE
C
ADE = PP/ADD(NI,2) + PP/ADD(NJ,1)
ADE = ADE * ADE
AQE = PP/ADD(NI,3) + PP/ADD(NJ,1)
AQE = AQE * AQE
AED = PP/ADD(NI,1) + PP/ADD(NJ,2)
AED = AED * AED
AEQ = PP/ADD(NI,1) + PP/ADD(NJ,3)
AEQ = AEQ * AEQ
AXX = PP/ADD(NI,2) + PP/ADD(NJ,2)
AXX = AXX * AXX
ADQ = PP/ADD(NI,2) + PP/ADD(NJ,3)
ADQ = ADQ * ADQ
AQD = PP/ADD(NI,3) + PP/ADD(NJ,2)
AQD = AQD * AQD
AQQ = PP/ADD(NI,3) + PP/ADD(NJ,3)
AQQ = AQQ * AQQ
RSQ = R * R
ARG(1) = RSQ + AEE
XXX = R + DA
ARG(2) = XXX * XXX + ADE
XXX = R - DA
ARG(3) = XXX*XXX + ADE
XXX = R - QA
ARG(4) = XXX*XXX + AQE
XXX = R + QA
ARG(5) = XXX*XXX + AQE
ARG(6) = RSQ + AQE
ARG(7) = ARG(6) + QA*QA
XXX = R-DB
ARG(8) = XXX*XXX + AED
XXX = R+DB
ARG(9) = XXX*XXX + AED
XXX = R - QB
ARG(10) = XXX*XXX + AEQ
XXX = R + QB
ARG(11) = XXX*XXX + AEQ
ARG(12) = RSQ + AEQ
ARG(13) = ARG(12) + QB*QB
XXX = DA-DB
ARG(14) = RSQ + AXX + XXX*XXX
XXX = DA+DB
ARG(15) = RSQ + AXX + XXX*XXX
XXX = R + DA - DB
ARG(16) = XXX*XXX + AXX
XXX = R - DA + DB
ARG(17) = XXX*XXX + AXX
XXX = R - DA - DB
ARG(18) = XXX*XXX + AXX
XXX = R + DA + DB
ARG(19) = XXX*XXX + AXX
XXX = R + DA
ARG(20) = XXX*XXX + ADQ
ARG(21) = ARG(20) + QB*QB
XXX = R - DA
ARG(22) = XXX*XXX + ADQ
ARG(23) = ARG(22) + QB*QB
XXX = R - DB
ARG(24) = XXX*XXX + AQD
ARG(25) = ARG(24) + QA*QA
XXX = R + DB
ARG(26) = XXX*XXX + AQD
ARG(27) = ARG(26) + QA*QA
XXX = R + DA - QB
ARG(28) = XXX*XXX + ADQ
XXX = R - DA - QB
ARG(29) = XXX*XXX + ADQ
XXX = R + DA + QB
ARG(30) = XXX*XXX + ADQ
XXX = R - DA + QB
ARG(31) = XXX*XXX + ADQ
XXX = R + QA - DB
ARG(32) = XXX*XXX + AQD
XXX = R + QA + DB
ARG(33) = XXX*XXX + AQD
XXX = R - QA - DB
ARG(34) = XXX*XXX + AQD
XXX = R - QA + DB
ARG(35) = XXX*XXX + AQD
ARG(36) = RSQ + AQQ
XXX = QA - QB
ARG(37) = ARG(36) + XXX*XXX
XXX = QA + QB
ARG(38) = ARG(36) + XXX*XXX
ARG(39) = ARG(36) + QA*QA
ARG(40) = ARG(36) + QB*QB
ARG(41) = ARG(39) + QB*QB
XXX = R - QB
ARG(42) = XXX*XXX + AQQ
ARG(43) = ARG(42) + QA*QA
XXX = R + QB
ARG(44) = XXX*XXX + AQQ
ARG(45) = ARG(44) + QA*QA
XXX = R + QA
ARG(46) = XXX*XXX + AQQ
ARG(47) = ARG(46) + QB*QB
XXX = R - QA
ARG(48) = XXX*XXX + AQQ
ARG(49) = ARG(48) + QB*QB
XXX = R + QA - QB
ARG(50) = XXX*XXX + AQQ
XXX = R + QA + QB
ARG(51) = XXX*XXX + AQQ
XXX = R - QA - QB
ARG(52) = XXX*XXX + AQQ
XXX = R - QA + QB
ARG(53) = XXX*XXX + AQQ
QA=QQ(NI)
QB=QQ(NJ)
XXX = DA - QB
XXX = XXX*XXX
YYY = R - QB
YYY = YYY*YYY
ZZZ = DA + QB
ZZZ = ZZZ*ZZZ
WWW = R + QB
WWW = WWW*WWW
ARG(54) = XXX + YYY + ADQ
ARG(55) = XXX + WWW + ADQ
ARG(56) = ZZZ + YYY + ADQ
ARG(57) = ZZZ + WWW + ADQ
XXX = QA - DB
XXX = XXX*XXX
YYY = QA + DB
YYY = YYY*YYY
ZZZ = R + QA
ZZZ = ZZZ*ZZZ
WWW = R - QA
WWW = WWW*WWW
ARG(58) = ZZZ + XXX + AQD
ARG(59) = WWW + XXX + AQD
ARG(60) = ZZZ + YYY + AQD
ARG(61) = WWW + YYY + AQD
XXX = QA - QB
XXX = XXX*XXX
ARG(62) = ARG(36) + TD*XXX
YYY = QA + QB
YYY = YYY*YYY
ARG(63) = ARG(36) + TD*YYY
ARG(64) = ARG(36) + TD*(QA*QA+QB*QB)
ZZZ = R + QA - QB
ZZZ = ZZZ*ZZZ
ARG(65) = ZZZ + XXX + AQQ
ARG(66) = ZZZ + YYY + AQQ
ZZZ = R + QA + QB
ZZZ = ZZZ*ZZZ
ARG(67) = ZZZ + XXX + AQQ
ARG(68) = ZZZ + YYY + AQQ
ZZZ = R - QA - QB
ZZZ = ZZZ*ZZZ
ARG(69) = ZZZ + XXX + AQQ
ARG(70) = ZZZ + YYY + AQQ
ZZZ = R - QA + QB
ZZZ = ZZZ*ZZZ
ARG(71) = ZZZ + XXX + AQQ
ARG(72) = ZZZ + YYY + AQQ
DO 30 I = 1,72
SQR(I) = SQRT(ARG(I))
30 CONTINUE
EE = EV/SQR(1)
DZE = -EV1/SQR(2) + EV1/SQR(3)
QZZE = EV2/SQR(4) + EV2/SQR(5) - EV1/SQR(6)
QXXE = EV1/SQR(7) - EV1/SQR(6)
EDZ = - EV1/SQR(8) + EV1/SQR(9)
EQZZ = EV2/SQR(10) + EV2/SQR(11) - EV1/SQR(12)
EQXX = EV1/SQR(13) - EV1/SQR(12)
DXDX = EV1/SQR(14) - EV1/SQR(15)
DZDZ = EV2/SQR(16) + EV2/SQR(17) - EV2/SQR(18) - EV2/SQR(19)
DZQXX = EV2/SQR(20) - EV2/SQR(21) - EV2/SQR(22) + EV2/SQR(23)
QXXDZ = EV2/SQR(24) - EV2/SQR(25) - EV2/SQR(26) + EV2/SQR(27)
DZQZZ = -EV3/SQR(28) + EV3/SQR(29) - EV3/SQR(30) + EV3/SQR(31)
1 - EV2/SQR(22) + EV2/SQR(20)
QZZDZ = -EV3/SQR(32) + EV3/SQR(33) - EV3/SQR(34) + EV3/SQR(35)
1 + EV2/SQR(24) - EV2/SQR(26)
QXXQXX = EV3/SQR(37) + EV3/SQR(38) - EV2/SQR(39) - EV2/SQR(40)
1 + EV2/SQR(36)
QXXQYY = EV2/SQR(41) - EV2/SQR(39) - EV2/SQR(40) + EV2/SQR(36)
QXXQZZ = EV3/SQR(43) + EV3/SQR(45) - EV3/SQR(42) - EV3/SQR(44)
1 - EV2/SQR(39) + EV2/SQR(36)
QZZQXX = EV3/SQR(47) + EV3/SQR(49) - EV3/SQR(46) - EV3/SQR(48)
1 - EV2/SQR(40) + EV2/SQR(36)
QZZQZZ = EV4/SQR(50) + EV4/SQR(51) + EV4/SQR(52) + EV4/SQR(53)
1 - EV3/SQR(48) - EV3/SQR(46) - EV3/SQR(42) - EV3/SQR(44)
2 + EV2/SQR(36)
DXQXZ = -EV2/SQR(54) + EV2/SQR(55) + EV2/SQR(56) - EV2/SQR(57)
QXZDX = -EV2/SQR(58) + EV2/SQR(59) + EV2/SQR(60) - EV2/SQR(61)
QXZQXZ = EV3/SQR(65) - EV3/SQR(67) - EV3/SQR(69) + EV3/SQR(71)
1 - EV3/SQR(66) + EV3/SQR(68) + EV3/SQR(70) - EV3/SQR(72)
RI(1) = EE
RI(2) = -DZE
RI(3) = EE + QZZE
RI(4) = EE + QXXE
RI(5) = -EDZ
RI(6) = DZDZ
RI(7) = DXDX
RI(8) = -EDZ -QZZDZ
RI(9) = -EDZ -QXXDZ
RI(10) = -QXZDX
RI(11) = EE + EQZZ
RI(12) = EE + EQXX
RI(13) = -DZE -DZQZZ
RI(14) = -DZE -DZQXX
RI(15) = -DXQXZ
RI(16) = EE +EQZZ +QZZE +QZZQZZ
RI(17) = EE +EQZZ +QXXE +QXXQZZ
RI(18) = EE +EQXX +QZZE +QZZQXX
RI(19) = EE +EQXX +QXXE +QXXQXX
RI(20) = QXZQXZ
RI(21) = EE +EQXX +QXXE +QXXQYY
RI(22) = PP * (QXXQXX -QXXQYY)
C
C CALCULATE CORE-ELECTRON ATTRACTIONS.
C
CORE(1,1) = TORE(NJ)*RI(1)
CORE(2,1) = TORE(NJ)*RI(2)
CORE(3,1) = TORE(NJ)*RI(3)
CORE(4,1) = TORE(NJ)*RI(4)
CORE(1,2) = TORE(NI)*RI(1)
CORE(2,2) = TORE(NI)*RI(5)
CORE(3,2) = TORE(NI)*RI(11)
CORE(4,2) = TORE(NI)*RI(12)
C
END IF
C
RETURN
C
END
|
