3. Practice in valence bond calculations with XMVB
3.1. BDE and RE of F2
3.1.1. Introduction
F2 is a typical diatimic molecule which is simple enough for the users as a starting point. There is only 1 chemical bonding in the molecule. The 3 structures of the bonding is shown below.
Structures of F2 molecule
Here S1 denotes the covalent structure in which two active electrons are shared between both F atoms while S2 and
S3 denote 2 quivalent ionic structures in which two active eletrons doubly occupy orbital on certain F atom.
In this exercise, we will try to proceed computations for the bond dissociation energy (BDE) and resnance energy (RE) of F2. This takes computations at stationary point and dissociation limit with various sets of VB structures. This exercise will provide a first glance at VB computation. The users will learn the struct and syntax of XMVB input, how to build a simple input file, how to run the job and what we will get from the output.
Note
This exercise just shows the users how to proceed a VBSCF computation for a specific molecule, what we can get from the output and how to analyze the results. The accurate computation of BDE of F2 requires higher level computational methods with delocalized inactive \(\pi\) orbitals.
3.1.2. Computations with 3 Structures at Stationary Point
The computations are proceeded with F-F bond length 1.4 Angstrom, and the basis set is cc-pVDZ. For simplicity, F atoms are located in the Z axis.
3.1.2.1. Input File
Here shows the XMVB input file for all 3 structures at stationary point:
F2 VBSCF with 3 structures
$CTRL
STR=FULL NAO=2 NAE=2 ISCF=5 IPRINT=3
ORBTYP=HAO FRGTYP=SAO
INT=LIBCINT BASIS=CC-PVDZ
$END
$FRAG
1*6
SPZDXXDYYDZZ 1
SPZDXXDYYDZZ 2
PXDXZ 1
PXDXZ 2
PYDYZ 1
PYDYZ 2
$END
$ORB
1*10
1
2
1
2
3
4
5
6
1
2
$END
$GEO
F 0.0 0.0 0.0
F 0.0 0.0 1.4
$END
The global keywords listed in $CTRL section are explained below:
STR=FULLXMVB generates all VB structures automatically according to a specific active space.ISCF=5VBSCF computation with RDM-based algorithm.IPRINT=3XMVB will print most information.NAO=2andNAE=2Specify the active space with 2 active orbital and 2 active electrons respectively.ORBTYP=HAOandFRGTYP=SAOThe VB orbitals are described with fragments.INT=LIBCINTIntegrals are evaluated by XMVB withLIBCINTlibrary.BASIS=CC-PVDZThe basis set is cc-pVDZ.
Note
The orbitals of a molecule can be devided into “inactive” and “active” parts. The inactive orbitals are always doubly occupied in all VB structures, while the occupation numbers of active orbitals can be 0, 1 or 2 in each VB structure.
$FRAG section describes the fragments used to construct VB orbitals. In this case, the first line 1*6 means that there are 6 fragments built and each fragment include only 1 atom. The details of fragments are described in the following lines. For example, SPZDXXDYYDZZ 1 means that the fragment includes s, pz, dxx, dyy and dzz basis functions on atom 1, which is the first F atom in this case.
$ORB section describes VB orbitals. The first line 1*10 means that there are 10 orbitals in this case, each consisting of only 1 fragment. Each line below describes one orbital. For example, the first orbital includes only fragment 1, meaning that this orbital locates on the first F atom and belongs to the \(\sigma\) space since the F-F lies on Z axis. Also, orbital 6 with fragment 4 shows that the orbital describes the \(\pi_x\) orbital on the first F atom.
$GEO section shows the geometry of F2 molecule. Both Cartesian and internal coordinates are supported.
Note
Since NAO=2 is specified in $CTRL section, the last 2 orbitals in $ORB should be the active orbitals.
It is highly recommended that active orbitals are always palced after the inactive ones. This may make the input file more readable and less possible to get error.
3.1.2.2. Computational Results
In this case, 3 VB structures are generated with 1 covalent structure (0th ion structure) and 2 ionic structures (1th ion structures). These structures can be expaned into 4 determinants.
Number of 0th ion structures is: 1 from 1 to 1
Number of 0th ion determinants is: 2 from 1 to 2
Number of 1th ion structures is: 2 from 2 to 3
Number of 1th ion determinants is: 2 from 3 to 4
Total number of structures is: 3
Total number of determinants is: 4
.
.
.
Number of Structures: 3
The following structures are used in calculation:
1 ***** 1:8 9 10
2 ***** 1:8 9 9
3 ***** 1:8 10 10
The user may find from the output file that the VBSCF converged after 25 iterations and the final energy is -198.75115493 hartree.
VBSCF converged in 25 iterations
Total Energy: -198.75115493
First Excited: -197.880879
The coefficients and weights shows the importance of each structure. Following are the coefficients and weights of generated VB structures. Both coefficients and weights show that the covalent structure is the dominant one. So the F-F bond should be a covalent bond.
****** COEFFICIENTS OF STRUCTURES ******
1 -0.80579 ****** 1:8 9 10
2 -0.21326 ****** 1:8 9 9
3 -0.21326 ****** 1:8 10 10
.
.
.
****** WEIGHTS OF STRUCTURES ******
1 0.77586 ****** 1:8 9 10
2 0.11207 ****** 1:8 9 9
3 0.11207 ****** 1:8 10 10
Finally, the bond order value (0.773) in atomic population analysis shows that F-F bond should be a single bond.
****** BOND ORDER ****** ATOM 1 ATOM 2 DIST BOND ORDER 1 F 2 F 1.400 0.773
3.1.3. Computations with 3 Structures at Dissociation Limit
3.1.3.1. Input File
The input file for such computation can be easily obtained by modifying the corresponding one at stationary point. As shown below, one just needs to modify the coordinate of the second F atom to change 1.4 to 10.0. This will increase the F-F bond distance to 10.0 Angstrom.
$GEO
F 0.0 0.0 0.0
F 0.0 0.0 10.0
$END
3.1.3.2. Computational Results
After SCF procedure, the user will get the final energy as shown below. The computational energy of dissociated F2 is -198.74386524 hartree.
Total Energy: -198.74386524
First Excited: -197.850852
Both coefficients and weights of VB structures show that the wave function includes only covalent structure, indicating that the molecule is dissociated to 2 F\(\cdot\) radicals.
****** COEFFICIENTS OF STRUCTURES ******
1 1.00000 ****** 1:8 9 10
2 0.00000 ****** 1:8 9 9
3 0.00000 ****** 1:8 10 10
.
.
.
****** WEIGHTS OF STRUCTURES ******
1 1.00000 ****** 1:8 9 10
2 0.00000 ****** 1:8 9 9
3 0.00000 ****** 1:8 10 10
By substracting energies at stationary point and dissociation limit, the BDE can be obtained as 4.4 kcal/mol.
3.1.4. Computations with Covalent Structure at Stationary Point
3.1.4.1. Input File
The input file can be obtained by replacing STR=FULL with STR=COV in the input file of 3 structures at stationary point, as shown below.
$CTRL
STR=COV NAO=2 NAE=2 ISCF=5 IPRINT=3
ORBTYP=HAO FRGTYP=SAO
INT=LIBCINT BASIS=CC-PVDZ
$END
3.1.4.2. Computational Results
The structure information is shown below. It can be seen that only 1 covalent structure is generated for this computation.
Number of 0th ion structures is: 1 from 1 to 1
Number of 0th ion determinants is: 2 from 1 to 2
Total number of structures is: 1
Total number of determinants is: 2
.
.
.
Number of Structures: 1
The following structures are used in calculation:
1 ***** 1:8 9 10
The final energy after SCF iteration is -198.67485969 hartree.
Total Energy: -198.67485969
The Last Change in Energy: -0.000000
The bond order result in atomic population analysis shows that the bond order with only covalent structure is 0.324, which is much smaller than computations with 3 structures.
****** BOND ORDER ****** ATOM 1 ATOM 2 DIST BOND ORDER 1 F 2 F 1.400 0.324
The RE value, 47.6 kcal/mol, can be obtained from energies by covalent and 3 structure computations at stationary point. Compared with the computational BDE 4.4, RE is much larger than BDE, indicating that the chemical bonding in F2 is an charge-shifting bond. The much smaller bond order data with only covalent structure also indicates that resonance plays an important role in the F-F bonding.
3.2. Resonance in C6H6
3.2.1. Introduction
Benzene (C6H6) is a classical aromatic molecule in which electrons in \(\pi\) space are delocalized. The covalent valence bond structures are shown in the following table.
Covalent Structures of C6H6
The 5 covalent structures can be classified as 2 types: the first 2 structures are Kekulé structures and the others are regarded as Dewar structures. In this exercise, the resonance energy in the benzene molecule will be computed to show how resonance stabilize the aromatic molecule.
3.2.2. Computations with 5 Covalent Structures
First, we will compute the energy with all 5 covalent structures.
3.2.2.1. Input File
The input file is shown below.
C6H6
$ctrl
str=cov nao=6 nae=6 iscf=5 iprint=3
orbtyp=hao frgtyp=sao
int=libcint basis=cc-pvdz
$end
$frag
12 2*6
spxpydxxdyydzzdxy 1-12
pzdxzdyz 1 2
pzdxzdyz 3 4
pzdxzdyz 5 6
pzdxzdyz 7 8
pzdxzdyz 9 10
pzdxzdyz 11 12
$end
$orb
1*18 1*6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
$end
$geo
C 0.6995000584 1.2115696411 0.0000000000
H 1.2460106991 2.1581538376 0.0000000000
C -0.6995000584 1.2115696411 0.0000000000
H -1.2460106991 2.1581538376 0.0000000000
C -1.3990001169 0.0000000000 0.0000000000
H -2.4920213982 0.0000000000 0.0000000000
C -0.6995000584 -1.2115696411 0.0000000000
H -1.2460106991 -2.1581538376 0.0000000000
C 0.6995000584 -1.2115696411 0.0000000000
H 1.2460106991 -2.1581538376 0.0000000000
C 1.3990001169 0.0000000000 0.0000000000
H 2.4920213982 0.0000000000 0.0000000000
$end
In this input file, the molecule lays in the XY plane. The fragments specified in $FRAG section are defined according to the symmetries. Since we concern on the resonance in \(\pi\)space, electrons locating in \(\sigma\)space is not in the interest. Thus eletrons in the \(\sigma\)orbitals can be treated as inactive ones and make them delocalized in all structures. To this reason, the first fragment is defined to include all basis functions in \(\sigma\) space in the molecule. The remained fragments denote \(\pi\) orbitals locates on each CH group.
3.2.2.2. Computational Results
5 VB structures will be generated in the computation and can be found in the output:
Number of Structures: 5
The following structures are used in calculation:
1 ***** 1:18 21 22 20 23 19 24
2 ***** 1:18 20 21 22 23 19 24
3 ***** 1:18 20 21 19 22 23 24
4 ***** 1:18 19 20 22 23 21 24
5 ***** 1:18 19 20 21 22 23 24
Final energy can be found after the VBSCF iteration as -230.63450 hartree.
Total Energy: -230.63449533
Both coefficients and weights of VB structures show that structures are in 2 groups. Structure 2 and 5 correspond to the Kekulé structures, which are the dominant ones, and the others denote Dewar structures.
****** COEFFICIENTS OF STRUCTURES ****** 1 0.14537 ****** 1:18 21 22 20 23 19 24 2 -0.40098 ****** 1:18 20 21 22 23 19 24 3 0.14537 ****** 1:18 20 21 19 22 23 24 4 0.14537 ****** 1:18 19 20 22 23 21 24 5 -0.40098 ****** 1:18 19 20 21 22 23 24
****** WEIGHTS OF STRUCTURES ****** 1 0.11245 ****** 1:18 21 22 20 23 19 24 2 0.33132 ****** 1:18 20 21 22 23 19 24 3 0.11245 ****** 1:18 20 21 19 22 23 24 4 0.11245 ****** 1:18 19 20 22 23 21 24 5 0.33132 ****** 1:18 19 20 21 22 23 24
The atomic population analysis shows that the bond orders of all CC bondings are the same as 1.188, showing the effect of conjugation.
****** BOND ORDER ****** ATOM 1 ATOM 2 DIST BOND ORDER 1 C 2 H 1.093 0.979 1 C 3 C 1.399 1.188 3 C 4 H 1.093 0.979 3 C 5 C 1.399 1.188 5 C 6 H 1.093 0.979 5 C 7 C 1.399 1.188 7 C 8 H 1.093 0.979 7 C 9 C 1.399 1.188 9 C 10 H 1.093 0.979 1 C 11 C 1.399 1.188 9 C 11 C 1.399 1.188 11 C 12 H 1.093 0.979
3.2.3. Computations with 2 Kekulé Structures
3.2.3.1. Input File
The input file is shown below.
C6H6
$ctrl
nstr=2 nao=6 nae=6 iscf=5 iprint=3
orbtyp=hao frgtyp=sao
int=libcint basis=cc-pvdz
guess=read
$end
$str
1:18 19-24
1:18 19 24 20 21 22 23
$end
$frag
12 2*6
spxpydxxdyydzzdxy 1-12
pzdxzdyz 1 2
pzdxzdyz 3 4
pzdxzdyz 5 6
pzdxzdyz 7 8
pzdxzdyz 9 10
pzdxzdyz 11 12
$end
$orb
1*18 1*6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
$end
$geo
C 0.6995000584 1.2115696411 0.0000000000
H 1.2460106991 2.1581538376 0.0000000000
C -0.6995000584 1.2115696411 0.0000000000
H -1.2460106991 2.1581538376 0.0000000000
C -1.3990001169 0.0000000000 0.0000000000
H -2.4920213982 0.0000000000 0.0000000000
C -0.6995000584 -1.2115696411 0.0000000000
H -1.2460106991 -2.1581538376 0.0000000000
C 0.6995000584 -1.2115696411 0.0000000000
H 1.2460106991 -2.1581538376 0.0000000000
C 1.3990001169 0.0000000000 0.0000000000
H 2.4920213982 0.0000000000 0.0000000000
$end
$gus
90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 5 5 5 5 5 5
# ORBITAL 1 NAO = 90
-0.4085807072 1 -0.0018715270 2 0.0001649808 3 0.0000999746 4
0.0001985368 5 0.0000470242 7 0.0000880828 8 0.0009574571 10
0.0000833088 11 0.0010378240 13 0.0011389938 15 -0.0001957425 16
-0.0001334195 17 0.0000477351 18 0.0000812855 19 -0.4085807076 21
-0.0018715190 22 0.0001649828 23 -0.0000999676 24 0.0001985300 25
-0.0000470232 27 0.0000880811 28 0.0009574481 30 -0.0000833266 31
0.0010378340 33 0.0011390026 35 -0.0001957414 36 -0.0001334204 37
-0.0000477371 38 0.0000812776 39 -0.4090845359 41 -0.0018966521 42
0.0001488619 43 -0.0002148556 44 0.0000001381 45 -0.0000988751 47
0.0000000169 48 0.0010810968 50 -0.0000001656 51 0.0009153322 53
0.0011399821 55 -0.0002143575 56 -0.0001372115 57 -0.0000966788 58
0.0000001529 59 -0.4085807085 61 -0.0018714717 62 0.0001649779 63
-0.0001000242 64 -0.0001983775 65 -0.0000470512 67 -0.0000879863 68
0.0009574723 70 0.0000839012 71 0.0010378364 73 0.0011390336 75
-0.0001956328 76 -0.0001334448 77 -0.0000479296 78 -0.0000811013 79
-0.4085807082 81 -0.0018714747 82 0.0001649755 83 0.0001000278 84
-0.0001983820 85 0.0000470479 87 -0.0000879885 88 0.0009574749 90
-0.0000838796 91 0.0010378346 93 0.0011390280 95 -0.0001956337 96
-0.0001334457 97 0.0000479178 98 -0.0000811144 99 -0.4090845352 101
-0.0018966413 102 0.0001488609 103 0.0002148576 104 0.0000001396 105
0.0000988788 107 0.0000000209 108 0.0010810705 110 0.0000001777 111
0.0009153543 113 0.0011399863 115 -0.0002143672 116 -0.0001372134 117
0.0000966809 118 0.0000001629 119
# ORBITAL 2 NAO = 90
0.2888930861 1 0.0012304770 2 -0.0002563966 3 0.0001336859 4
-0.0001561191 5 0.0001914831 7 -0.0001481897 8 -0.0008221343 10
-0.0001557600 11 -0.0005906595 13 -0.0007980351 15 0.0001543642 16
0.0000791296 17 0.0000125324 18 -0.0000788689 19 -0.2888931497 21
-0.0012304753 22 0.0002562013 23 0.0001337942 24 0.0001566737 25
0.0001915140 27 0.0001494777 28 0.0008219804 30 -0.0001516843 31
0.0005907316 33 0.0007979421 35 -0.0001550608 36 -0.0000790540 37
0.0000136909 38 0.0000800072 39 -0.5781904466 41 -0.0024581181 42
0.0005050109 43 -0.0001390292 44 0.0000000205 45 -0.0000746810 47
0.0000000140 48 0.0015287631 50 -0.0000000553 51 0.0012982685 53
0.0015971801 55 -0.0003048222 56 -0.0001585226 57 -0.0001238936 58
0.0000000479 59 -0.2888930865 61 -0.0012304541 62 0.0002561993 63
0.0001337970 64 -0.0001566499 65 0.0001915245 67 -0.0001494674 68
0.0008219645 70 0.0001517465 71 0.0005907569 73 0.0007979557 75
-0.0001550484 76 -0.0000790645 77 0.0000136980 78 -0.0000799949 79
0.2888931500 81 0.0012304673 82 -0.0002563957 83 0.0001337007 84
0.0001561303 85 0.0001914997 87 0.0001482011 88 -0.0008221145 90
0.0001556889 91 -0.0005906834 93 -0.0007980414 95 0.0001543768 96
0.0000791346 97 0.0000125801 98 0.0000788956 99 0.5781904449 101
0.0024591332 102 -0.0005052562 103 -0.0001393968 104 0.0000000109 105
-0.0000739491 107 -0.0000000104 108 -0.0015297884 110 -0.0000000183 111
-0.0012968826 113 -0.0015966043 115 0.0003041670 116 0.0001581403 117
-0.0001241023 118 -0.0000000148 119
# ORBITAL 3 NAO = 90
0.5006118878 1 0.0021171792 2 -0.0004445363 3 -0.0001718795 4
-0.0000528411 5 -0.0001543791 7 0.0000142568 8 -0.0010905424 10
-0.0000444470 11 -0.0013582539 13 -0.0013824483 15 0.0002505625 16
0.0001341232 17 -0.0000778672 18 -0.0000745639 19 0.5006118515 21
0.0021171388 22 -0.0004445339 23 0.0001718621 24 -0.0000528197 25
0.0001543481 27 0.0000142554 28 -0.0010905019 30 0.0000444391 31
-0.0013583104 33 -0.0013824752 35 0.0002505629 36 0.0001341408 37
0.0000778110 38 -0.0000745770 39 -0.0000000362 41 0.0000000221 42
-0.0000000048 43 0.0000000087 44 0.0002083308 45 -0.0000000157 47
0.0002704667 48 -0.0000000212 50 0.0002206198 51 0.0000000294 53
0.0000000132 55 -0.0000000141 56 -0.0000000081 57 0.0000000045 58
0.0000602462 59 -0.5006118875 61 -0.0021171392 62 0.0004445257 63
-0.0001718574 64 -0.0000528443 65 -0.0001543471 67 0.0000142010 68
0.0010904959 70 0.0000442655 71 0.0013583140 73 0.0013824713 75
-0.0002505931 76 -0.0001341382 77 -0.0000777637 78 -0.0000746227 79
-0.5006118506 81 -0.0021171793 82 0.0004445278 83 0.0001718746 84
-0.0000528666 85 0.0001543776 87 0.0000142018 88 0.0010905358 90
-0.0000442668 91 0.0013582572 93 0.0013824439 95 -0.0002505929 96
-0.0001341203 97 0.0000778157 98 -0.0000746149 99 0.0000000372 101
0.0000000233 102 -0.0000000051 103 -0.0000000081 104 0.0002082947 105
0.0000000157 107 0.0002704090 108 -0.0000000235 110 -0.0002208132 111
0.0000000315 113 0.0000000132 115 -0.0000000150 116 -0.0000000085 117
-0.0000000048 118 0.0000600832 119
# ORBITAL 4 NAO = 90
-0.2891567875 1 -0.0011788380 2 0.0006696401 3 0.0001162136 4
-0.0000434029 5 0.0000569096 7 -0.0002181218 8 0.0005581052 10
-0.0000173221 11 0.0007001594 13 0.0007639834 15 -0.0000761592 16
-0.0000306619 17 0.0000222375 18 0.0000003327 19 -0.2891568478 21
-0.0011788552 22 0.0006696375 23 -0.0001162265 24 -0.0000433901 25
-0.0000569145 27 -0.0002181183 28 0.0005581234 30 0.0000173582 31
0.0007001375 33 0.0007639670 35 -0.0000761610 36 -0.0000306572 37
-0.0000222376 38 0.0000003522 39 0.5781677329 41 0.0024208733 42
-0.0012969300 43 -0.0000049661 44 -0.0000000187 45 -0.0003380963 47
0.0000000028 48 -0.0013034129 50 0.0000000076 51 -0.0012070190 53
-0.0015287103 55 0.0002187599 56 0.0000735925 57 0.0000329236 58
-0.0000000083 59 -0.2891567879 61 -0.0011788549 62 0.0006696380 63
-0.0001162154 64 0.0000433692 65 -0.0000569033 67 0.0002181026 68
0.0005581117 70 -0.0000174532 71 0.0007001480 73 0.0007639674 75
-0.0000761793 76 -0.0000306569 77 -0.0000221958 78 -0.0000003814 79
-0.2891568468 81 -0.0011788535 82 0.0006696419 83 0.0001162088 84
0.0000433741 85 0.0000569103 87 0.0002181062 88 0.0005581088 90
0.0000174178 91 0.0007001487 93 0.0007639740 95 -0.0000761773 96
-0.0000306542 97 0.0000222162 98 -0.0000003606 99 0.5781677327 101
0.0024208558 102 -0.0012969285 103 0.0000049612 104 -0.0000000253 105
0.0003380902 107 -0.0000000083 108 -0.0013033682 110 -0.0000000436 111
-0.0012070582 113 -0.0015287170 115 0.0002187773 116 0.0000735959 117
-0.0000329255 118 -0.0000000388 119
# ORBITAL 5 NAO = 90
-0.5007497195 1 -0.0020926701 2 0.0011274729 3 -0.0000664898 4
0.0000686296 5 -0.0002263515 7 -0.0001918806 8 0.0011015128 10
0.0000674501 11 0.0010736729 13 0.0013237329 15 -0.0001590050 16
-0.0000498765 17 0.0000054571 18 0.0000298585 19 0.5007496847 21
0.0020926790 22 -0.0011275085 23 -0.0000664796 24 -0.0000685616 25
-0.0002263533 27 0.0001920864 28 -0.0011015340 30 0.0000680448 31
-0.0010736610 33 -0.0013237436 35 0.0001589047 36 0.0000498846 37
0.0000056242 38 -0.0000296943 39 0.0000000348 41 0.0000000890 42
-0.0000000212 43 0.0000000320 44 0.0001851945 45 -0.0000000646 47
0.0002002088 48 -0.0000000915 50 0.0000942443 51 0.0000001220 53
0.0000000504 55 -0.0000000578 56 -0.0000000328 57 0.0000000176 58
0.0000247770 59 -0.5007497199 61 -0.0020926786 62 0.0011274738 63
0.0000664970 64 -0.0000686556 65 0.0002263560 67 0.0001918646 68
0.0011015108 70 0.0000673487 71 0.0010736709 73 0.0013237272 75
-0.0001590238 76 -0.0000498723 77 -0.0000054290 78 -0.0000298875 79
0.5007496855 81 0.0020926723 82 -0.0011275078 83 0.0000664707 84
0.0000685365 85 0.0002263476 87 -0.0001921026 88 -0.0011015386 90
0.0000681438 91 -0.0010736605 93 -0.0013237484 95 0.0001588863 96
0.0000498882 97 -0.0000056552 98 0.0000296659 99 0.0000000336 101
0.0000000883 102 -0.0000000217 103 -0.0000000323 104 -0.0001852396 105
0.0000000644 107 -0.0002002133 108 -0.0000000900 110 0.0000941944 111
0.0000001203 113 0.0000000496 115 -0.0000000565 116 -0.0000000328 117
-0.0000000169 118 -0.0000248210 119
# ORBITAL 6 NAO = 90
0.4091251475 1 0.0018241997 2 -0.0036592202 3 0.0000020694 4
-0.0000011859 5 0.0007741716 7 0.0013387077 8 -0.0007515405 10
0.0000812994 11 -0.0006732113 13 -0.0009930082 15 -0.0000359553 16
-0.0002099914 17 0.0000257544 18 0.0000416529 19 -0.4091251464 21
-0.0018242229 22 0.0036594107 23 0.0000019865 24 0.0000007218 25
0.0007741606 27 -0.0013398977 28 0.0007516717 30 0.0000776616 31
0.0006731473 33 0.0009930840 35 0.0000365738 36 0.0002099303 37
0.0000247332 38 -0.0000426613 39 0.4088400900 41 0.0018185067 42
-0.0036610579 43 -0.0000000395 44 0.0000000662 45 -0.0015467853 47
0.0000000329 48 -0.0006312514 50 -0.0000001499 51 -0.0007924283 53
-0.0009926163 55 -0.0000380211 56 -0.0002097659 57 -0.0000506940 58
0.0000001297 59 -0.4091251455 61 -0.0018241642 62 0.0036594070 63
0.0000019879 64 -0.0000006481 65 0.0007741792 67 0.0013399307 68
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# ORBITAL 7 NAO = 90
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# ORBITAL 8 NAO = 90
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# ORBITAL 9 NAO = 90
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# ORBITAL 10 NAO = 90
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# ORBITAL 11 NAO = 90
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# ORBITAL 12 NAO = 90
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# ORBITAL 13 NAO = 90
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# ORBITAL 14 NAO = 90
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# ORBITAL 15 NAO = 90
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# ORBITAL 16 NAO = 90
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# ORBITAL 17 NAO = 90
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# ORBITAL 18 NAO = 90
-0.0022422568 1 -0.0117861316 2 0.0017961586 3 -0.0149685697 4
0.2293271422 5 -0.0041574297 7 0.0961923012 8 -0.0046743391 10
0.0297488877 11 0.0035011315 13 0.0005353083 15 0.1890734811 16
0.0980836424 17 -0.0081565837 18 -0.0061626988 19 0.0022422568 21
0.0117861306 22 -0.0017961592 23 -0.0149685686 24 -0.2293271406 25
-0.0041574294 27 -0.0961923006 28 0.0046743386 30 0.0297488899 31
-0.0035011317 33 -0.0005353092 35 -0.1890734813 36 -0.0980836425 37
-0.0081565829 38 0.0061626996 39 0.0000000000 41 -0.0000000000 42
0.0000000000 43 0.0000000001 44 0.2552406577 45 0.0000000001 47
0.1034033602 48 0.0000000001 50 0.0215474843 51 -0.0000000000 53
0.0000000001 55 -0.0000000000 56 -0.0000000000 57 0.0000000000 58
0.0079649290 59 -0.0022422568 61 -0.0117861306 62 0.0017961592 63
0.0149685685 64 -0.2293271407 65 0.0041574294 67 -0.0961923005 68
-0.0046743388 70 0.0297488900 71 0.0035011319 73 0.0005353091 75
0.1890734813 76 0.0980836425 77 0.0081565830 78 0.0061626997 79
0.0022422568 81 0.0117861315 82 -0.0017961586 83 0.0149685698 84
0.2293271424 85 0.0041574298 87 0.0961923012 88 0.0046743391 90
0.0297488876 91 -0.0035011315 93 -0.0005353084 95 -0.1890734810 96
-0.0980836423 97 0.0081565838 98 -0.0061626989 99 0.0000000000 101
0.0000000000 102 -0.0000000000 103 -0.0000000000 104 -0.2552406531 105
-0.0000000000 107 -0.1034033615 108 -0.0000000001 110 0.0215474869 111
0.0000000001 113 -0.0000000001 115 -0.0000000001 116 -0.0000000000 117
-0.0000000000 118 -0.0079649287 119
# ORBITAL 19 NAO = 5
-0.6069137242 6 -0.5288219485 9 0.0160778803 12 0.0278520511 14
-0.0182054019 20
# ORBITAL 20 NAO = 5
-0.6069137241 26 -0.5288219486 29 -0.0160778803 32 0.0278520509 34
-0.0182054020 40
# ORBITAL 21 NAO = 5
-0.6069128657 46 -0.5288236221 49 -0.0321586274 52 0.0000000002 54
-0.0182031846 60
# ORBITAL 22 NAO = 5
-0.6069137243 66 -0.5288219484 69 -0.0160778802 72 -0.0278520508 74
-0.0182054020 80
# ORBITAL 23 NAO = 5
-0.6069137243 86 -0.5288219484 89 0.0160778802 92 -0.0278520511 94
-0.0182054019 100
# ORBITAL 24 NAO = 5
-0.6069128633 106 -0.5288236244 109 0.0321586294 112 0.0000000002 114
-0.0182031848 120
$end
In the input file, VB structures are specified by the users rather than automatically generated. The keyword NSTR=2 in $CTRL section specifies 2 VB structures in the computation, and the 2 Kekulé structures are described in section $STR. The keyword GUESS=READ means that the initial guess is obtained by the user in $GUS section. The initial guess comes from the optmized orbitals of previous computation, stored in corresponding ORB file.
3.2.3.2. Computational Results
The final energy of the computation can be found after VBSCF iterations as -230.62995 hartree. Compared with the energy including 5 covalent structures, the corresponding resonance energy from Dewar structures can be obtained as 2.8 kcal/mol.
****** BOND ORDER ****** ATOM 1 ATOM 2 DIST BOND ORDER 1 C 2 H 1.093 0.979 1 C 3 C 1.399 1.186 3 C 4 H 1.093 0.979 3 C 5 C 1.399 1.186 5 C 6 H 1.093 0.979 5 C 7 C 1.399 1.186 7 C 8 H 1.093 0.979 7 C 9 C 1.399 1.186 9 C 10 H 1.093 0.979 1 C 11 C 1.399 1.186 9 C 11 C 1.399 1.186 11 C 12 H 1.093 0.979
The atomic population analysis also shows that the bonder orders of CC bondings are the same as 1.186. Compared with the bond order from 5 covalent structures and the resonance energy from Dewar structures, the conjugation and stability mainly come from the resonance of Kekulé structures.
3.2.4. Computations with 1 Kekulé Structure
Finally, the computation including only 1 Kekulé structure, which represents a cycloalkene, will be proceeded to check the resonance from Kekulé structures.
3.2.4.1. Input File
The input file of this computation is shown below. The initial guess comes from the optimized orbitals of the computation including 2 Kekulé structures.
C6H6
$ctrl
nstr=1 nao=6 nae=6 iscf=5 iprint=3
orbtyp=hao frgtyp=sao
int=libcint basis=cc-pvdz
guess=read
$end
$str
1:18 19-24
$end
$frag
12 2*6
spxpydxxdyydzzdxy 1-12
pzdxzdyz 1 2
pzdxzdyz 3 4
pzdxzdyz 5 6
pzdxzdyz 7 8
pzdxzdyz 9 10
pzdxzdyz 11 12
$end
$orb
1*18 1*6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
$end
$geo
C 0.6995000584 1.2115696411 0.0000000000
H 1.2460106991 2.1581538376 0.0000000000
C -0.6995000584 1.2115696411 0.0000000000
H -1.2460106991 2.1581538376 0.0000000000
C -1.3990001169 0.0000000000 0.0000000000
H -2.4920213982 0.0000000000 0.0000000000
C -0.6995000584 -1.2115696411 0.0000000000
H -1.2460106991 -2.1581538376 0.0000000000
C 0.6995000584 -1.2115696411 0.0000000000
H 1.2460106991 -2.1581538376 0.0000000000
C 1.3990001169 0.0000000000 0.0000000000
H 2.4920213982 0.0000000000 0.0000000000
$end
$gus
90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 5 5 5 5 5 5
# ORBITAL 1 NAO = 90
-0.4085796783 1 -0.0018719283 2 0.0001665818 3 0.0001010685 4
0.0001981258 5 0.0000450438 7 0.0000863179 8 0.0009553396 10
0.0000836069 11 0.0010374634 13 0.0011387900 15 -0.0001957720 16
-0.0001340753 17 0.0000469703 18 0.0000827563 19 -0.4085796727 21
-0.0018719292 22 0.0001665812 23 -0.0001010727 24 0.0001981248 25
-0.0000450425 27 0.0000863186 28 0.0009553426 30 -0.0000836019 31
0.0010374618 33 0.0011387887 35 -0.0001957726 36 -0.0001340767 37
-0.0000469715 38 0.0000827567 39 -0.4090835453 41 -0.0018962542 42
0.0001483676 43 -0.0002144425 44 0.0000004419 45 -0.0001064444 47
0.0000000620 48 0.0010795224 50 -0.0000005324 51 0.0009089949 53
0.0011398054 55 -0.0002140828 56 -0.0001424123 57 -0.0000967357 58
0.0000004933 59 -0.4085796762 61 -0.0018717962 62 0.0001665571 63
-0.0001012559 64 -0.0001976491 65 -0.0000451304 67 -0.0000860262 68
0.0009554043 70 0.0000853899 71 0.0010374754 73 0.0011388868 75
-0.0001954373 76 -0.0001341537 77 -0.0000475649 78 -0.0000822130 79
-0.4085796747 81 -0.0018717874 82 0.0001665574 83 0.0001012488 84
-0.0001976456 85 0.0000451252 87 -0.0000860254 88 0.0009553937 90
-0.0000853972 91 0.0010374881 93 0.0011388931 95 -0.0001954365 96
-0.0001341565 97 0.0000475538 98 -0.0000822115 99 -0.4090835098 101
-0.0018962560 102 0.0001483691 103 0.0002144405 104 0.0000004455 105
0.0001064418 107 0.0000000681 108 0.0010795349 110 0.0000005509 111
0.0009089845 113 0.0011398035 115 -0.0002140768 116 -0.0001424127 117
0.0000967353 118 0.0000005091 119
# ORBITAL 2 NAO = 90
0.2888921826 1 0.0012283761 2 -0.0002515233 3 0.0001334436 4
-0.0001583616 5 0.0001866742 7 -0.0001486589 8 -0.0008194761 10
-0.0001545655 11 -0.0005903612 13 -0.0007993769 15 0.0001561841 16
0.0000815611 17 0.0000143387 18 -0.0000796338 19 -0.2888922723 21
-0.0012282896 22 0.0002516068 23 0.0001334933 24 0.0001581461 25
0.0001866825 27 0.0001482790 28 0.0008195384 30 -0.0001557097 31
0.0005903305 33 0.0007993976 35 -0.0001560171 36 -0.0000815893 37
0.0000140002 38 0.0000793106 39 -0.5781886874 41 -0.0024517953 42
0.0004960627 43 -0.0001410124 44 0.0000000144 45 -0.0000703152 47
0.0000000565 48 0.0015346481 50 -0.0000001631 51 0.0013051183 53
0.0016011118 55 -0.0003076892 56 -0.0001586915 57 -0.0001240234 58
0.0000001386 59 -0.2888922230 61 -0.0012282282 62 0.0002515995 63
0.0001335274 64 -0.0001581270 65 0.0001867496 67 -0.0001482931 68
0.0008194516 70 0.0001556375 71 0.0005904439 73 0.0007994395 75
-0.0001560266 76 -0.0000816204 77 0.0000141380 78 -0.0000793592 79
0.2888922537 81 0.0012283054 82 -0.0002515181 83 0.0001334812 84
0.0001583237 85 0.0001867191 87 0.0001486497 88 -0.0008194148 90
0.0001546034 91 -0.0005904524 93 -0.0007994211 95 0.0001561754 96
0.0000815940 97 0.0000144233 98 0.0000796423 99 0.5781886588 101
0.0024515577 102 -0.0004959802 103 -0.0001409979 104 -0.0000000307 105
-0.0000705453 107 -0.0000000454 108 -0.0015343653 110 -0.0000001509 111
-0.0013054893 113 -0.0016012734 115 0.0003078240 116 0.0001587913 117
-0.0001239620 118 -0.0000001283 119
# ORBITAL 3 NAO = 90
0.5006101737 1 0.0021131041 2 -0.0004386602 3 -0.0001720820 4
-0.0000537351 5 -0.0001544833 7 0.0000103521 8 -0.0010913048 10
-0.0000446596 11 -0.0013590329 13 -0.0013847882 15 0.0002530053 16
0.0001361579 17 -0.0000788740 18 -0.0000770243 19 0.5006101452 21
0.0021129625 22 -0.0004386520 23 0.0001720253 24 -0.0000536574 25
0.0001543765 27 0.0000103495 28 -0.0010911679 30 0.0000446577 31
-0.0013592283 33 -0.0013848833 35 0.0002530062 36 0.0001362215 37
0.0000786944 38 -0.0000770459 39 -0.0000000492 41 -0.0000000438 42
0.0000000133 43 -0.0000000140 44 0.0002083475 45 0.0000000368 47
0.0002656048 48 0.0000000488 50 0.0002187797 51 -0.0000000628 53
-0.0000000239 55 0.0000000279 56 0.0000000168 57 -0.0000000076 58
0.0000604882 59 -0.5006102068 61 -0.0021129621 62 0.0004386735 63
-0.0001720307 64 -0.0000536122 65 -0.0001543752 67 0.0000104714 68
0.0010911805 70 0.0000450132 71 0.0013592249 73 0.0013848909 75
-0.0002529465 76 -0.0001362288 77 -0.0000787963 78 -0.0000769463 79
-0.5006101688 81 -0.0021131026 82 0.0004386817 83 0.0001720878 84
-0.0000536878 85 0.0001544821 87 0.0000104746 88 0.0010913171 90
-0.0000450214 91 0.0013590299 93 0.0013847960 95 -0.0002529452 96
-0.0001361656 97 0.0000789791 98 -0.0000769196 99 0.0000000225 101
-0.0000000446 102 0.0000000134 103 0.0000000135 104 0.0002082166 105
-0.0000000368 107 0.0002654040 108 0.0000000506 110 -0.0002194550 111
-0.0000000653 113 -0.0000000248 115 0.0000000293 116 0.0000000173 117
0.0000000083 118 0.0000599174 119
# ORBITAL 4 NAO = 90
-0.2893480425 1 -0.0011811095 2 0.0006744406 3 0.0001189419 4
-0.0000446067 5 0.0000569570 7 -0.0002197480 8 0.0005592017 10
-0.0000156074 11 0.0006968256 13 0.0007625480 15 -0.0000777904 16
-0.0000296491 17 0.0000238435 18 0.0000028641 19 -0.2893481096 21
-0.0011811399 22 0.0006744442 23 -0.0001189574 24 -0.0000445949 25
-0.0000569839 27 -0.0002197505 28 0.0005592352 30 0.0000155929 31
0.0006967797 33 0.0007625291 35 -0.0000777899 36 -0.0000296344 37
-0.0000238983 38 0.0000028476 39 0.5779780421 41 0.0024236036 42
-0.0013095349 43 -0.0000033117 44 -0.0000000730 45 -0.0003415559 47
0.0000000126 48 -0.0012987191 50 0.0000000214 51 -0.0012017051 53
-0.0015230608 55 0.0002233907 56 0.0000742468 57 0.0000352458 58
-0.0000000253 59 -0.2893480526 61 -0.0011811337 62 0.0006744475 63
-0.0001189109 64 0.0000445154 65 -0.0000569376 67 0.0002196894 68
0.0005591878 70 -0.0000159673 71 0.0006968259 73 0.0007625328 75
-0.0000778596 76 -0.0000296337 77 -0.0000237314 78 -0.0000029671 79
-0.2893481027 81 -0.0011811672 82 0.0006744484 83 0.0001189251 84
0.0000444960 85 0.0000569605 87 0.0002196888 88 0.0005592200 90
0.0000159731 91 0.0006967804 93 0.0007625097 95 -0.0000778598 96
-0.0000296196 97 0.0000237689 98 -0.0000029652 99 0.5779780591 101
0.0024236073 102 -0.0013095365 103 0.0000033130 104 -0.0000000990 105
0.0003415570 107 -0.0000000336 108 -0.0012987290 110 -0.0000001709 111
-0.0012016972 113 -0.0015230594 115 0.0002233876 116 0.0000742455 117
-0.0000352451 118 -0.0000001515 119
# ORBITAL 5 NAO = 90
-0.5007499006 1 -0.0020932788 2 0.0011339536 3 -0.0000684881 4
0.0000697482 5 -0.0002271535 7 -0.0001934040 8 0.0010981889 10
0.0000685550 11 0.0010726975 13 0.0013215420 15 -0.0001608701 16
-0.0000525753 17 0.0000029695 18 0.0000308210 19 0.5007498476 21
0.0020932696 22 -0.0011339307 23 -0.0000684705 24 -0.0000697471 25
-0.0002271239 27 0.0001933327 28 -0.0010982033 30 0.0000684523 31
-0.0010726842 33 -0.0013215463 35 0.0001608813 36 0.0000525762 37
0.0000029679 38 -0.0000308358 39 0.0000000362 41 -0.0000000393 42
0.0000000128 43 -0.0000000095 44 0.0001873871 45 0.0000000353 47
0.0002028610 48 0.0000000422 50 0.0000930299 51 -0.0000000564 53
-0.0000000238 55 0.0000000220 56 0.0000000158 57 -0.0000000073 58
0.0000255403 59 -0.5007498869 61 -0.0020932596 62 0.0011339537 63
0.0000684717 64 -0.0000696927 65 0.0002271254 67 0.0001934495 68
0.0010982216 70 0.0000687936 71 0.0010726748 73 0.0013215517 75
-0.0001608273 76 -0.0000525822 77 -0.0000030701 78 -0.0000307435 79
0.5007498440 81 0.0020932955 82 -0.0011339306 83 0.0000684810 84
0.0000698075 85 0.0002271480 87 -0.0001932870 88 -0.0010981803 90
0.0000681955 91 -0.0010726973 93 -0.0013215327 95 0.0001609262 96
0.0000525662 97 -0.0000028726 98 0.0000309235 99 0.0000000242 101
-0.0000000429 102 0.0000000121 103 0.0000000074 104 -0.0001872809 105
-0.0000000363 107 -0.0002028699 108 0.0000000512 110 0.0000931069 111
-0.0000000660 113 -0.0000000272 115 0.0000000283 116 0.0000000166 117
0.0000000105 118 -0.0000254667 119
# ORBITAL 6 NAO = 90
0.4091242805 1 0.0018190810 2 -0.0036449243 3 0.0000003109 4
-0.0000029945 5 0.0007740556 7 0.0013380065 8 -0.0007544593 10
0.0000780477 11 -0.0006748974 13 -0.0009960142 15 -0.0000423640 16
-0.0002163202 17 0.0000245090 18 0.0000435846 19 -0.4091242314 21
-0.0018191745 22 0.0036448420 23 0.0000002969 24 0.0000032856 25
0.0007740526 27 -0.0013375548 28 0.0007543969 30 0.0000795334 31
0.0006749172 33 0.0009959764 35 0.0000421336 36 0.0002163607 37
0.0000249463 38 -0.0000431647 39 0.4088374571 41 0.0018140837 42
-0.0036448324 43 0.0000011734 44 0.0000001409 45 -0.0015470931 47
0.0000001187 48 -0.0006363791 50 -0.0000004489 51 -0.0007950336 53
-0.0009967424 55 -0.0000464723 56 -0.0002169062 57 -0.0000506419 58
0.0000003853 59 -0.4091242365 61 -0.0018190027 62 0.0036448289 63
0.0000003326 64 -0.0000031321 65 0.0007741531 67 0.0013375953 68
0.0007542579 70 -0.0000792764 71 0.0006751316 73 0.0009960980 75
0.0000421797 76 0.0002162805 77 0.0000250537 78 0.0000432185 79
0.4091242781 81 0.0018189398 82 -0.0036449221 83 0.0000004009 84
0.0000029779 85 0.0007741877 87 -0.0013379594 88 -0.0007542979 90
-0.0000783208 91 -0.0006751119 93 -0.0009961062 95 -0.0000423138 96
-0.0002162634 97 0.0000247982 98 -0.0000434744 99 -0.4088374402 101
-0.0018138102 102 0.0036447434 103 0.0000011435 104 -0.0000000067 105
-0.0015468397 107 -0.0000001002 108 0.0006360602 110 -0.0000002972 111
0.0007954525 113 0.0009969239 115 0.0000463126 116 0.0002167944 117
-0.0000507097 118 -0.0000002434 119
# ORBITAL 7 NAO = 90
-0.0105310908 1 0.1791319489 2 0.0923971303 3 -0.0318962677 4
-0.0553214746 5 -0.0062990419 7 -0.0109406130 8 0.0108261423 10
-0.0038130194 11 0.0070179874 13 -0.0063573590 15 0.0456220599 16
0.0036425281 17 -0.0036155711 18 -0.0062523687 19 -0.0105314089 21
0.1791319474 22 0.0923971349 23 0.0318962676 24 -0.0553214745 25
0.0062990427 27 -0.0109406141 28 0.0108261425 30 0.0038130195 31
0.0070179875 33 -0.0063573581 35 0.0456220596 36 0.0036425283 37
0.0036155718 38 -0.0062523691 39 -0.0106286110 41 0.1791775670 42
0.0924119143 43 0.0638644527 44 -0.0000000012 45 0.0126250153 47
-0.0000000001 48 0.0051125578 50 0.0000000011 51 0.0127368885 53
-0.0063570874 55 0.0456280497 56 0.0036351310 57 0.0072220519 58
-0.0000000009 59 -0.0105311113 61 0.1791319485 62 0.0923971342 63
0.0318962682 64 0.0553214734 65 0.0062990428 67 0.0109406133 68
0.0108261418 70 -0.0038130232 71 0.0070179867 73 -0.0063573593 75
0.0456220589 76 0.0036425285 77 0.0036155729 78 0.0062523682 79
-0.0105311036 81 0.1791319484 82 0.0923971305 83 -0.0318962682 84
0.0553214734 85 -0.0062990421 87 0.0109406123 88 0.0108261422 90
0.0038130230 91 0.0070179872 93 -0.0063573596 95 0.0456220592 96
0.0036425281 97 -0.0036155721 98 0.0062523679 99 -0.0106297497 101
0.1791775616 102 0.0924119206 103 -0.0638644524 104 -0.0000000012 105
-0.0126250177 107 -0.0000000000 108 0.0051125593 110 -0.0000000010 111
0.0127368898 113 -0.0063570850 115 0.0456280500 116 0.0036351304 117
-0.0072220520 118 -0.0000000009 119
# ORBITAL 8 NAO = 90
0.0076028895 1 -0.1247833094 2 -0.0702498150 3 -0.0785132216 4
0.0639777661 5 -0.0281449519 7 0.0270091285 8 0.0056384214 10
0.0119231520 11 -0.0143970361 13 0.0039295681 15 -0.0517335466 16
-0.0069559347 17 0.0014213923 18 0.0074921988 19 -0.0076028888 21
0.1247833182 22 0.0702498194 23 -0.0785132193 24 -0.0639777657 25
-0.0281449519 27 -0.0270091281 28 -0.0056384209 30 0.0119231587 31
0.0143970362 33 -0.0039295685 35 0.0517335493 36 0.0069559353 37
0.0014213952 38 -0.0074922001 39 -0.0151821569 41 0.2495710190 42
0.1404874823 43 0.0322982227 44 0.0000000019 45 0.0186231256 47
0.0000000007 48 0.0009086803 50 0.0000000010 51 0.0166300085 53
-0.0078591029 55 0.1034526736 56 0.0139125616 57 0.0143887842 58
-0.0000000004 59 -0.0076028851 61 0.1247833096 62 0.0702498147 63
-0.0785132218 64 0.0639777655 65 -0.0281449531 67 0.0270091281 68
-0.0056384214 70 -0.0119231586 71 0.0143970359 73 -0.0039295685 75
0.0517335459 76 0.0069559349 77 0.0014213945 78 0.0074921998 79
0.0076028868 81 -0.1247833174 82 -0.0702498196 83 -0.0785132191 84
-0.0639777655 85 -0.0281449509 87 -0.0270091286 88 0.0056384206 90
-0.0119231525 91 -0.0143970358 93 0.0039295688 95 -0.0517335500 96
-0.0069559352 97 0.0014213925 98 -0.0074921991 99 0.0151821472 101
-0.2495710187 102 -0.1404874829 103 0.0322982228 104 0.0000000027 105
0.0186231264 107 0.0000000008 108 -0.0009086819 110 0.0000000004 111
-0.0166300072 113 0.0078591049 115 -0.1034526738 116 -0.0139125612 117
0.0143887828 118 0.0000000005 119
# ORBITAL 9 NAO = 90
0.0131251465 1 -0.2161385559 2 -0.1216727085 3 0.0639730896 4
-0.0046068035 5 0.0270059763 7 0.0030477106 8 -0.0179156928 10
0.0021926302 11 0.0027320071 13 0.0068069785 15 -0.0895734340 16
-0.0120431889 17 0.0074864530 18 0.0100635578 19 0.0131251217 21
-0.2161385511 22 -0.1216727056 23 -0.0639730923 24 -0.0046068060 25
-0.0270059769 27 0.0030477096 28 -0.0179156936 30 -0.0021926297 31
0.0027320083 33 0.0068069785 35 -0.0895734318 36 -0.0120431888 37
-0.0074864525 38 0.0100635578 39 -0.0000000465 41 0.0000000049 42
0.0000000028 43 0.0000000007 44 -0.1154806636 45 0.0000000001 47
-0.0437490908 48 -0.0000000002 50 -0.0184557093 51 0.0000000009 53
0.0000000000 55 0.0000000019 56 0.0000000002 57 0.0000000004 58
-0.0029085310 59 -0.0131252134 61 0.2161385558 62 0.1216727087 63
0.0639730895 64 -0.0046068039 65 0.0270059757 67 0.0030477102 68
0.0179156937 70 -0.0021926324 71 -0.0027320077 73 -0.0068069787 75
0.0895734335 76 0.0120431889 77 0.0074864531 78 0.0100635579 79
-0.0131251919 81 0.2161385514 82 0.1216727057 83 -0.0639730926 84
-0.0046068062 85 -0.0270059772 87 0.0030477091 88 0.0179156935 90
0.0021926320 91 -0.0027320077 93 -0.0068069785 95 0.0895734316 96
0.0120431885 97 -0.0074864534 98 0.0100635574 99 -0.0000000629 101
-0.0000000047 102 -0.0000000024 103 0.0000000005 104 -0.1154806635 105
0.0000000006 107 -0.0437490900 108 -0.0000000003 110 0.0184557112 111
0.0000000003 113 0.0000000003 115 -0.0000000021 116 -0.0000000004 117
0.0000000002 118 -0.0029085291 119
# ORBITAL 10 NAO = 90
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0.0164355039 17 -0.0072749056 18 -0.0060278708 19 -0.0049056971 21
0.1006640036 22 0.0846904176 23 0.1397564569 24 0.1141784844 25
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0.0072749056 38 -0.0060278707 39 0.0099053219 41 -0.2012723368 42
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0.0038346686 55 -0.1542323428 56 -0.0329233571 57 -0.0177384123 58
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0.1397564543 64 -0.1141784844 65 0.0456691920 67 -0.0234357583 68
0.0117723757 70 0.0056723403 71 -0.0100538948 73 -0.0019191218 75
0.0770189499 76 0.0164355037 77 0.0072749057 78 0.0060278712 79
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-0.0056723404 91 -0.0100538949 93 -0.0019191216 95 0.0770189470 96
0.0164355031 97 -0.0072749055 98 0.0060278709 99 0.0099053293 101
-0.2012723391 102 -0.1693914579 103 -0.0583006644 104 0.0000000023 105
0.0049813014 107 0.0000000005 108 0.0007093780 110 0.0000000002 111
-0.0041287656 113 0.0038346685 115 -0.1542323426 116 -0.0329233566 117
0.0177384131 118 0.0000000002 119
# ORBITAL 11 NAO = 90
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0.0284803972 17 -0.0060295874 18 -0.0142387079 19 0.0085817066 21
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0.0000000015 43 -0.0000000006 44 -0.2057189432 45 -0.0000000001 47
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0.1334722315 76 0.0284803970 77 0.0060295877 78 0.0142387083 79
0.0085817260 81 -0.1743307096 82 -0.1466700567 83 -0.1142616213 84
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0.0000000018 102 0.0000000020 103 0.0000000006 104 0.2057189443 105
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# ORBITAL 12 NAO = 90
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0.0353806840 17 -0.0067287801 18 -0.0116586245 19 -0.0036801487 21
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0.0067287796 38 -0.0116586240 39 -0.0037706044 41 0.0115958520 42
0.0326192354 43 -0.1891354471 44 -0.0000000001 45 -0.0646757241 47
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0.0005071362 70 -0.0050238629 71 -0.0045215347 73 0.0010077684 75
0.1492702215 76 0.0353806829 77 0.0067287799 78 0.0116586241 79
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0.0050238628 91 -0.0045215349 93 0.0010077686 95 0.1492702219 96
0.0353806835 97 -0.0067287807 98 0.0116586245 99 -0.0037694668 101
0.0115958596 102 0.0326192295 103 0.1891354472 104 -0.0000000001 105
0.0646757261 107 0.0000000000 108 -0.0070415657 110 -0.0000000006 111
0.0030215803 113 0.0010143087 115 0.1491037928 116 0.0353238322 117
-0.0134440812 118 -0.0000000004 119
# ORBITAL 13 NAO = 90
-0.0075512224 1 0.1114726348 2 0.1678599129 3 0.0636737890 4
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0.0206625187 11 0.0059162564 13 0.0000670171 15 0.1838227411 16
0.0692803796 17 -0.0071326782 18 -0.0123576817 19 0.0075512222 21
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0.0071157446 27 -0.0123065681 28 0.0147668120 30 0.0206625205 31
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0.1678699600 43 -0.1273340648 44 0.0000000002 45 -0.0142192259 47
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0.0000000003 59 0.0075512263 61 -0.1114726350 62 -0.1678599130 63
0.0636737898 64 0.1102660184 65 0.0071157445 67 0.0123065680 68
0.0147668119 70 -0.0206625199 71 -0.0059162563 73 -0.0000670168 75
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0.0692803794 97 -0.0071326781 98 0.0123576822 99 0.0075377838 101
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0.0250878041 113 -0.0000679680 115 -0.1838193399 116 -0.0692809135 117
0.0142604366 118 -0.0000000000 119
# ORBITAL 14 NAO = 90
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0.0832832749 27 0.0480626416 28 0.0082077197 30 -0.0054692758 31
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0.0000306102 76 0.0000082652 77 -0.0045627709 78 0.0026348913 79
0.0000243167 81 -0.0000211335 82 -0.0000197398 83 0.2396956060 84
0.1383354953 85 0.0832832746 87 0.0480626416 88 -0.0082077199 90
0.0054692764 91 0.0082072205 93 0.0000008337 95 0.0000306105 96
0.0000082651 97 0.0045627706 98 0.0026348910 99 0.0000000566 101
0.0000000007 102 -0.0000000000 103 -0.0000000000 104 -0.2767109937 105
0.0000000000 107 -0.0961484638 108 -0.0000000005 110 0.0109288338 111
0.0000000001 113 -0.0000000005 115 0.0000000001 116 -0.0000000001 117
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# ORBITAL 15 NAO = 90
-0.0009983767 1 -0.0386214684 2 -0.0485455904 3 0.1633421841 4
0.1962473237 5 0.0509807373 7 0.0877733678 8 -0.0121832761 10
0.0001162009 11 0.0084147730 13 0.0010223542 15 0.1927411229 16
0.0682210653 17 -0.0045132574 18 -0.0126863282 19 -0.0009983769 21
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0.0084147732 33 0.0010223542 35 0.1927411233 36 0.0682210653 37
0.0045132578 38 -0.0126863281 39 0.0000000963 41 0.0000000005 42
0.0000000001 43 -0.0000000002 44 -0.0868168628 45 -0.0000000004 47
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-0.0048842722 59 0.0009985499 61 0.0386214692 62 0.0485455904 63
0.1633421850 64 0.1962473253 65 0.0509807366 67 0.0877733671 68
0.0121832762 70 -0.0001162013 71 -0.0084147740 73 -0.0010223547 75
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0.0009985050 81 0.0386214693 82 0.0485455908 83 -0.1633421847 84
0.1962473254 85 -0.0509807370 87 0.0877733675 88 0.0121832760 90
0.0001162015 91 -0.0084147736 93 -0.0010223547 95 -0.1927411232 96
-0.0682210651 97 0.0045132576 98 -0.0126863286 99 0.0000001212 101
0.0000000009 102 -0.0000000000 103 -0.0000000009 104 -0.0868168632 105
0.0000000001 107 -0.0005743183 108 -0.0000000006 110 0.0204836287 111
0.0000000000 113 -0.0000000004 115 -0.0000000005 116 -0.0000000001 117
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# ORBITAL 16 NAO = 90
-0.0005894251 1 -0.0223088039 2 -0.0280654665 3 0.0075643177 4
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0.0118868073 11 -0.0128757602 13 0.0005926770 15 0.1112764638 16
0.0393823208 17 -0.0074782289 18 -0.0045126110 19 0.0005894222 21
0.0223088033 22 0.0280654662 23 0.0075643166 24 -0.1633898807 25
0.0288954662 27 -0.0510111513 28 -0.0106960596 30 0.0118868066 31
0.0128757604 33 -0.0005926768 35 -0.1112764634 36 -0.0393823205 37
-0.0074782291 38 0.0045126111 39 0.0011830149 41 0.0446313651 42
0.0560606696 43 0.2905583224 44 0.0000000000 45 0.1172071367 47
0.0000000000 48 -0.0038785631 50 -0.0000000003 51 0.0082267364 53
-0.0011834653 55 -0.2225345572 56 -0.0787777804 57 -0.0152898732 58
0.0000000001 59 0.0005894244 61 0.0223088033 62 0.0280654664 63
0.0075643175 64 0.1633898819 65 0.0288954663 67 0.0510111514 68
-0.0106960595 70 -0.0118868065 71 0.0128757604 73 -0.0005926768 75
-0.1112764638 76 -0.0393823205 77 -0.0074782294 78 -0.0045126114 79
-0.0005894255 81 -0.0223088036 82 -0.0280654663 83 0.0075643174 84
-0.1633898808 85 0.0288954658 87 -0.0510111516 88 0.0106960598 90
-0.0118868073 91 -0.0128757604 93 0.0005926770 95 0.1112764630 96
0.0393823204 97 -0.0074782290 98 0.0045126113 99 -0.0011830119 101
-0.0446313639 102 -0.0560606692 103 0.2905583232 104 -0.0000000002 105
0.1172071362 107 -0.0000000001 108 0.0038785629 110 -0.0000000005 111
-0.0082267365 113 0.0011834651 115 0.2225345571 116 0.0787777798 117
-0.0152898742 118 -0.0000000002 119
# ORBITAL 17 NAO = 90
-0.0014020326 1 -0.0068956525 2 0.0009658087 3 0.2467463560 4
-0.0150840636 5 0.1010428983 7 -0.0041186505 8 -0.0213912436 10
0.0047152733 11 0.0207049577 13 0.0003249521 15 0.1090368977 16
0.0565120453 17 0.0032595528 18 -0.0081550919 19 -0.0014020678 21
-0.0068956523 22 0.0009658091 23 -0.2467463563 24 -0.0150840638 25
-0.1010428983 27 -0.0041186508 28 -0.0213912436 30 -0.0047152734 31
0.0207049580 33 0.0003249521 35 0.1090368981 36 0.0565120453 37
-0.0032595527 38 -0.0081550918 39 0.0028093586 41 0.0137482733 42
-0.0019741520 43 0.2207188322 44 -0.0000000000 45 0.0939446698 47
0.0000000001 48 -0.0274316281 50 -0.0000000006 51 0.0288061575 53
-0.0006463540 55 -0.2181730829 56 -0.1130340303 57 -0.0108702108 58
0.0000000003 59 -0.0014020302 61 -0.0068956520 62 0.0009658091 63
-0.2467463568 64 0.0150840636 65 -0.1010428979 67 0.0041186509 68
-0.0213912440 70 0.0047152734 71 0.0207049583 73 0.0003249522 75
0.1090368979 76 0.0565120450 77 -0.0032595523 78 0.0081550920 79
-0.0014020296 81 -0.0068956524 82 0.0009658087 83 0.2467463565 84
0.0150840633 85 0.1010428980 87 0.0041186504 88 -0.0213912437 90
-0.0047152733 91 0.0207049580 93 0.0003249522 95 0.1090368978 96
0.0565120452 97 0.0032595526 98 0.0081550920 99 0.0028092657 101
0.0137482731 102 -0.0019741520 103 -0.2207188329 104 0.0000000001 105
-0.0939446697 107 0.0000000002 108 -0.0274316280 110 0.0000000006 111
0.0288061582 113 -0.0006463534 115 -0.2181730832 116 -0.1130340301 117
0.0108702120 118 0.0000000003 119
# ORBITAL 18 NAO = 90
-0.0023749933 1 -0.0118884368 2 0.0017334005 3 -0.0150505701 4
0.2293750064 5 -0.0041065876 7 0.0962994757 8 -0.0046652132 10
0.0297409795 11 0.0034826782 13 0.0005612091 15 0.1889435721 16
0.0978899218 17 -0.0081612949 18 -0.0061659303 19 0.0023750060 21
0.0118884365 22 -0.0017334006 23 -0.0150505706 24 -0.2293750071 25
-0.0041065875 27 -0.0962994755 28 0.0046652135 30 0.0297409784 31
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-0.0081612954 38 0.0061659300 39 0.0000000032 41 0.0000000001 42
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0.1034266384 48 0.0000000003 50 0.0215760829 51 -0.0000000002 53
0.0000000002 55 -0.0000000000 56 -0.0000000001 57 -0.0000000001 58
0.0079574230 59 -0.0023750295 61 -0.0118884363 62 0.0017334008 63
0.0150505703 64 -0.2293750078 65 0.0041065877 67 -0.0962994753 68
-0.0046652137 70 0.0297409788 71 0.0034826785 73 0.0005612087 75
0.1889435718 76 0.0978899212 77 0.0081612957 78 0.0061659304 79
0.0023750118 81 0.0118884367 82 -0.0017334007 83 0.0150505701 84
0.2293750071 85 0.0041065877 87 0.0962994753 88 0.0046652134 90
0.0297409792 91 -0.0034826785 93 -0.0005612092 95 -0.1889435718 96
-0.0978899216 97 0.0081612954 98 -0.0061659305 99 0.0000000018 101
0.0000000003 102 0.0000000001 103 0.0000000001 104 -0.2554222907 105
0.0000000000 107 -0.1034266382 108 -0.0000000003 110 0.0215760822 111
0.0000000001 113 -0.0000000004 115 0.0000000000 116 -0.0000000001 117
0.0000000000 118 -0.0079574229 119
# ORBITAL 19 NAO = 5
-0.6051361517 6 -0.5306934722 9 0.0161429500 12 0.0279606935 14
-0.0181292011 20
# ORBITAL 20 NAO = 5
-0.6051361519 26 -0.5306934721 29 -0.0161429499 32 0.0279606936 34
-0.0181292011 40
# ORBITAL 21 NAO = 5
-0.6051369321 46 -0.5306928695 49 -0.0322859902 52 0.0000000004 54
-0.0181286009 60
# ORBITAL 22 NAO = 5
-0.6051361524 66 -0.5306934715 69 -0.0161429500 72 -0.0279606933 74
-0.0181292011 80
# ORBITAL 23 NAO = 5
-0.6051361522 86 -0.5306934717 89 0.0161429499 92 -0.0279606934 94
-0.0181292011 100
# ORBITAL 24 NAO = 5
-0.6051369320 106 -0.5306928697 109 0.0322859897 112 0.0000000007 114
-0.0181286008 120
$end
3.2.4.2. Computational Results
The final energy can be found as -230.59097 hartree, and the resonance Kekulé structures is 24.5 kcal/mol, which is the stablization energy to delocalize the \(\pi\) orbitals in a cycloalkene.
****** BOND ORDER ****** ATOM 1 ATOM 2 DIST BOND ORDER 1 C 2 H 1.093 0.980 1 C 3 C 1.399 1.425 3 C 4 H 1.093 0.980 3 C 5 C 1.399 1.011 5 C 6 H 1.093 0.980 5 C 7 C 1.399 1.425 7 C 8 H 1.093 0.980 7 C 9 C 1.399 1.012 9 C 10 H 1.093 0.980 1 C 11 C 1.399 1.011 9 C 11 C 1.399 1.425 11 C 12 H 1.093 0.980
The bond orders show that the CC bondings are not equivalent now, there are 3 CC bondings with bond order 1.425, close to double bonding, and 3 bondings with 1.011, close to single bonding. The computational results suggest that the resonance from Kekulé structrues mainly stabilizes the molecule and makes all CC bondings equivalent. Both resonance from Kekulé structures and equalization of CC bonds thus present the aromaticity in C6H6.
3.3. Menshutkin Reaction NH3 + CH3Cl \(\rightarrow\) [NH3CH3]+ + Cl-
3.3.1. Chemical question to be addressed
The last exercise is the Menshutkin reaction NH3 + CH3Cl \(\rightarrow\) [NH3CH3]+ + Cl-. The reaction is exothermic in solution. In this example, the reaction barrier in gas phase will be calculated with L-VBSCF and L-BOVB. For more information of the reaction and the computations in solution, please refer to:
3.3.2. Active/inactive electrons and orbitals
The reaction involves the breaking of the CH3-Cl bond and building of an NH3-CH3 bond. As such, the lone pair on NH3 and the CH3-Cl bond in the reactants constitute the active space, which involves 4 electrons on 3 orbitals. The remaining 32 electrons and 16 orbitals constitute the inactive space, including the core orbitals of N, C and Cl, 3 N-H bonds, 3 C-H bonds, and 3 s, 3 px and 3 py orbitals on Cl.
3.3.3. Fragmentation and important VB structures
The reaction involves 3 fragments: NH3, CH3 and Cl. The reactants include non-interacting NH3 and CH3Cl moieties while the product includes non-interacting [NH3CH3]+ and Cl- moieties. Following figure shows the important VB structures in reactant (a) and product (b).
Lewis structure for the reactant (a) and product (b).
3.3.4. Basis set and its subsets based on orbital symmetry
6–31G* is the basis set used in this example. The basis functions are simply separated into subsets according to the atoms. The basis functions on each atom will be treated as a subset and the VB orbitals will be built with these subsets.
3.3.5. Structures
There are 6 VB structures involved in the active space as shown in the figure. Structures S1-S3 describe the reactant, and S3-S5 describe the product. S6 describes the electron transfer between NH3 and Cl, and will appear in the TS region.
6 VB structures for Menshutkin Reaction.
3.3.6. Input File
The input files of L-VBSCF for reactant and TS are given below:
Reactant:
NH3CH3cl reactant
$ctrl
nmul=1 nstr=6 iprint=3 iscf=5 nao=3 nae=4
orbtyp=hao frgtyp=atom
int=libcint basis=6-31G*
guess=read
$end
$stru
1:16 17 17 18 19
1:16 17 17 18 18
1:16 17 17 19 19
1:16 18 18 17 19
1:16 19 19 17 18
1:16 18 18 19 19
$end
$orb
1*5 4 4 1*3 4*3 4*3 4 4 1
6
6
6
6
6
1 7 8 9
2 3 4 5
6
6
6
1 7 8 9
1 7 8 9
1 7 8 9
2 3 4 5
2 3 4 5
2 3 4 5
1 7 8 9
2 3 4 5
6
$end
$geo
N 0.000000 0.000000 0.000000
C 0.000000 0.000000 10.000000
H -1.029985 0.000000 9.647297
H 0.514992 0.891993 9.647297
H 0.514992 -0.891993 9.647297
Cl 0.000000 0.000000 11.778400
H 0.939678 0.000000 -0.389227
H -0.469839 0.813785 -0.389227
H -0.469839 -0.813785 -0.389227
$end
TS:
NH3CH3cl
$ctrl
nmul=1 nstr=6 iprint=3 nao=3 nae=4 iscf=5 itmax=300
guess=read orbtyp=hao frgtyp=atom
int=libcint basis=6-31G*
$end
$stru
1:16 17 17 18 19
1:16 17 17 18 18
1:16 17 17 19 19
1:16 18 18 17 19
1:16 19 19 17 18
1:16 18 18 19 19
$end
$orb
1*5 4 4 1*3 4*3 4*3 4 4 1
6
6
6
6
6
1 7 8 9
2 3 4 5
6
6
6
1 7 8 9
1 7 8 9
1 7 8 9
2 3 4 5
2 3 4 5
2 3 4 5
1 7 8 9
2 3 4 5
6
$end
$geo
N 0.0000000000 0.0000000000 -2.4403680000
C 0.0000000000 0.0000000000 -0.6327610000
H 1.0651490000 0.0000000000 -0.4753840000
H -0.5325745000 -0.9224460928 -0.4753840000
H -0.5325745000 0.9224460928 -0.4753840000
CL 0.0000000000 0.0000000000 1.8067450000
H -0.9550790000 0.0000000000 -2.8031240000
H 0.4775395000 0.8271226766 -2.8031240000
H 0.4775395000 -0.8271226766 -2.8031240000
$end
The input files are almost the same except the initial guess and geometry. The initial guess of reactant is given here. The initial guess of TS can be obtained from the computational results of reactant. For L-BOVB computations, the user may simply change ISCF=5 to ISCF=2 and append BOVB in $CTRL section. The initial guess of L-BOVB computations are from the computational results of correpsonding L-VBSCF computation.
3.3.7. Computational Results
3.3.7.1. The VB structures
Following table shows the VB structures involved in the calculation. The first 16 doubly occupied orbitals are inactive ones, orbital 17 corresponds to the lone pair on NH3, and orbitals 18 and 19 are singly occupied orbitals on CH3 and Cl respectively. The correspondence to the structures is also listed.
VB structure |
Structure |
|---|---|
1 ***** 1:16 17 17 18 19 |
S1 |
2 ***** 1:16 17 17 18 18 |
S2 |
3 ***** 1:16 17 17 19 19 |
S3 |
4 ***** 1:16 18 18 17 19 |
S6 |
5 ***** 1:16 19 19 17 18 |
S4 |
6 ***** 1:16 18 18 19 19 |
S5 |
3.3.7.2. Energies
Following table shows the total energies (in a.u.) and reaction barrier at the L-VBSCF and L-BOVB levels. Compared with the reference value 33.0 kcal mol -1 (138.1 kJ mol -1) by Webb and Gordon, L-VBSCF overestimates the reaction barrier due to the lack of dynamic correlation, and L-BOVB significantly improves the result. Compared with the energies obtained by L-VBSCF and L-BOVB, L-BOVB decreases the energy at the TS geometry much more than in the reactants. The results show that dynamic correlation plays an important role in reaction barrier calculations.
L-VBSCF |
L-BOVB |
|
|---|---|---|
\(E^{react}_{tot}\) |
-555.27775 |
-555.29156 |
\(E^{TS}_{tot}\) |
-555.21152 |
-555.24558 |
\(\Delta E^\neq\) |
41.6 |
28.8 |
3.3.7.3. VB wavefunction and weights
Table shows the weights of VB structures in the reactant and TS geometries. It is clear that the most important contribution comes from S1 in the reactant geometry and S3 in the TS geometry. In the TS, S4 represents the “covalent” structure of product and S3 represents the major “ionic” structure in both reactant and product. Thus, S3 represents the “bond breaking” of C-Cl and S4 shows the “bond forming” of N-C. Similar to the previous examples, L-BOVB provides larger weights for the secondary ionic structures as compared with L-VBSCF weights, which indicates that dynamic correlation plays a more important role for ionic structures than covalent ones, as already explained.
Reactant |
TS |
|||
|---|---|---|---|---|
L-VBSCF |
L-BOVB |
L-VBSCF |
L-BOVB |
|
S1 |
0.663 |
0.621 |
0.091 |
0.178 |
S2 |
0.105 |
0.120 |
-0.001 |
0.002 |
S3 |
0.232 |
0.259 |
0.532 |
0.487 |
S4 |
0.000 |
0.000 |
0.364 |
0.286 |
S5 |
0.000 |
0.000 |
-0.004 |
0.010 |
S6 |
0.000 |
0.000 |
0.017 |
0.037 |
3.4. Potential Energy Surface of LiF (Optional)
3.4.1. Introduction
LiF is a simple hetero diatomic molecule with a single bond between atoms Li and F. The dissociation of LiF is always in the interest of chemists. The so-called “Harpoon effect” makes electron transfer when the distance between Li and F even larger than the sum of their van der Waals radius, indicating an electron transfer due to the crossing of diabatic states. For details, please refer to the reference.
In this optional exercise, the user should compute a series of points along the dissociation of LiF, get the energies of total wave function and each VB structure, and plot the potential energy surface. This exercise should be done by the users themselves. Only essential clues will be given. The basis set in this exercise is cc-pVDZ, and the active space is the minimal space.
3.4.2. Computations near equilibrium
The distance RLi-F is set to 1.5 Angstrom.
3.4.2.1. Computation with all VB structures
Note
There is only a single bond in the molecule, so the minimal active space should be (2,2).
VB structures can be automatically generated as we have seen in the example of F2.
Use keywords
ORBTYP=HAOandFRGTYP=SAOwith proper definition of fragmenets in$FRAGto build the orbitals.The active orbitals should always be placed at the last in
$ORBsection.
3.4.2.2. Computation with all possible covalent structures
Note
The covalent VB structures can be either picked from all VB structure computation, or generated automatically.
Orbitals obtained in previous computation can be used as initial guess.
3.4.2.3. Computation for all possible Li+F- ionic structures
Note
VB structures can be picked from all VB structure computation.
Initial guess can be obtained from the orbitals of previous computation.
3.4.2.4. Computation for all possible Li-F+ ionic structures
Note
VB structures can be picked from all VB structure computation.
Initial guess can be obtained from the orbitals of previous computation.
3.4.3. Computations for Other distances
Repeat the above computations at RLi-F= 1.1, 1.3, 1.7, 2.0, 2.6, 2.8, 3.0, 4.0, 7.0 Angstrom, get the energies and plot the potential energy surface. See at which distance the diabatic states cross. Following is the example of the potential energy surface.
Potential Energy Surface of LiF with cc-pVDZ