2 p oxygen
c = 80.000960067, 0.003928763, 0.007805307, 0.033564047, 0.203660575,
0.591784752, 1.402994766, 2.104431092, 2.375859618, 2.637298266<
80.000960067, 0.00392876, 0.00780531, 0.033564,
0.203661, 0.591785, 1.40299, 2.10443, 2.37586, 2.6373<
80.000960067‘, 0.003928763‘, 0.007805307‘, 0.033564047‘, 0.203660575‘,
0.591784752‘, 1.402994766‘, 2.104431092‘, 2.375859618‘, 2.637298266‘<
80.000960067, 0.00392876, 0.00780531, 0.033564,
0.203661, 0.591785, 1.40299, 2.10443, 2.37586, 2.6373<
d = 80.01122, 0.02222, 0.0438, 0.127725, 0.31165, 0.758, 1.87, 4.72, 12.82, 46<
80.01122, 0.02222, 0.0438, 0.127725, 0.31165, 0.758, 1.87, 4.72, 12.82, 46<
80.01122‘, 0.02222‘, 0.0438‘, 0.127725‘,
0.31165‘, 0.758‘, 1.87‘, 4.72‘, 12.82‘, 46<
80.01122, 0.02222, 0.0438, 0.127725, 0.31165, 0.758, 1.87, 4.72, 12.82, 46<
3 d , vanadii
e = 80.0129025, 0.261291, 1.40221, 4.40518, 8.78691, 12.8518, 14.5512, 17.8858<
80.0129025, 0.261291, 1.40221, 4.40518, 8.78691, 12.8518, 14.5512, 17.8858<
f = 80.248487, 0.546423, 1.20158, 2.64228, 5.81038, 12.777, 28.0967, 61.7846<
80.248487, 0.546423, 1.20158, 2.64228, 5.81038, 12.777, 28.0967, 61.7846<
V1 - V2___ ___ ___
xy, xy
H0.5 - 2 * 0.09788L * 21.37470071450573
R = 6.503038945381224‘
H15  8L * Pi ^ H1  2L * Sum@e@@iDD * e@@jDD * H1  Hf@@iDD + f@@jDDLL ^ H7  2L *
HH1  2L - f@@iDD * f@@jDD * H1  Hf@@iDD + f@@jDDLL * H6.50304L ^ 2L *
Exp@- f@@iDD * f@@jDD * H1  Hf@@iDD + f@@jDDLL * H6.5L ^ 2D, 8i, 1, 8<, 8j, 1, 8<D
- 0.000476253
V1 - O11___ ___ ___
y, xy
H0.25 - 0.09788L * 21.37470071450573
3.25152
HH3 * 3.25152L  8L * H5 * PiL ^ H1  2L *
Sum@c@@iDD * e@@jDD * d@@iDD * H1  Hd@@iDD + f@@jDDLL ^ H7  2L * Exp@
- d@@iDD * f@@jDD * H1  Hd@@iDD + f@@jDDLL * H3.25152L ^ 2D, 8i, 1, 10<, 8j, 1, 8<D
0.0702178
O31 - O32___ ___ ___
H0.5 - 2 * 0.07302L * 21.37470071450573
R = 7.565789064906449‘
2
two2var2.nb
x, x ; r = Hxo, 0, 0L
H3  4L * Pi ^ H1  2L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H5  2L *
HH1  2L - d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLL * H7.56579L ^ 2L * Exp@
- d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLL * H7.56579L ^ 2D, 8i, 1, 10<, 8j, 1, 10<D
- 0.073346
z, z; r = Hxo, 0, 0L
H3  8L * Pi ^ H1  2L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H5  2L * Exp@
- d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLL * H7.56579L ^ 2D, 8i, 1, 10<, 8j, 1, 10<D
0.0946679
NaV2O5___ ___ ___
O31 - O32 two center
Hpx, HLR, pxL
F H100L ___ ___ ___
H0.427 - 0.073L
0.354
H0.427 - 0.073L * 21.37470071450573
7.56664
xo = 7.566644052935029‘
variant2
- H1  PiL ^ H1  2L * H1  H21.37470071450573 * 6.82285889220431 * 9.070689013316905LL *
Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H5  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
Sum@H7.566644052935029 * d@@jDD *
Cos@2 * Pi * nx H0.073 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLL +
Pi * 0.5 * ny + 2 * Pi * 0.48769 * nzD - HPi  21.37470071450573L *
nx * Sin@2 * Pi * nx H0.073 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLL +
Pi * 0.5 * ny + 2 * Pi * 0.48769 * nzDL *
HCos@Pi * H0.2816 * nz + 0.5 * Hnx + nyLLD - 2 Cos@Pi * H0.961 * nz + 0.5 Hnx - nyLLD 4 * Cos@Pi * H0.729 * nxLD * Cos@Pi * H0.11606 * nz + 0.5 * Hnx + nyLLD 4 * Cos@Pi * 0.354 * nxD * Cos@Pi * H0.97538 * nz + 0.5 * Hnx + nyLLD +
9 * Cos@Pi * 0.6958 * nxD * Cos@Pi * H0.78438 * nz + 0.5 * Hnx + nyLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HHPi  21.37470071450573L ^ 2 * nx ^ 2 +
HPi  6.82285889220431L ^ 2 * ny ^ 2 + HPi  9.070689013316905L ^ 2 * nz ^ 2LD *
H1  HHnx  21.37470071450573L ^ 2 + Hny  6.82285889220431L ^ 2 +
Hnz  9.070689013316905L ^ 2 + 0.000000000000001LL,
8nx, - 100, 100<, 8ny, - 50, 50<, 8nz, - 50, 50<D, 8i, 6, 10<, 8j, 6, 10<D
blok H1, 1 - 5, 5L = 0.0032277036899622247,
blok H1, 6 - 5, 10L = 0.046727227213266435,
blok H6, 1 - 10, 5L = 0.000441889729026796,
blok H6, 6 - 10, 10L = 2.468624665186031‘*^-11
sumblok = 0.0032277036899622247 + 0.046727227213266435 +
0.000441889729026796 + 2.468624665186031‘*^-11
two2var2.nb
3
0.050396820656941704‘
F H100L = sumblok = 0.050396820656941704
F H200L ___ ___ ___
xo = 0.354 * 21.37470071450573
7.566644052935029‘
variant2
- H1  PiL ^ H1  2L * H1  H21.37470071450573 * 6.82285889220431 * 9.070689013316905LL *
Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H5  2L *
Exp@- H7.566216558920739L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL Pi ^ 2 * H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@Pi * HH0.146 + 0.708 * Hd@@jDD  Hd@@iDD + d@@jDDLLL * nx + 0.5 * ny +
0.97538 * nzLD - 2 * HH7.566644052935029 * d@@jDDL  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx * Sin@Pi * HH0.146 + 0.708 *
Hd@@jDD  Hd@@iDD + d@@jDDLLL * nx + 0.5 * ny + 0.97538 * nzLDL *
HCos@Pi * H0.2816 * nz + 0.5 * Hnx + nyLLD - 2 Cos@Pi * H0.961 * nz + 0.5 Hnx - nyLLD 4 * Cos@Pi * H0.729 * nxLD * Cos@Pi * H0.11606 * nz + 0.5 * Hnx + nyLLD 4 * Cos@Pi * 0.354 * nxD * Cos@Pi * H0.97538 * nz + 0.5 * Hnx + nyLLD +
9 * Cos@Pi * 0.6958 * nxD * Cos@Pi * H0.78438 * nz + 0.5 * Hnx + nyLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HHPi  21.37470071450573L ^ 2 * nx ^ 2 +
HPi  6.82285889220431L ^ 2 * ny ^ 2 + HPi  9.070689013316905L ^ 2 * nz ^ 2LD *
H1  HHnx  21.37470071450573L ^ 2 + Hny  6.82285889220431L ^ 2 +
Hnz  9.070689013316905L ^ 2 + 0.000000000000001LL,
8nx, - 100, 100<, 8ny, - 50, 50<, 8nz, - 50, 50<D, 8i, 6, 10<, 8j, 6, 10<D
blok H1, 1 - 5, 5L = 0.014121681931788432, blok H1, 6 - 5, 10L = 0.3510493000773635
blok H6, 1 - 10, 5L = 0.0007644963902249763,
blok H6, 6 - 10, 10L = 9.581539883917661‘*^-11
Hpx, HLR, pxL = 3  2 HF H200L - xo * F H100LL
variant2
sumblok = 0.014121681931788432 + 0.3510493000773635 +
0.0007644963902249763 + 9.581539883917661‘*^-11
F H200L = 0.3659354784951923‘
E = H3  2L HF H200L - x0 * F H100LL
H3  2L * H0.3659354784951923 - 7.566644052935029 * 0.050396820656941704L
- 0.023099
- 0.023098987223233253 * H219 470  8065L
- 0.628585
Hpx, HLR, pxL = - 0.6285845909340362 ev___ ___ ___‘
Integrate___ ___ ___
NIntegrate@Exp@- H1  xL ^ 2D * H1  xL ^ 3, 8x, 0, 1<D
0.18394
4
two2var2.nb
Na1
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.177 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx * H0.177 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 1000<DL *
H1 + 2 * Sum@Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  6.82285889220431L ^ 2 *
ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 1000<DL *
H1 + 2 * Sum@Cos@Pi * H0.34689 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 1000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
Na2
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.677 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx * H0.677 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.5 * nyLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  6.82285889220431L ^ 2 * ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.37151 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
O11
two2var2.nb
5
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.177 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566216558920739 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx * H0.177 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.5 * nyLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  6.82285889220431L ^ 2 * ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.00719 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
O12
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.677 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx * H0.677 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  6.82285889220431L ^ 2 *
ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.03181 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
O21
6
two2var2.nb
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.0415 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx * H0.0415 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.5 * nyLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  6.82285889220431L ^ 2 * ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.45428 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
O22
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.3125 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566216558920739 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx * H0.3125 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.5 * nyLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  6.82285889220431L ^ 2 * ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.45428 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
O23
two2var2.nb
7
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.5415 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx * H0.5415 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  6.82285889220431L ^ 2 *
ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.42966 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
O24
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.8125 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx * H0.8125 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.5 * nyLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  6.82285889220431L ^ 2 * ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.42966 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
O31
8
two2var2.nb
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566216558920739 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx * Sin@2 * Pi * nx * H0.354 * Hd@@jDD 
Hd@@iDD + d@@jDDLLLDL * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L ^ 2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  6.82285889220431L ^ 2 *
ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  9.070689013316905L ^ 2 *
nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
O32
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.354 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx H0.354 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  6.82285889220431L ^ 2 *
ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  9.070689013316905L ^ 2 *
nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
O33
two2var2.nb
9
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.5 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx H0.5 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.5 * nyLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  6.82285889220431L ^ 2 * ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.02462 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
O34
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.854 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx H0.854 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.5 * nyLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  6.82285889220431L ^ 2 * ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.02462 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
V1
10
two2var2.nb
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.0249 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx H0.0249 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.5 * nyLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  6.82285889220431L ^ 2 * ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.12012 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
V2
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.3291 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx H0.3291 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.5 * nyLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  6.82285889220431L ^ 2 * ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.12012 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
V3
two2var2.nb
11
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.5249 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx H0.5249 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  6.82285889220431L ^ 2 *
ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.0955 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
V4
- HPiL ^ H3  2L * H1  21.37470071450573L * H1  6.82285889220431L *
H1  9.070689013316905L * Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H7  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD *
NIntegrate@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL + H1  2L +
2 * Sum@HHH7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - Pi ^ 2 *
H1  Hd@@iDD + d@@jDDLL * Hnx  21.37470071450573L ^ 2 + H1  2LL *
Cos@2 * Pi * nx * H0.8291 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLD 2 * 7.566644052935029 * d@@jDD * H1  Hd@@iDD + d@@jDDLL *
HPi  21.37470071450573L * nx *
Sin@2 * Pi * nx H0.5 + 0.354 * Hd@@jDD  Hd@@iDD + d@@jDDLLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  21.37470071450573L ^
2 * nx ^ 2 * H1  xL ^ 2D, 8nx, 1, 2000<DL *
H1 + 2 * Sum@Exp@- H1  Hd@@iDD + d@@jDDLL * HPi  6.82285889220431L ^ 2 *
ny ^ 2 * H1  x ^ 2LD, 8ny, 1, 2000<DL *
H1 + 2 * Sum@Cos@Pi * H0.0955 * nzLD * Exp@- H1  Hd@@iDD + d@@jDDLL *
HPi  9.070689013316905L ^ 2 * nz ^ 2 * H1  xL ^ 2D, 8nz, 1, 2000<DL H7.566644052935029 * d@@jDDL ^ 2 * H1  Hd@@iDD + d@@jDDLL - H1  2LL *
H1  xL ^ 3, 8x, 0, 1<D, 8i, 1, 10<, 8j, 1, 10<D
NaV2O5
O31 - O32 two center ___ ___ ___
Hpz, HLR, pzL
F H002L
Summation___ ___ ___
variant2
12
two2var2.nb
H1  PiL ^ H1  2L * H1  H21.37470071450573 * 6.82285889220431 * 9.070689013316905LL *
Sum@c@@iDD * c@@jDD * H1  Hd@@iDD + d@@jDDLL ^ H5  2L *
Exp@- H7.566644052935029L ^ 2 * d@@iDD * d@@jDD * H1  Hd@@iDD + d@@jDDLLD * Sum@
HPi ^ 2 * H1  Hd@@iDD + d@@jDDLL * Hnz  9.070689013316905L ^ 2 - H1  2LL * Cos@Pi *
HH0.146 + 0.708 * Hd@@jDD  Hd@@iDD + d@@jDDLLL * nx + 0.5 * ny + 0.97538 * nzLD *
HCos@Pi * H0.2816 * nz + 0.5 * Hnx + nyLLD - 2 Cos@Pi * H0.961 * nz + 0.5 Hnx - nyLLD 4 * Cos@Pi * H0.729 * nxLD * Cos@Pi * H0.11606 * nz + 0.5 * Hnx + nyLLD 4 * Cos@Pi * 0.354 * nxD * Cos@Pi * H0.97538 * nz + 0.5 * Hnx + nyLLD +
9 * Cos@Pi * 0.6958 * nxD * Cos@Pi * H0.78438 * nz + 0.5 * Hnx + nyLLDL *
Exp@- H1  Hd@@iDD + d@@jDDLL * HHPi  21.37470071450573L ^ 2 * nx ^ 2 +
HPi  6.82285889220431L ^ 2 * ny ^ 2 + HPi  9.070689013316905L ^ 2 * nz ^ 2LD *
H1  HHnx  21.37470071450573L ^ 2 + Hny  6.82285889220431L ^ 2 +
Hnz  9.070689013316905L ^ 2 + 0.000000000000001LL,
8nx, - 100, 100<, 8ny, - 50, 50<, 8nz, - 50, 50<D, 8i, 6, 10<, 8j, 6, 10<D
blok H1, 1 -> 5, 5L = 0.004458176747762882,
blok H1, 6 -> 5, 10L = 0.000760454433761477,
blok H6, 1 - 10, 5L = 0.0007604544337614774,
blok H6, 6 - 10, 10L = 1.4724001438123465‘*^-12
0.004458176747762882 + 0.000760454433761477 +
0.0007604544337614774 + 1.4724001438123465‘*^-12
0.00597909
0.005979085616758237 * H219 470  8065L
0.162707
E12 = H3  2L F H002L
H3  2L * 0.16270674771356855‘
0.24406012157035284‘
Hpz, HLR, pzL = 0.24406012157035284 ev