10. Charge-shift bonding in propellane
10.1. Introduction
In this section, the charge-shift bonding nature of the C-C bridge bond (shown in the following figue) in the [1.1.1]propellane compound (propellane for short in this section) is investigated. As mentioned in Section 3.2.1, the charge-shift bond is identified if the resonance energy of the bond exceeds 50% of the bonding energy.
The structure of the propellane compound.
The computations are proceeded with the given geometry in the following input files, and the basis set is cc-pVDZ. The calulation is at BOVB level.
10.2. Computations of the resonance energy
propellane BOVB calculation with 3 structures
$CTRL
STR=FULL NAO=2 NAE=2 IPRINT=3 BOVB
ORBTYP=HAO GUESS=READ
BASIS=CC-PVDZ
$END
$ORB
1*5 2*12 1*2
1 # 1 C1 1s
2 # 2 C2 1s
3 # 3 C3 1s
4 # 4 C4 1s
5 # 5 C5 1s
1 3 # 6 C1-C3 sigma
2 3 # 7 C2-C3 sigma
1 4 # 8 C1-C4 sigma
2 4 # 9 C2-C4 sigma
1 5 # 10 C1-C5 sigma
2 5 # 11 C2-C5 sigma
3 6 # 12 C3-H6 sigma
3 7 # 13 C3-H7 sigma
4 8 # 14 C4-H8 sigma
4 9 # 15 C4-H9 sigma
5 10 # 16 C5-H10 sigma
5 11 # 17 C5-H11 sigma
1 # 18 C1-C2 sigma C1
2 # 19 C1-C2 sigma C2
$END
$GEO
C -0.80339320 -0.00000002 -0.00026581
C 0.80339315 0.00000002 -0.00026580
C -0.00000000 0.00000000 1.30328491
C 0.00000001 1.12889613 -0.65192077
C -0.00000002 -1.12889613 -0.65192076
H 0.00000002 0.90072681 1.88197724
H 0.00000001 -0.90072681 1.88197723
H -0.00000001 2.07996500 -0.16030252
H 0.00000003 1.18070087 -1.72126710
H 0.00000001 -1.18070087 -1.72126709
H 0.00000000 -2.07996501 -0.16030253
$END
$VEC
15 15 15 15 15 30 30 30 30 30 30 20 20 20 20 20 20 15 15
# ORBITAL 1 NAO = 15
1.0013044300 1 -0.0148185006 2 -0.0270614351 3 0.0014157398 4
-0.0000001541 5 0.0000015008 6 -0.0017992610 7 -0.0000067568 8
-0.0000032993 9 -0.0008838473 10 -0.0000009796 11 0.0000002515 12
-0.0015986173 13 0.0000013752 14 -0.0016010424 15
# ORBITAL 2 NAO = 15
1.0013053868 16 -0.0148178712 17 -0.0270673561 18 -0.0014157125 19
-0.0000002118 20 0.0000016740 21 0.0018009244 22 -0.0000010308 23
0.0000054004 24 -0.0008824051 25 -0.0000002306 26 -0.0000009051 27
-0.0015985372 28 0.0000006106 29 -0.0015993992 30
# ORBITAL 3 NAO = 15
0.9991206001 31 -0.0171860691 32 -0.0162161271 33 0.0000007618 34
0.0000013055 35 -0.0006957167 36 -0.0000014569 37 0.0000001571 38
0.0000790563 39 -0.0020670891 40 -0.0000011719 41 0.0000010731 42
-0.0021065954 43 -0.0000022108 44 -0.0023469285 45
# ORBITAL 4 NAO = 15
0.9991202122 46 -0.0171853822 47 -0.0162125157 48 0.0000006933 49
-0.0005994343 50 0.0003494060 51 -0.0000008239 52 0.0000652009 53
-0.0000372870 54 -0.0020683845 55 -0.0000009837 56 -0.0000004101 57
-0.0022864381 58 0.0001199393 59 -0.0021660489 60
# ORBITAL 5 NAO = 15
0.9991212097 61 -0.0171850657 62 -0.0162182626 63 0.0000004025 64
0.0006008934 65 0.0003484130 66 0.0000035522 67 -0.0000702075 68
-0.0000394260 69 -0.0020683512 70 0.0000006972 71 0.0000002999 72
-0.0022870879 73 -0.0001190917 74 -0.0021658981 75
# ORBITAL 6 NAO = 30
-0.0177774926 1 -0.2162705930 2 -0.2298798504 3 0.0706361562 4
0.0000024378 5 -0.3238519858 6 0.0667063348 7 -0.0000256996 8
-0.1556546218 9 0.0097518542 10 -0.0000027624 11 -0.0301554752 12
0.0092026397 13 -0.0000002305 14 -0.0263744821 15 -0.0147709460 31
-0.1460413984 32 -0.1155006162 33 0.2650092251 34 0.0000006955 35
0.1839524192 36 0.1404511764 37 0.0000407801 38 0.0925295733 39
-0.0107900693 40 0.0000018292 41 -0.0282003496 42 0.0136549918 43
0.0000054096 44 -0.0097832753 45
# ORBITAL 7 NAO = 30
-0.0177658023 16 -0.2162486406 17 -0.2299525549 18 -0.0706350937 19
-0.0000014106 20 -0.3238462405 21 -0.0666827544 22 -0.0000053780 23
-0.1555802125 24 0.0097646308 25 -0.0000018502 26 0.0301631205 27
0.0092087511 28 0.0000029753 29 -0.0263731317 30 -0.0147687986 31
-0.1460413510 32 -0.1155156453 33 -0.2649967418 34 -0.0000072210 35
0.1839401239 36 -0.1405170026 37 -0.0000348214 38 0.0924884616 39
-0.0107989165 40 -0.0000016736 41 0.0282085984 42 0.0136617248 43
-0.0000053124 44 -0.0097795494 45
# ORBITAL 8 NAO = 30
-0.0177577308 1 -0.2162013994 2 -0.2299673947 3 0.0706110630 4
-0.2804620260 5 0.1619371044 6 0.0666333857 7 -0.1348756187 8
0.0778258361 9 0.0097734916 10 -0.0261267575 11 0.0150869471 12
-0.0174618406 13 0.0178097102 14 0.0003162100 15 -0.0147732236 46
-0.1460578616 47 -0.1155220923 48 0.2650144529 49 0.1592704233 50
-0.0920250702 51 0.1404068731 52 0.0800667609 53 -0.0462473103 54
-0.0107879126 55 -0.0244083850 56 0.0141015632 57 -0.0039034180 58
0.0117339554 59 0.0077884189 60
# ORBITAL 9 NAO = 30
0.0177761911 16 0.2162548982 17 0.2298552881 18 0.0706285957 19
0.2805096055 20 -0.1619483728 21 0.0667282475 22 0.1348077090 23
-0.0778328435 24 -0.0097796081 25 -0.0261254688 26 0.0150935495 27
0.0174656722 28 -0.0178011546 29 -0.0003043329 30 0.0147931236 46
0.1461082080 47 0.1153584115 48 0.2650336900 49 -0.1592773444 50
0.0920130590 51 0.1405345297 52 -0.0800770669 53 0.0462541047 54
0.0108069299 55 -0.0244257552 56 0.0141067392 57 0.0039234196 58
-0.0117232129 59 -0.0077872362 60
# ORBITAL 10 NAO = 30
0.0177805057 1 0.2162405637 2 0.2298076785 3 -0.0706044220 4
-0.2804965339 5 -0.1619531390 6 -0.0666833559 7 -0.1347393815 8
-0.0777019246 9 -0.0097445984 10 -0.0261176194 11 -0.0150718170 12
0.0174729106 13 0.0177945974 14 -0.0002864287 15 0.0147874057 61
0.1460888402 62 0.1154517089 63 -0.2650232945 64 0.1592757818 65
0.0920142609 66 -0.1405860261 67 0.0801337784 68 0.0462885854 69
0.0108070870 70 -0.0244331942 71 -0.0141107441 72 0.0039410936 73
0.0117131673 74 -0.0078047684 75
# ORBITAL 11 NAO = 30
0.0177799561 16 0.2162227894 17 0.2298148247 18 0.0705868963 19
-0.2804588970 20 -0.1619115261 21 0.0666441698 22 -0.1348267513 23
-0.0778975430 24 -0.0097385288 25 0.0261260325 26 0.0150938317 27
0.0174863028 28 0.0178098786 29 -0.0003106634 30 0.0147619518 61
0.1460362911 62 0.1156613683 63 0.2650100271 64 0.1592697337 65
0.0920215396 66 0.1403723237 67 0.0801289455 68 0.0462892649 69
0.0107835415 70 0.0244067802 71 0.0140992591 72 0.0039118995 73
0.0117295466 74 -0.0077996863 75
# ORBITAL 12 NAO = 20
0.0172973458 31 0.2021529787 32 0.1246606235 33 -0.0000031809 34
0.3042972540 35 0.1970108564 36 0.0000068028 37 0.1300804271 38
0.0908986389 39 -0.0079455903 40 0.0000048018 41 -0.0000039238 42
0.0117793218 43 0.0139996205 44 -0.0073463152 45 0.4270402124 76
0.1295468232 77 -0.0000053093 78 -0.0294631198 79 -0.0195166579 80
# ORBITAL 13 NAO = 20
-0.0173282009 31 -0.2022108198 32 -0.1243909531 33 -0.0000096109 34
0.3043243458 35 -0.1970216211 36 -0.0000042424 37 0.1300749867 38
-0.0909331248 39 0.0079484887 40 -0.0000056809 41 0.0000028882 42
-0.0117996319 43 0.0139959547 44 0.0073369181 45 -0.4270900640 81
-0.1296000887 82 0.0000006580 83 -0.0294618950 84 0.0195172636 85
# ORBITAL 14 NAO = 20
0.0173002408 46 0.2021118790 47 0.1246240723 48 0.0000022713 49
0.3227889720 50 0.1649529052 51 -0.0000148620 52 0.1438492365 53
0.0672219489 54 -0.0079367406 55 0.0000175697 56 -0.0000089690 57
0.0079591066 58 0.0165643938 59 -0.0034869406 60 0.4270093758 86
0.1295884488 87 0.0000016180 88 -0.0316194875 89 -0.0157531870 90
# ORBITAL 15 NAO = 20
-0.0173086687 46 -0.2021939367 47 -0.1245611168 48 0.0000003610 49
-0.0183875471 50 0.3620460821 51 0.0000673331 52 -0.0136415635 53
0.1580963305 54 0.0079527536 55 -0.0000113874 56 0.0000032002 57
0.0130569871 58 -0.0025806853 59 -0.0175049037 60 -0.4270744827 91
-0.1295400125 92 0.0000001650 93 0.0021637053 94 -0.0352738044 95
# ORBITAL 16 NAO = 20
-0.0173183346 61 -0.2022026360 62 -0.1245109940 63 0.0000075545 64
0.0183988865 65 0.3620424314 66 -0.0000395096 67 0.0136658395 68
0.1581128420 69 0.0079480868 70 -0.0000049906 71 -0.0000080201 72
0.0130454991 73 0.0025855278 74 -0.0175242163 75 -0.4270686231 96
-0.1295457954 97 -0.0000005864 98 -0.0021655869 99 -0.0352696895 100
# ORBITAL 17 NAO = 20
0.0173197873 61 0.2021511454 62 0.1244587778 63 -0.0000011094 64
-0.3228115619 65 0.1649560698 66 0.0000052783 67 -0.1438497907 68
0.0671949240 69 -0.0079405965 70 0.0000104455 71 -0.0000034930 72
0.0079482684 73 -0.0165642389 74 -0.0034671716 75 0.4270459111 101
0.1296314976 102 -0.0000009897 103 0.0316266447 104 -0.0157561697 105
# ORBITAL 18 NAO = 15
-0.0163776922 1 -0.0583204663 2 0.1324850019 3 -0.6739726665 4
-0.0000444708 5 -0.0000310706 6 -0.4551573242 7 -0.0000875557 8
-0.0000314392 9 -0.0756705415 10 -0.0000033820 11 -0.0000057832 12
0.0323892303 13 0.0000190463 14 0.0323603700 15
# ORBITAL 19 NAO = 15
-0.0163754625 16 -0.0583193461 17 0.1324498525 18 0.6739423059 19
0.0000015891 20 -0.0000003256 21 0.4551921058 22 -0.0000787438 23
-0.0000153122 24 -0.0756649095 25 0.0000030203 26 -0.0000219594 27
0.0323852880 28 -0.0000064669 29 0.0323956416 30
$END
Careful readers may wonder why the $FRAG section is missing in this input file. This is because, each atom is defined as a fragment in default, if $FRAG section is not specified by the user. In the default case, atom 1 is defined as fragment 1, atom 2 is defined as fragment 2, and so on. The description of each orbital in the calculation is shown in the $ORB section. In the input file, the contents after “#” in a line is regarded as comments, and will not be read by the program. The “GUESS=READ” keyword is specified for the BOVB calculation, and the VBSCF optimal orbitals are provided as initial guess in the $VEC section.
To obtain the resonance energy, another input file to comput the energy with one covalent structure is needed. The BOVB energy of the total 3 structures is -192.68236940 hartree,
and that of one covalent structure is -192.58034082 hartree. Therefore, the resonance enenrgy of the C-C bridge bond is 64.02 kcal/mol at BOVB level.
Note
Careful readers may notice the BOVB energy with one covalent structure is exactly identical to the VBSCF enenrgy. This is because BOVB includes dynamic corrlation by allowing different orbitals in different structures. When the wave funtion contains only one structure, the BOVB and VBSCF wave functions are identical.
10.3. Computations of the bonding energy
The bodning energy is the energy difference between the equilibrium geometry and the geometry after bond breaking. In the previous F2 moleucle, the bond breaking geometry is simply described by setting the F-F distance as a large value (10 Å for instance). In this propellane case, however, it’s impossible to stretch the C-C bridge bond while keeping the molecular skeleton.
To approximately estimated the bonding energy of the C-C bridge bond, we define a quasiclassical (QC) state as a reference non-bonded state. For a single bond, the bonded state is the covalent state \(\Phi^{cov}=\frac{1}{\sqrt{2+2s_{ab}}}(|\phi_a\overline{\phi}_b|-|\overline{\phi}_a\phi_b|)\), and the QC state can be either \(|\phi_a\overline{\phi}_b|\) or \(|\overline{\phi}_a\phi_b|\). Each of these determinants has only quasi-classical interactions between the two fragments and is therefore non-bonding, while the covalent bonding arises from the interaction of the two determinants that give rise to the singlet-coupled covalent state \(\Phi^{cov}\). This covalent bond energy, complemented by the resonance energy stabilization due to the mixing of the ionic structures into the covalent structure measures the “in-situ” bonding energy. As such, the “in-situ” bonidng energy, which is the energy difference between the QC state and state with totally 3 structures provides an approximated measure of the C-C bridge boning energy.
The following is a input file to compuete the QC state.
QC state calculation of propellane
$CTRL
WFNTYP=DET NSTR=1 NAO=2 NAE=2 IPRINT=3
ORBTYP=HAO GUESS=READ
BASIS=CC-PVDZ
$END
$STR
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19
$END
$ORB
1*5 2*12 1*2
1 # 1 C1 1s
2 # 2 C2 1s
3 # 3 C3 1s
4 # 4 C4 1s
5 # 5 C5 1s
1 3 # 6 C1-C3 sigma
2 3 # 7 C2-C3 sigma
1 4 # 8 C1-C4 sigma
2 4 # 9 C2-C4 sigma
1 5 # 10 C1-C5 sigma
2 5 # 11 C2-C5 sigma
3 6 # 12 C3-H6 sigma
3 7 # 13 C3-H7 sigma
4 8 # 14 C4-H8 sigma
4 9 # 15 C4-H9 sigma
5 10 # 16 C5-H10 sigma
5 11 # 17 C5-H11 sigma
1 # 18 C1-C2 sigma C1
2 # 19 C1-C2 sigma C2
$END
$GEO
C -0.80339320 -0.00000002 -0.00026581
C 0.80339315 0.00000002 -0.00026580
C -0.00000000 0.00000000 1.30328491
C 0.00000001 1.12889613 -0.65192077
C -0.00000002 -1.12889613 -0.65192076
H 0.00000002 0.90072681 1.88197724
H 0.00000001 -0.90072681 1.88197723
H -0.00000001 2.07996500 -0.16030252
H 0.00000003 1.18070087 -1.72126710
H 0.00000001 -1.18070087 -1.72126709
H 0.00000000 -2.07996501 -0.16030253
$END
$VEC
15 15 15 15 15 30 30 30 30 30 30 20 20 20 20 20 20 15 15
# ORBITAL 1 NAO = 15
1.0013044300 1 -0.0148185006 2 -0.0270614351 3 0.0014157398 4
-0.0000001541 5 0.0000015008 6 -0.0017992610 7 -0.0000067568 8
-0.0000032993 9 -0.0008838473 10 -0.0000009796 11 0.0000002515 12
-0.0015986173 13 0.0000013752 14 -0.0016010424 15
# ORBITAL 2 NAO = 15
1.0013053868 16 -0.0148178712 17 -0.0270673561 18 -0.0014157125 19
-0.0000002118 20 0.0000016740 21 0.0018009244 22 -0.0000010308 23
0.0000054004 24 -0.0008824051 25 -0.0000002306 26 -0.0000009051 27
-0.0015985372 28 0.0000006106 29 -0.0015993992 30
# ORBITAL 3 NAO = 15
0.9991206001 31 -0.0171860691 32 -0.0162161271 33 0.0000007618 34
0.0000013055 35 -0.0006957167 36 -0.0000014569 37 0.0000001571 38
0.0000790563 39 -0.0020670891 40 -0.0000011719 41 0.0000010731 42
-0.0021065954 43 -0.0000022108 44 -0.0023469285 45
# ORBITAL 4 NAO = 15
0.9991202122 46 -0.0171853822 47 -0.0162125157 48 0.0000006933 49
-0.0005994343 50 0.0003494060 51 -0.0000008239 52 0.0000652009 53
-0.0000372870 54 -0.0020683845 55 -0.0000009837 56 -0.0000004101 57
-0.0022864381 58 0.0001199393 59 -0.0021660489 60
# ORBITAL 5 NAO = 15
0.9991212097 61 -0.0171850657 62 -0.0162182626 63 0.0000004025 64
0.0006008934 65 0.0003484130 66 0.0000035522 67 -0.0000702075 68
-0.0000394260 69 -0.0020683512 70 0.0000006972 71 0.0000002999 72
-0.0022870879 73 -0.0001190917 74 -0.0021658981 75
# ORBITAL 6 NAO = 30
-0.0177774926 1 -0.2162705930 2 -0.2298798504 3 0.0706361562 4
0.0000024378 5 -0.3238519858 6 0.0667063348 7 -0.0000256996 8
-0.1556546218 9 0.0097518542 10 -0.0000027624 11 -0.0301554752 12
0.0092026397 13 -0.0000002305 14 -0.0263744821 15 -0.0147709460 31
-0.1460413984 32 -0.1155006162 33 0.2650092251 34 0.0000006955 35
0.1839524192 36 0.1404511764 37 0.0000407801 38 0.0925295733 39
-0.0107900693 40 0.0000018292 41 -0.0282003496 42 0.0136549918 43
0.0000054096 44 -0.0097832753 45
# ORBITAL 7 NAO = 30
-0.0177658023 16 -0.2162486406 17 -0.2299525549 18 -0.0706350937 19
-0.0000014106 20 -0.3238462405 21 -0.0666827544 22 -0.0000053780 23
-0.1555802125 24 0.0097646308 25 -0.0000018502 26 0.0301631205 27
0.0092087511 28 0.0000029753 29 -0.0263731317 30 -0.0147687986 31
-0.1460413510 32 -0.1155156453 33 -0.2649967418 34 -0.0000072210 35
0.1839401239 36 -0.1405170026 37 -0.0000348214 38 0.0924884616 39
-0.0107989165 40 -0.0000016736 41 0.0282085984 42 0.0136617248 43
-0.0000053124 44 -0.0097795494 45
# ORBITAL 8 NAO = 30
-0.0177577308 1 -0.2162013994 2 -0.2299673947 3 0.0706110630 4
-0.2804620260 5 0.1619371044 6 0.0666333857 7 -0.1348756187 8
0.0778258361 9 0.0097734916 10 -0.0261267575 11 0.0150869471 12
-0.0174618406 13 0.0178097102 14 0.0003162100 15 -0.0147732236 46
-0.1460578616 47 -0.1155220923 48 0.2650144529 49 0.1592704233 50
-0.0920250702 51 0.1404068731 52 0.0800667609 53 -0.0462473103 54
-0.0107879126 55 -0.0244083850 56 0.0141015632 57 -0.0039034180 58
0.0117339554 59 0.0077884189 60
# ORBITAL 9 NAO = 30
0.0177761911 16 0.2162548982 17 0.2298552881 18 0.0706285957 19
0.2805096055 20 -0.1619483728 21 0.0667282475 22 0.1348077090 23
-0.0778328435 24 -0.0097796081 25 -0.0261254688 26 0.0150935495 27
0.0174656722 28 -0.0178011546 29 -0.0003043329 30 0.0147931236 46
0.1461082080 47 0.1153584115 48 0.2650336900 49 -0.1592773444 50
0.0920130590 51 0.1405345297 52 -0.0800770669 53 0.0462541047 54
0.0108069299 55 -0.0244257552 56 0.0141067392 57 0.0039234196 58
-0.0117232129 59 -0.0077872362 60
# ORBITAL 10 NAO = 30
0.0177805057 1 0.2162405637 2 0.2298076785 3 -0.0706044220 4
-0.2804965339 5 -0.1619531390 6 -0.0666833559 7 -0.1347393815 8
-0.0777019246 9 -0.0097445984 10 -0.0261176194 11 -0.0150718170 12
0.0174729106 13 0.0177945974 14 -0.0002864287 15 0.0147874057 61
0.1460888402 62 0.1154517089 63 -0.2650232945 64 0.1592757818 65
0.0920142609 66 -0.1405860261 67 0.0801337784 68 0.0462885854 69
0.0108070870 70 -0.0244331942 71 -0.0141107441 72 0.0039410936 73
0.0117131673 74 -0.0078047684 75
# ORBITAL 11 NAO = 30
0.0177799561 16 0.2162227894 17 0.2298148247 18 0.0705868963 19
-0.2804588970 20 -0.1619115261 21 0.0666441698 22 -0.1348267513 23
-0.0778975430 24 -0.0097385288 25 0.0261260325 26 0.0150938317 27
0.0174863028 28 0.0178098786 29 -0.0003106634 30 0.0147619518 61
0.1460362911 62 0.1156613683 63 0.2650100271 64 0.1592697337 65
0.0920215396 66 0.1403723237 67 0.0801289455 68 0.0462892649 69
0.0107835415 70 0.0244067802 71 0.0140992591 72 0.0039118995 73
0.0117295466 74 -0.0077996863 75
# ORBITAL 12 NAO = 20
0.0172973458 31 0.2021529787 32 0.1246606235 33 -0.0000031809 34
0.3042972540 35 0.1970108564 36 0.0000068028 37 0.1300804271 38
0.0908986389 39 -0.0079455903 40 0.0000048018 41 -0.0000039238 42
0.0117793218 43 0.0139996205 44 -0.0073463152 45 0.4270402124 76
0.1295468232 77 -0.0000053093 78 -0.0294631198 79 -0.0195166579 80
# ORBITAL 13 NAO = 20
-0.0173282009 31 -0.2022108198 32 -0.1243909531 33 -0.0000096109 34
0.3043243458 35 -0.1970216211 36 -0.0000042424 37 0.1300749867 38
-0.0909331248 39 0.0079484887 40 -0.0000056809 41 0.0000028882 42
-0.0117996319 43 0.0139959547 44 0.0073369181 45 -0.4270900640 81
-0.1296000887 82 0.0000006580 83 -0.0294618950 84 0.0195172636 85
# ORBITAL 14 NAO = 20
0.0173002408 46 0.2021118790 47 0.1246240723 48 0.0000022713 49
0.3227889720 50 0.1649529052 51 -0.0000148620 52 0.1438492365 53
0.0672219489 54 -0.0079367406 55 0.0000175697 56 -0.0000089690 57
0.0079591066 58 0.0165643938 59 -0.0034869406 60 0.4270093758 86
0.1295884488 87 0.0000016180 88 -0.0316194875 89 -0.0157531870 90
# ORBITAL 15 NAO = 20
-0.0173086687 46 -0.2021939367 47 -0.1245611168 48 0.0000003610 49
-0.0183875471 50 0.3620460821 51 0.0000673331 52 -0.0136415635 53
0.1580963305 54 0.0079527536 55 -0.0000113874 56 0.0000032002 57
0.0130569871 58 -0.0025806853 59 -0.0175049037 60 -0.4270744827 91
-0.1295400125 92 0.0000001650 93 0.0021637053 94 -0.0352738044 95
# ORBITAL 16 NAO = 20
-0.0173183346 61 -0.2022026360 62 -0.1245109940 63 0.0000075545 64
0.0183988865 65 0.3620424314 66 -0.0000395096 67 0.0136658395 68
0.1581128420 69 0.0079480868 70 -0.0000049906 71 -0.0000080201 72
0.0130454991 73 0.0025855278 74 -0.0175242163 75 -0.4270686231 96
-0.1295457954 97 -0.0000005864 98 -0.0021655869 99 -0.0352696895 100
# ORBITAL 17 NAO = 20
0.0173197873 61 0.2021511454 62 0.1244587778 63 -0.0000011094 64
-0.3228115619 65 0.1649560698 66 0.0000052783 67 -0.1438497907 68
0.0671949240 69 -0.0079405965 70 0.0000104455 71 -0.0000034930 72
0.0079482684 73 -0.0165642389 74 -0.0034671716 75 0.4270459111 101
0.1296314976 102 -0.0000009897 103 0.0316266447 104 -0.0157561697 105
# ORBITAL 18 NAO = 15
-0.0163776922 1 -0.0583204663 2 0.1324850019 3 -0.6739726665 4
-0.0000444708 5 -0.0000310706 6 -0.4551573242 7 -0.0000875557 8
-0.0000314392 9 -0.0756705415 10 -0.0000033820 11 -0.0000057832 12
0.0323892303 13 0.0000190463 14 0.0323603700 15
# ORBITAL 19 NAO = 15
-0.0163754625 16 -0.0583193461 17 0.1324498525 18 0.6739423059 19
0.0000015891 20 -0.0000003256 21 0.4551921058 22 -0.0000787438 23
-0.0000153122 24 -0.0756649095 25 0.0000030203 26 -0.0000219594 27
0.0323852880 28 -0.0000064669 29 0.0323956416 30
$END
In this input file, the “WFNTYP=DET” keyword means the wave function will be expressed in the basis of determinants. In this case, the wave function consists only one determinant, so we specify “NSTR=1” keyword. This determinant should be provided in $STR section. The format of writing a determinant is different from a structure. To write a determinant, we first write all the occupied \(\alpha\) orbitals (“1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18” in this case), followed by all the occupied \(\beta\) orbitals (“1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19” in this case).
Note
In this case, the wave funtion contains only one determinant, and therefore the BOVB and VBSCF wave functions are identical.
The energy of QC state is -192.49514835 hartree, compared with the energy of totally 3 structures (-192.68236940 hartree),
the bonding energy of the C-C bridge bond is 117.5 kcal/mol. Therefore, one can find the resonance energy of the C-C bond
is 54 % of the bonding energy, and thus conclude the C-C bridge bond in the propellane compound is a charge-shift bond.