Electronic Supplementary Material
Nonorthogonal Orbital Based N-body Reduced Density Matrices and Their
Applications to Valence Bond Theory. III. Second-Order Perturbation Theory
Using Valence Bond Self-Consist Field Function as Reference
Zhenhua Chen, Xun Chen, Fuming Ying, Junjing Gu, Huaiyu Zhang and Wei Wu*
The State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative
Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key
Laboratory of Theoretical and Computational Chemistry and College of Chemistry
and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China.
E-mail: weiwu@xmu.edu.cn, Fax: (86)592-2183047
*
To whom correspondence should be addressed.
1
Table of contents
Table S1. Spectroscopic constants for some diatomic molecules by VBSCF and
icVBPT2 methods with OEO.
Table S2. The icVBPT2 total energies of H2 at various distances.
Table S3. The icVBPT2 total energies of N2 at various distances.
Table S4. The icVBPT2 total energies of O2 at various distances.
Table S5. The icVBPT2 total energies of F2 at various distances.
Table S6. The icVBPT2 total energies of D-A reaction of butadiene and ethylene.
2
Table S2. Spectroscopic constants for some diatomic molecules by VBSCF and icVBPT2 methods with OEO.
ωe (cm-1)
re (a0)
Molecule
H2
NVB
3
N2
17
O2
175
12
105
F2
H2
3
3
N2
17
De (eV)
O2
175
12
105
F2
H2
3
3
N2
17
O2
175
12
F2
105
3
VBSCF
1.427 2.117 2.119 2.321 2.322 2.768
4206 2353 2342 1567 1567 783.0
4.135 8.246 8.333 3.574 3.614
0.714
icVBPT2
1.408 2.119 2.122 2.320 2.319 2.692
4371 2358 2354 1588 1712 906.3
4.612 8.546 8.636 4.711 4.761
1.508
3
Table S2. The icVBPT2 total energies (E, in a.u.) of H2 at various distances, (r, in a0).
r
HAO
OEO
1.347375
-1.168305
-1.168408
1.404067
-1.169023
-1.169123
1.460759
-1.168552
-1.168651
188.972688
-0.999642
-0.999642
4
Table S3. The icVBPT2 total energies (E, in a.u.) of N2 at various distances, (r, in a0).
HAO
OEO
r
NVB = 17
NVB = 175
NVB = 17
NVB = 175
2.05
-109.136460
-109.139818
-109.138996
-109.141995
2.10
-109.139669
-109.143365
-109.142500
-109.145713
2.15
-109.138992
-109.143046
-109.142104
-109.145514
50.00
-108.828715
-108.828715
-108.828715
-108.828715
5
Table S4. The icVBPT2 total energies (E, in a.u.) of O2 at various distances, (r, in a0).
HAO
OEO
r
NVB = 12
NVB = 105
NVB = 12
NVB = 105
2.25
-149.863159
-149.865685
-149.869801
-149.871335
2.30
-149.865201
-149.867699
-149.871629
-149.873441
2.35
-149.865200
-149.867655
-149.871443
-149.873208
100.00
-149.698649
-149.698649
-149.698649
-149.698649
6
Table S5. The icVBPT2 total energies (E, in a.u.) of F2 at various distances, (r, in a0).
r
HAO
OEO
2.679633
-199.274789
-199.276918
2.736325
-199.275794
-199.277645
2.793016
-199.275814
-199.277393
188.972688
-199.222254
-199.222254
7
Table S6. The icVBPT2 total energies (in a.u.) of D-A reaction of butadiene and
ethylene.
Orbital
LFO
OEO
NVBa
Reactant
Transition state
Product
5
-233.7469354
-233.6805364
-233.7699336
17
-233.7469505
-233.7078866
-233.8099284
175
-233.7479637
-233.7143718
-233.8136158
5
-233.7473106
-233.7080892
-233.8124686
17
-233.7473119
-233.711077
-233.8128245
175
-233.7483275
-233.7138082
-233.8140334
a. The number of VB structures involved in the VBSCF wave function.
8