Structure and Stability of Polynitrogen Molecules
and Their Spectroscopic Characteristics
Rodney J. Bartlett
Stefan Fau
Motoi Tobita
Ken Wilson
Ajith Perera
Quantum Theory Project
P.O. Box 118435
University of Florida
Gainesville, FL 32611-8435
(352)–392-6974
[email protected]
This work is supported by AFOSR-DARPA (F49620-98-1-0477)
To be published
Table of Contents
Abstract ......................................................................................................................................7
Computational Methods ..............................................................................................................7
Molecular Description.................................................................................................................8
N2+ D∞ h 2Σ g (B3LYP/aug-cc-pVDZ) .....................................................................................................8
N2 D∞ h 1Σ g(B3LYP/aug-cc-pVDZ) .......................................................................................................8
N2 D∞ h 1Σ g(CCSD(T)/aug-cc-pVTZ) ....................................................................................................8
N2 D∞ h 1Σ g(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ) .........................................................................9
N3+ D∞ h 1Σ g (B3LYP/aug-cc-pVDZ) ...................................................................................................10
N3+ D∞ h 1Σ g (CCSD(T)/cc-pVTZ) .......................................................................................................10
N3+ D∞ h 1Σ g(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ) ......................................................................11
N3+ D3h 1A1’(B3LYP/aug-cc-pVDZ) ..................................................................................................12
N3+ D3h 1A1’ (CCSD(T)/cc-pVTZ) ......................................................................................................12
N3+ D3h 1A1’ (EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ) ....................................................................13
N3 D∞ h 2Σ g (B3LYP/aug-cc-pVDZ) ....................................................................................................13
N3- C2v 1A1 (B3LYP/aug-cc-pVDZ)....................................................................................................14
N3- C2v 1A1EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ) ........................................................................14
N3- D3h 3A1’ (B3LYP/aug-cc-pVDZ)...................................................................................................15
N3- D∞ h 1Σ g (B3LYP/aug-cc-pVDZ) ...................................................................................................15
N3- D∞ h 1Σ g (CCSD(T)/aug-cc-pVTZ).................................................................................................15
N3- D∞ h 1Σ g(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ) ......................................................................16
N4+ D2h 2B 2u (B3LYP/aug-cc-pVDZ) ..................................................................................................17
N4 C2v 3B 1 (B3LYP/aug-cc-pVDZ).....................................................................................................17
N4 C2v 3B 1 (CCSD(T)/aug-cc-pVDZ)..................................................................................................18
N4 D2d 3A2 (B3LYP/aug-cc-pVDZ) ....................................................................................................18
N4 D2d 3A2 (CCSD(T)/aug-cc-pVDZ) .................................................................................................19
N4 Td 1A1 (B3LYP/aug-cc-pVDZ) ......................................................................................................19
N4 Td 1A1 (B3LYP/TZ2P) ..................................................................................................................19
N4 Td 1A1 (CCSD(T)/aug-cc-pVTZ) ...................................................................................................20
N4 Td 1A1(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ) .........................................................................20
N4 D2h 1Ag (B3LYP/aug-cc-pVDZ) ....................................................................................................21
N4 D2h 1Ag(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)........................................................................22
N4 C2h 3B u (B3LYP/aug-cc-pVDZ).....................................................................................................23
N4 C2h 3B u (CCSD(T)/aug-cc-pVDZ)..................................................................................................23
N4- D2h 2B1g (B3LYP/aug-cc-pVDZ) ..................................................................................................24
N4- C2h 4B g (B3LYP/aug-cc-pVDZ) ....................................................................................................24
N5+ D3h 1A1’(B3LYP/aug-cc-pVDZ)..................................................................................................25
N5+ D2d 1A1’(B3LYP/aug-cc-pVDZ)..................................................................................................25
N5+ C2v 1A1 (B3LYP/aug-cc-pVDZ) ...................................................................................................26
N5+ C2v 1A1 CCSD(T)/6-311+G(2d)....................................................................................................26
N5+ C2v 1A1 (EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ) ......................................................................27
N5 D2d 2B1 (B3LYP/aug-cc-pVDZ) ....................................................................................................28
N5- D3h 1A1’ (B3LYP/aug-cc-pVDZ)...................................................................................................28
N5- D3h 1A1’(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ) .....................................................................29
N5- D5h 1A1’ (B3LYP/aug-cc-pVDZ)...................................................................................................30
N5- D5h 1A1’ (CCSD(T)/aug-cc-pVTZ) ................................................................................................30
N5- D5h 1A1’(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ) .....................................................................31
N5- D2d 1A1 (B3LYP/aug-cc-pVDZ) ...................................................................................................32
N6+ C2h 2Ag (B3LYP/aug-cc-pVDZ) ...................................................................................................33
N6+ C2h planar 2B g (B3LYP/aug-cc-pVDZ) .........................................................................................33
N6+ C2v 2B g (B3LYP/aug-cc-pVDZ) ...................................................................................................34
N6 D3h 1A1’ (B3LYP/aug-cc-pVDZ) ...................................................................................................34
N6 D3h 1A1’(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ) ......................................................................35
N6 C2 book 1A (B3LYP/aug-cc-pVDZ)...............................................................................................36
N6 D2 1A (B3LYP/aug-cc-pVDZ).......................................................................................................37
N6 C2h 1Ag (B3LYP/aug-cc-pVDZ) ....................................................................................................37
N6 C2h 1Ag (CCSD(T)/cc-pVDZ) ........................................................................................................38
N6 C2 1A (CCSD(T)/cc-pVDZ)...........................................................................................................38
N6- C2 2A (B3LYP/aug-cc-pVDZ) ......................................................................................................39
N6- Cs 2A’ (B3LYP/aug-cc-pVDZ)......................................................................................................39
N7+ C2v 1A1 (B3LYP/aug-cc-pVDZ) ...................................................................................................40
N7 Cs 2A’trigonal (B3LYP/aug-cc-pVDZ) .........................................................................................41
N7 Cs 2A’(B3LYP/aug-cc-pVDZ) ......................................................................................................42
N7 C2v 2B 1 (B3LYP/aug-cc-pVDZ).....................................................................................................43
N7 D2d 2A2 (B3LYP/aug-cc-pVDZ) ....................................................................................................44
N7 C2 2B (B3LYP/aug-cc-pVDZ) .......................................................................................................45
N7 C2v 2B 1 (B3LYP/aug-cc-pVDZ).....................................................................................................46
N7 Cs 2A’(B3LYP/aug-cc-pVDZ) ......................................................................................................47
N7- C2v 1A1 (B3LYP/aug-cc-pVDZ)....................................................................................................48
N8 Oh 1A1g (B3LYP/aug-cc-pVDZ) ....................................................................................................49
N8 D2h 1A1g (B3LYP/aug-cc-pVDZ) ...................................................................................................50
N8 C2h ladder 1Ag (B3LYP/aug-cc-pVDZ) ..........................................................................................51
N8 C2v ring 1A1 (B3LYP/aug-cc-pVDZ)..............................................................................................52
N8 C2v 1A1 (B3LYP/aug-cc-pVDZ) ....................................................................................................53
N8 C1 ZZE 1A (B3LYP/aug-cc-pVDZ) ...............................................................................................54
N8 C2h ZEZ 1Ag (B3LYP/aug-cc-pVDZ) .............................................................................................55
N8 Cs 1A’(B3LYP/aug-cc-pVDZ) ......................................................................................................56
N8 D2h planar 1A1g (B3LYP/aug-cc-pVDZ) .........................................................................................57
N8 C2h EEE 1Ag (B3LYP/aug-cc-pVDZ) .............................................................................................58
N8 C2v EZE 1A1 (B3LYP/aug-cc-pVDZ) .............................................................................................59
N8 Cs pentagonal 1A’ (B3LYP/aug-cc-pVDZ) .....................................................................................60
N8- C2h 2B g (B3LYP/aug-cc-pVDZ) ....................................................................................................61
N8- C2h ZEZ 2B g (B3LYP/aug-cc-pVDZ) ............................................................................................62
N9+ C2v rings 1A1 (B3LYP/aug-cc-pVDZ) ...........................................................................................63
N9+ C2v 1A1 (B3LYP/aug-cc-pVDZ) ...................................................................................................64
N9 C2v rings 2B 1 (B3LYP/aug-cc-pVDZ) ............................................................................................65
N9 C2v 2A2 (B3LYP/aug-cc-pVDZ) ....................................................................................................66
N9- C2 1A (B3LYP/aug-cc-pVDZ) ......................................................................................................67
N9- C2v 1A1 (B3LYP/aug-cc-pVDZ)....................................................................................................68
N9- Cs 1A’(B3LYP/aug-cc-pVDZ) .....................................................................................................69
N10+ C1 2A (B3LYP/aug-cc-pVDZ) ....................................................................................................70
N10+ C1 chain 2A (B3LYP/aug-cc-pVDZ)............................................................................................71
N10 C2v 1A1 (B3LYP/aug-cc-pVDZ) ...................................................................................................72
N10 D5h 1A1’(B3LYP/aug-cc-pVDZ)..................................................................................................73
N10 Cs 1A’7-ring (B3LYP/aug-cc-pVDZ) ..........................................................................................74
N10 C2 1A (B3LYP/aug-cc-pVDZ)......................................................................................................75
N10 C2v 1A1 (B3LYP/aug-cc-pVDZ) ...................................................................................................76
N10 C1 1A (B3LYP/aug-cc-pVDZ)......................................................................................................77
N10 C1 1A n5-ring (B3LYP/aug-cc-pVDZ)..........................................................................................79
N10 Cs 1A’(B3LYP/aug-cc-pVDZ).....................................................................................................80
N10 D2d 1A1 (B3LYP/aug-cc-pVDZ) ...................................................................................................81
N10- D2h 2B 3u (B3LYP/aug-cc-pVDZ)..................................................................................................82
Absolute and Relative Electronic Energies ................................................................................83
Heats of Formation (Direct method)..........................................................................................85
Heats of Formation (Quasi-isodesmic method)..........................................................................87
References ................................................................................................................................89
Acknowledgements...................................................................................................................93
Abstract
The most pressing problem with characterizing any synthesized polynitrogen is that
except for N2, N3-, N4+ and N5+, none are known experimentally. Consequently, we require
predictive quantum chemical results to assist the experimental effort. Using Density Functional
Theory (DFT), which we calibrate against CCSD(T), we report a survey of all polynitrogen
molecules from N2 to N10, and their cations and anions that appear to be stable. These are
characterized by vibrational frequencies including their associated infrared and Raman
intensities. For the most interesting candidates, we also provide the more predictive CCSD(T)
results. We also obtain STEOM-CC excitation spectra and IP-EOM-CC photoelectron spectra
that can aid spectroscopic identification.
Computational Methods
Our initial survey for bound polynitrogen molecules was performed using DFT. The
exchange-correlation potential was constructed from Becke’s three parameter formula for
exchange (B3) along with the Lee-Yang-Parr parameterization for correlation (LYP). These
calculations were performed within a valence double-ζ basis set augmented with both diffuse
and polarization functions (aug-cc-pVDZ). This basis set was contracted as: (10s5p2d/4s3p2d)
and used pure spherical harmonic (i.e. 5 d-type), one-particle Gaussian functions.
For selected molecules, we present more accurate and reliable structures and energetics
obtained at the CCSD(T) level of theory. The CCSD(T) calculations were performed within a
much larger valence triple-ζ basis set augmented with a polarization function (cc-pVTZ). Raman
intensities are based upon the CCSD model and were computed within the POL1 basis. For
select closed shell molecules, excitation spectra from the similarity-transformed equation of
motion (STEOM) method are presented along with ionization potentials and electron affinities.
All of the coupled-cluster calculations were performed with the ACES II program system.
Normal harmonic vibrational frequencies and their related information are given in
tables. Bond lengths are shown in units of Angstroms, frequencies are in cm-1, IR intensities are
in km mol-1, and Raman intensities is Angstroms4 AMU-1. To avoid overloading each picture, we
have not included the dihedral angles, which are necessary to completely specify non-planar
structures. These may be obtained upon request from the authors.
7
N2 D∞ h Σ g (B3LYP/aug-cc-pVDZ)
Structure
+
Molecular Description
2
1.1166
Vibrational frequency
1
Symm.
Frequency
Σg
2329.5
IR Intensity
0
Raman
Intensity
284.5
Depolarization Ratio
0.195
N2 D∞ h 1Σ g(B3LYP/aug-cc-pVDZ)
Structure
1.1044
Vibrational frequency
1
Symm.
Frequency
Σg
2444.1
IR Intensity
0
Raman
Intensity
22.4
Depolarization Ratio
0.116
N2 D∞ h 1Σ g(CCSD(T)/aug-cc-pVTZ)
Structure
1.1035
(1.0977)*
Vibrational frequency
Symm.
Frequency
Calc.
Σg
2355.5
Exp. Harmonic*
Σg
2358.57
IR Intensity
0.0
Raman
Intensity
19.7
Depolarization Ratio
0.08
* K.P. Huber and G. Herzberg, Constants of Diatomic Molecule, in W.G. Mallard and P.J.
Linstrom, editors, NIST Chemistry Webbook, http://webbook.nist.gov
8
N2 D∞ h 1Σ g(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)
Vertical Excitation Energies by EE-STEOM
Mult.
Symmetry
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Σu
Πg
∆u
Σg
Πu
Σu
Πu
Σu
Πg
∆u
Σu
∆g
Πu
Σg
Πu
Excitation energy (eV)
9.19
12.57
13.29
13.03
13.58
7.46
8.01
11.21
11.99
13.27
Experimental*
Adiabatic (eV)
8.45
859
8.94
12.40
12.61
12.96
12.95
6.22
7.39
7.42
8.22
10.90
11.05
11.88
12.19
Osc. Strength
0
0
0.322
0.332
0
0
0
0
0
0
0
0
Vertical Ionization Potentials by IP-EOM
Mult.
Symmetry
IP (eV)
Doublet
Doublet
Doublet
Σg
Πu
Σu
15.41
17.02
18.72
Experimental*
Adiabatic (eV)
15.581±0.008
Vertical Electron Affinities by EA-EOM
Mult.
Symmetry
EA (eV)
Doublet
Doublet
Doublet
Doublet
Doublet
Doublet
Σg
Σu
Πg
Πu
Σg
Πg
1.90
2.31
2.62
3.55
4.86
5.77
Experimental*
Adiabatic (eV)
2.35
* K.P. Huber and G. Herzberg, Constants of Diatomic Molecule, in W.G. Mallard and P.J.
Linstrom, editors, NIST Chemistry Webbook, http://webbook.nist.gov
9
N3+ D∞ h 1Σ g (B3LYP/aug-cc-pVDZ)
Structure
1.1891
Vibrational frequencies
1
2
3
4
Symm.
Frequency
Πu
Πu
Σg
Σu
262.4
521.2
1359.1
1523.7
IR Intensity
6.9
0.2
0.0
27.6
Raman
Intensity
0.0
0.0
26.5
0.0
Depolarization Ratio
0.43
0.75
0.19
0.75
N3+ D∞ h 1Σ g (CCSD(T)/cc-pVTZ)
Structure
1.1887
Vibrational frequencies
1
2
3
10
Symm.
Frequency
Πu
Σg
Σu
307.5
1307.5
1426.4
IR Intensity
6.2
0.0
31.0
Raman
Intensity
Depolarization Ratio
N3+ D∞ h 1Σ g(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)
Vertical Excitation Energies by EE-STEOM
Mult.
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Symmetry
Σg
Σu
Σu
Σu
Σu
Σg
Σg
Σg
Σu
Σg
Σg
Σg
Σu
Σu
Σu
Σg
Σu
Σg
Σu
Σu
Σu
Excitation energy (eV)
-0.14
4.63
4.93
4.96
5.59
6.35
10.05
10.58
10.63
10.70
11.08
11.19
12.67
13.10
14.41
-1.55
2.84
4.04
4.19
5.02
5.86
Osc. Strength
0
0.024
0
0
0
0
0
0
0.855
0
0
0
0.077
0.108
0.049
0
0
0
0
0
0
Vertical Ionization Potentials by IP-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Symmetry
Σg
Σu
Σg
Σu
IP (eV)
20.98
25.30
26.78
26.80
Vertical Electron Affinities by EA-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
Doublet
Doublet
Symmetry
Σg
Σu
Σu
Σg
Σu
Σu
Σu
EA (eV)
-12.34
-6.00
-5.50
-3.96
-2.06
-1.99
-1.71
11
N3+ D3h 1A1’(B3LYP/aug-cc-pVDZ)
Structure
1.3253
Vibrational frequencies
1
2
Symm.
Frequency
E’
A1 ’
1080.0
1612.5
IR Intensity
9.0
0.0
Raman
Intensity
5.3
23.5
Depolarization Ratio
0.75
0.06
N3+ D3h 1A1’ (CCSD(T)/cc-pVTZ)
Structure
1.3271
Vibrational frequencies
1
2
12
Symm.
Frequency
E’
A1 ’
1060.2
1549.8
IR Intensity
7.4
0.0
Raman
Intensity
6.8
29.2
Depolarization Ratio
0.75
0.06
N3+ D3h 1A1’ (EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)
Vertical Excitation Energies by EE-STEOM
Mult.
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Symmetry
E’’
A2’’
A2’’
E’’
A2 ’
A1 ’
A1 ’
A2 ’
A2’’
E’’
A2’’
E’’
A2 ’
A1 ’
E’
Excitation energy (eV)
4.89
4.96
5.13
5.14
9.84
9.92
13.83
13.85
3.59
3.62
3.68
4.19
7.72
7.83
10.52
Osc. Strength
0
0.014
0.004
0
0.035
0.036
0.173
0.177
0
0
0
0
0
0
0
Vertical Ionization Potentials by IP-EOM
Mult.
Doublet
Doublet
Doublet
Symmetry
E’
A1 ’
A2’’
IP (eV)
24.02
26.08
28.41
Vertical Electron Affinities by EA-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
Doublet
Symmetry
E’’
A1 ’
E’
A2 ’
E’’
A1 ’
EA (eV)
-9.65
-3.06
-2.73
-2.71
-2.14
-0.69
N3 D∞ h 2Σ g (B3LYP/aug-cc-pVDZ)
Structure
1.1846
Vibrational frequencies
1
2
3
4
Symm.
Frequency
Πu
Πu
Σg
Σu
472.1
582.1
1371.8
1714.5
IR Intensity
9.0
1.9
0.0
222.4
Raman
Intensity
0.0
0.0
31.5
0.0
Depolarization Ratio
0.69
0.75
0.18
0.75
13
N3- C2v 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.2942
84.76
Vibrational frequencies
Symm.
Frequency
A1
B2
A1
676.8
832.5
1535.2
1
2
3
IR Intensity
0.8
359.0
0.0
Raman
Intensity
10.6
50.5
12.6
Depolarization Ratio
0.32
0.75
0.07
N3- C2v 1A1EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)
Vertical Excitation Energies by EE-STEOM
Mult.
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Irrep.
B2
B1
A2
A2
B1
B3
A1
A1
B1
B2
B2
A2
B1
A2
A1
A1
Excitation energy (eV)
2.22
2.25
3.14
3.57
3.87
4.71
5.10
5.59
1.37
1.55
2.88
3.11
3.38
3.59
5.02
5.53
Vertical Ionization Potentials by IP-EOM
Mult.
Doublet
Doublet
Doublet
Irrep.
A2
A1
B2
IP (eV)
1.37
3.39
6.44
Vertical Electron Affinities by EA-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
Doublet
14
Irrep.
A1
B2
A1
B1
B2
B1
EA (eV)
5.76
5.89
6.14
7.53
8.31
8.45
Osc. Strength
0.023
0.008
0
0
0.023
0.112
0.010
0.062
0
0
0
0
0
0
0
0
N3- D3h 3A1’ (B3LYP/aug-cc-pVDZ)
Structure
1.4055
Vibrational frequencies
1
2
Symm.
Frequency
E’
A1 ’
894.9
1342.1
IR Intensity
0.0
0.0
Raman
Intensity
2.9
34.0
Depolarization Ratio
0.75
0.26
N3- D∞ h 1Σ g (B3LYP/aug-cc-pVDZ)
Structure
1.1902
Vibrational frequencies
1
2
3
Symm.
Frequency
Πu
Σg
Σu
627.9
1352.0
2072.3
IR Intensity
1.4
0.0
1273.0
Raman
Intensity
0.0
37.3
0.0
Depolarization Ratio
0.31
0.18
0.67
N3- D∞ h 1Σ g (CCSD(T)/aug-cc-pVTZ)
Structure
1.1897
Vibrational frequencies
1
2
3
Symm.
Frequency
Πu
Σg
Σu
662.6
1309.0
2102.6
IR Intensity
12.6
0.0
730.6
Raman
Intensity
0.0
63.7
0.0
Depolarization Ratio
0.75
0.16
0.13
15
N3- D∞ h 1Σ g(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)
Vertical Excitation Energies by EE-STEOM
Mult.
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Symmetry
Πg
Πu
Πu
Σu
Σu
Πg
Πg
Σg
Σg
Πu
Πg
Σu
Πu
Πu
Σu
Πg
Σg
Πg
Σg
Πu
Excitation energy (eV)
3.94
4.64
4.66
4.69
5.20
5.66
7.28
7.31
7.70
8.42
3.86
4.20
4.56
4.63
4.80
5.66
6.91
7.16
7.31
8.38
Vertical Ionization Potentials by IP-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Symmetry
Πg
Σu
Σg
Πu
IP (eV)
2.53
7.21
8.68
8.82
Vertical Electron Affinities by EA-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
Doublet
Doublet
16
Symmetry
Σg
Σu
Σg
Πu
Πg
Σg
Πu
EA (eV)
5.50
5.80
7.08
7.51
9.26
10.20
10.46
Osc. Strength
0
0
0.038
0.038
0
0.403
0
0
0
0.077
0
0
0
0
0
0
0
0
0
0
N4+ D2h 2B2u (B3LYP/aug-cc-pVDZ)
Structure
1.6314
1.2085
Vibrational frequencies
1
2
3
4
5
6
Symm.
Frequency
B2u
Au
B3g
Ag
B1u
Ag
311.8*
365.5
620.9
805.6
1543.5
1844.1
IR Intensity
0.5
0.0
0.0
0.0
1.3
0.0
Raman
Intensity
0.0
0.0
0.0
7.4
0.0
20.9
Depolarization Ratio
0.64
0.69
0.75
0.19
0.72
0.09
*
asymmetric stretch along the longer bond
N4 C2v 3B1 (B3LYP/aug-cc-pVDZ)
Structure
90.46
65.03
57.48
1.5423
1.4346
Vibrational frequencies
1
2
3
4
5
6
Symm.
Frequency
A2
A1
B2
A1
B1
A1
145.7*
692.0
751.0
832.1
959.8
1242.5
IR Intensity
0.0
0.1
5.8
4.0
16.9
0.1
Raman
Intensity
7.8
3.5
4.7
4.5
5.7
31.6
Depolarization Ratio
0.75
0.47
0.75
0.66
0.75
0.02
*
dissociative mode
17
N4 C2v 3B1 (CCSD(T)/aug-cc-pVDZ)
Structure
89.92
65.16
57.42
1.5644
1.4527
Vibrational frequencies
1
2
3
4
5
6
Symm.
Frequency
A2
A1
A1
B1
B2
A1
188.0
665.4
808.7
891.9
1113.8
1169.3
IR Intensity
Raman
Intensity
Depolarization Ratio
0.0
0.1
3.4
15.3
33.9
0.1
N4 D2d 3A2 (B3LYP/aug-cc-pVDZ)
Structure
88.50
1.3758
Vibrational frequencies
1
2
3
4
5
*
Symm.
Frequency
B1
A1
E
B2
A1
409.9*
697.2
792.0
1041.9
1272.3
dissociative mode
18
IR Intensity
0
0
0.1
9.6
0
Raman
Intensity
11.5
0.5
0.9
0.0
22.1
Depolarization Ratio
0.75
0.71
0.75
0.75
0.03
N4 D2d 3A2 (CCSD(T)/aug-cc-pVDZ)
Structure
88.39
1.3943
Vibrational frequencies
1
2
3
4
5
Symm.
Frequency
B1
A1
B2
A1
E
535.8
656.6
1029.4
1196.5
2570.7
IR Intensity
Raman
Intensity
Depolarization Ratio
0.0
0.0
9.6
0.0
146.4
N4 Td 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.4537
Vibrational frequencies
1
2
3
Symm.
Frequency
E
T2
A1
753.4*
973.7
1362.6
IR Intensity
0.0
3.2
0.0
Raman
Intensity
4.2
9.9
41.0
Depolarization Ratio
0.75
0.75
0.00
*
rocking around N-N bond
N4 Td 1A1 (B3LYP/TZ2P)
Structure
1.4512
Vibrational frequencies
1
2
3
Symm.
Frequency
E
T2
A1
752.2*
966.7
1360.5
IR Intensity
Raman
Intensity
Depolarization Ratio
0.0
3.7
0.0
19
N4 Td 1A1 (CCSD(T)/aug-cc-pVTZ)
Structure
1.4613
Vibrational frequencies
Symm.
Frequency
E
T2
A1
723.9
936.0
1296.2
1
2
3
IR Intensity
0.0
3.3
0.0
Raman
Intensity
4.7
10.2
45.6
Depolarization Ratio
0.75
0.75
0.00
N4 Td 1A1(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)
Vertical Excitation Energies by EE-STEOM
Mult.
Singlet
Singlet
Singlet
Singlet
Triplet
Triplet
Triplet
Triplet
Symmetry
T1
T2
E
T2
T2
T1
A1
T1
Excitation energy (eV)
9.51
10.15
10.21
10.67
7.70
8.78
9.41
9.74
Vertical Ionization Potentials by IP-EOM
Mult.
Doublet
Doublet
Symmetry
E
T2
IP (eV)
14.28
14.38
Vertical Electron Affinities by EA-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
Doublet
20
Symmetry
A1
T2
T1
T2
E
T2
EA (eV)
1.68
1.74
3.65
4.19
4.47
5.55
Osc. Strength
0
0.007
0
0
0
0
0
0
N4 D2h 1Ag (B3LYP/aug-cc-pVDZ)
Structure
1.5372
1.2562
Vibrational frequencies
1
2
3
4
5
6
Symm.
Frequency
Au
B2u
Ag
B3g
B1u
Ag
522.3
559.1
987.8
1048.7
1449.1
1675.6
IR Intensity
0.0
3.7
0.0
0.0
0.0
0.0
Raman
Intensity
0.0
0.0
25.5
2.0
0.0
14.8
Depolarization Ratio
0.11
0.74
0.33
0.75
0.73
0.20
Note: not a local minimum structure at higher level of theory
21
N4 D2h 1Ag(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)
Vertical Excitation Energies by EE-STEOM
Mult.
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Irrep.
B1u
Au
B1g
B2g
B1g
B3g
B1u
Ag
B2u
B2g
B3g
Ag
B2u
B3u
B3u
Au
B1u
B1g
B1g
Au
B2g
B2u
B3g
Ag
B1u
B2g
B2u
Excitation energy (eV)
1.43
3.91
3.97
5.36
5.46
6.65
7.02
7.04
7.87
7.99
8.29
8.66
8.83
9.80
10.08
10.59
1.05
2.29
3.17
3.45
4.74
5.07
5.83
6.29
6.46
7.19
7.80
Vertical Ionization Potentials by IP-EOM
Mult.
Doublet
Doublet
Doublet
Irrep.
B2u
B3u
B2g
IP (eV)
10.80
13.42
13.69
Vertical Electron Affinities by EA-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
22
Irrep.
B3g
B3u
Ag
B2u
Au
EA (eV)
-1.61
1.12
1.57
2.10
2.32
Osc. Strength
0.003
0
0
0
0
0
0.001
0
0.049
0
0
0
0
0.202
0.060
0
0
0
0
0
0
0
0
0
0
0
0
N4 C2h 3Bu (B3LYP/aug-cc-pVDZ)
Structure
1.1839
1.5055
114.82
Vibrational frequencies
1
2
3
4
5
6
Symm.
Frequency
Au
Bu
Ag
Ag
Bu
Ag
77.6*
287.4
520.1
683.5
1779.9
1808.2
IR Intensity
0.7
9.8
0.0
0.0
31.7
0.0
Raman
Intensity
0.0
0.0
25.1
6.8
0.0
12.4
Depolarization Ratio
0.45
0.38
0.20
0.46
0.75
0.41
*
out of plane bend
N4 C2h 3Bu (CCSD(T)/aug-cc-pVDZ)
Structure
1.1987
1.5292
113.15
Vibrational frequencies
1
2
3
4
5
6
Symm.
Frequency
Au
Bu
Ag
Ag
Bu
Ag
88.6
264.3
493.4
650.2
1681.3
1757.0
IR Intensity
Raman
Intensity
Depolarization Ratio
0.6
7.9
0.0
0.0
28.2
0.0
23
N4- D2h 2B1g (B3LYP/aug-cc-pVDZ)
Structure
1.4524
1.3136
Vibrational frequencies
1
2
3
4
5
6
Symm.
Frequency
Au
B2u
B3g
Ag
B1u
Ag
599.5*
667.6
1059.3
1110.7
1134.4
1459.0
IR Intensity
0.0
0.6
0.0
0.0
79.8
0.0
Raman
Intensity
0.0
0.0
0.8
40.9
0.0
8.1
Depolarization Ratio
0.44
0.50
0.75
0.28
0.73
0.73
*
out of plane bend
N4- C2h 4Bg (B3LYP/aug-cc-pVDZ)
Structure
1.2519
1.3442
121.14
Vibrational frequencies
1
2
3
4
5
6
*
Symm.
Frequency
Au
Bu
Ag
Ag
Bu
Ag
272.4*
302.1
621.0
1013.6
1299.6
1509.8
out of plane bend
24
IR Intensity
3.3
0.8
0.0
0.0
353.3
0.0
Raman
Intensity
0.0
0.0
27.3
57.8
0.0
49.9
Depolarization Ratio
0.63
0.33
0.15
0.64
0.51
0.13
N5+ D3h 1A1’(B3LYP/aug-cc-pVDZ)
Structure
59.5
1.469 61.0
1.448
96.6
Vibrational frequencies
1
2
3
4
5
6
Symm.
Frequency
E’
E”
A2 ”
A1 ’
E’
A1 ’
305.4
372.5
464.8
991.7
1047.3
1274.2
IR Intensity
5.8
0
8.9
0
16.5
0
Raman
Intensity
5.1
3.9
0
21.9
4.9
21.4
Depolarization Ratio
0.75
0.75
0.75
0.14
0.75
0.01
N5+ D2d 1A1’(B3LYP/aug-cc-pVDZ)
Structure
1.422
1.253
63.8
Vibrational frequencies
1
2
3
4
5
6
7
Symm.
Frequency
E
B1
A1
E
B2
A1
B2
252.7
444.7
674.4
881.5
1348.1
1569.3
1674.4
IR Intensity
2.0
0
0
0
10.2
0
9.0
Raman
Intensity
1.0
1.4
13.1
8.2
2.2
35.5
4.8
Depolarization Ratio
0.75
0.75
0.36
0.75
0.75
0.00
0.75
25
N5+ C2v 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.3082
165.92
111.94
1.1184
Vibrational frequencies
1
2
3
4
5
6
7
8
9
Symm.
Frequency
A1
B1
B2
A2
A1
A1
B2
B2
A1
185.4*
403.8
419.3
485.1
667.7
862.3
1175.3
2294.1
2349.3
IR Intensity
Raman
Intensity
6.6
0.0
0.3
0.6
9.0
1.9
0.0
23.7
188.4
0.4
5.8
0.5
0.0
0.8
3.4
135.7
141.6
20.3
Depolarization Ratio
0.57
0.75
0.75
0.75
0.20
0.33
0.75
0.75
0.24
*
out of plane bend
N5+ C2v 1A1 CCSD(T)/6-311+G(2d)
Structure*
1.33
166.4
108.3
1.12
Vibrational frequencies*
1
2
3
4
5
6
7
8
9
*
Symm.*
A1
B2
B1
A2
A1
A1
B2
B2
A1
Experimental Frequency*
209
CCSD(T) Frequency*
181
Exp. Raman Intensity*
strong
871-872
1088
2210-2211
2270-2271
818
weak
2175
2229
weak
strong
data from N5+: A Novel Homoleptic Polynitrogen Ion as a High Energy Density Material. Karl
O. Christe, William W. Wilson, Jeffrey A. Sheehy, and Jerry A. Boatz, Angew Chem Int. Ed.
1999, vol 38, 2004.
26
N5+ C2v 1A1 (EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)
Vertical Excitation Energies by EE-STEOM
Mult.
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Irrep.
A2
B1
B2
A2
B1
A1
B2
A1
A1
B1
B2
A1
B1
A2
A2
B2
A2
B2
B1
A1
B2
B1
A1
A2
A1
B2
B1
B1
A2
Excitation energy (eV)
5.16
5.85
6.15
7.74
7.93
7.99
8.22
9.51
9.62
9.76
9.77
9.92
10.16
10.32
10.64
11.30
4.80
4.98
5.42
6.12
6.39
7.00
7.07
7.57
7.61
7.68
8.78
8.91
9.03
Osc. Strength
0
0.002
0.154
0
0.001
0.758
0.009
0.122
0.013
0.023
0.068
0.018
0
0
0.073
0
0
0
0
0
0
0
0
0
0
0
0
0
Vertical Ionization Potentials by IP-EOM
Mult.
Doublet
Doublet
Doublet
Irrep.
B1
A1
B2
EA (eV)
18.44
20.49
23.12
Vertical Electron Affinities by EA-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Irrep.
B2
A2
A1
A1
IP (eV)
-6.04
-5.63
-5.53
-3.93
27
N5 D2d 2B1 (B3LYP/aug-cc-pVDZ)
Structure
1.392
1.327
57.0
61.5
140.6
Vibrational frequencies
1
2
3
4
5
6
7
Symm.
Frequency
E
B2
B1
A1
E
A1
B2
311.2
355.3
509.7
677.4
930.6
1355.8
1623.1
IR Intensity
6.3
1835.5
0
0
1.6
0
26.2
Raman
Intensity
2.2
14.2
1.4
154.4
2.8
53.6
3.0
Depolarization Ratio
0.75
0.75
0.75
0.37
0.75
0.01
0.75
N5- D3h 1A1’ (B3LYP/aug-cc-pVDZ)
Structure
84.16
78.60
1.4716
Vibrational frequencies
1
2
3
4
5
6
*
Symm.
Frequency
E’
A2 ”
E’
E”
A1 ’
A1 ’
311.0*
829.1
852.0
874.6
1067.8
1231.2
rocking on triangular plane
28
IR Intensity
67.2
8.3
0.6
0.0
0.0
0.0
Raman
Intensity
0.7
0.0
30.9
11.8
10.6
24.1
Depolarization Ratio
0.75
0.74
0.75
0.75
0.04
0.20
N5- D3h 1A1’(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)
Vertical Excitation Energies by EE-STEOM
Mult.
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Symmetry
E’
A1 ’
E’
E’’
E’’
E’
A1 ’
A1 ’
A2’’
E’’
E’
A1’’
E’’
E’
E’
E’
E’
A2 ’
A2 ’
A2’’
E’’
A2’’
E’’
Excitation energy (eV)
2.69
2.90
4.82
4.83
4.95
4.95
5.24
5.30
5.80
6.17
0.84
2.85
4.71
4.72
4.74
4.75
5.00
5.08
5.22
5.72
6.01
6.68
6.70
Osc. Strength
0.018
0
0.094
0.097
0.017
0.019
0
0
0.063
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Vertical Ionization Potentials by IP-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
Symmetry
E’
A2’’
E’
A1 ’
E’’
IP (eV)
3.33
4.28
7.23
9.60
10.07
Vertical Electron Affinities by EA-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
Symmetry
A1 ’
A2 ’
A2’’
E’
A1 ’
EA (eV)
5.33
5.36
5.60
5.80
6.63
29
N5- D5h 1A1’ (B3LYP/aug-cc-pVDZ)
Structure
1.3291
Vibrational frequencies
1
2
3
4
5
Symm.
Frequency
E2 ”
E2 ’
E2 ’
A1 ’
E1 ’
769.5*
1016.6
1106.5
1189.7
1243.7
IR Intensity
0.0
0.0
0.0
0.0
17.5
Raman
Intensity
0.0
2.4
0.3
38.6
0.0
Depolarization Ratio
0.75
0.75
0.75
0.05
0.65
*
out of plane bend
N5- D5h 1A1’ (CCSD(T)/aug-cc-pVTZ)
Structure
1.3294
Vibrational frequencies
1
2
3
4
5
30
Symm.
Frequency
E2 ”
E2 ’
E2 ’
A1 ’
E1 ’
754.6
1075.1
1113.3
1207.8
1276.7
IR Intensity
0.0
0.0
0.0
0.0
13.6
Raman
Intensity
0.0
1.5
1.8
47.8
0.0
Depolarization Ratio
0.75
0.75
0.75
0.04
0.57
N5- D5h 1A1’(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)
Vertical Excitation Energies by EE-STEOM
Mult.
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Singlet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Triplet
Symmetry
E1’’
E2 ’
E1 ’
E2 ’
E2’’
A2’’
A1’’
E2 ’
E1’’
A2 ’
A1 ’
A2’’
E2 ’
E1 ’
E1’’
E1 ’
E1’’
E2 ’
A2’’
E2’’
E1 ’
E1’’
E2 ’
A1’’
E2’’
Excitation energy (eV)
6.65
6.68
6.74
6.96
7.02
7.47
7.48
7.49
7.67
7.81
7.83
7.88
7.91
7.94
9.76
5.63
5.77
5.95
6.10
6.28
6.87
6.97
7.19
7.33
7.47
Osc. Strength
0
0
0
0.156
0
0.081
0
0
0
0
0.026
0
193800
0.165
0
0
0
0
0
0
0
0
0
0
0
Vertical Ionization Potentials by IP-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
Symmetry
E1 ’
E1’’
E2 ’
A1 ’
A2’’
IP (eV)
5.58
5.65
6.14
9.98
10.58
Vertical Electron Affinities by EA-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
Symmetry
A1 ’
E1 ’
E2 ’
A2’’
E2’’
EA (eV)
5.36
5.95
6.53
7.72
7.84
31
N5- D2d 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.371
1.419
62.3
58.8
Vibrational frequencies
1
2
3
4
5
6
7
32
Symm.
Frequency
IR Intensity
E
B2
B1
A1
E
A1
B2
362.7
568.1
569.8
643.7
1013.8
1155.1
1607.6
5.3
477.8
0
0
6.5
0
31.4
Raman
Intensity
4.7
5.2
0.8
54.6
33.3
14.3
2.9
Depolarization Ratio
0.75
0.75
0.75
0.30
0.75
0.00
0.75
N6+ C2h 2Ag (B3LYP/aug-cc-pVDZ)
Structure
64.83
50.34
115.72
1.4711
1.4467
1.2306
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
Symm.
Frequency
IR Intensity
Au
Bu
Au
Bg
Ag
Ag
Au
Bu
Bg
Ag
Bu
Ag
70.0
262.5
285.3
342.8
423.2
563.2
807.4
833.8
855.6
975.9
1696.3
1710.1
0.0
17.2
0.2
0.0
0.0
0.0
0.9
45.2
0.0
0.0
4.7
0.0
Raman
Intensity
0.0
0.0
0.0
0.8
3.4
6.5
0.0
0.0
16.2
14.3
0.0
75.4
Depolarization Ratio
0.41
0.74
0.73
0.75
0.19
0.54
0.73
0.52
0.75
0.30
0.58
0.09
N6+ C2h planar 2Bg (B3LYP/aug-cc-pVDZ)
Structure
167.30
109.55
1.3427
1.1233
1.2999
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
Symm.
Frequency
IR Intensity
Au
Bu
Ag
Bg
Au
Bu
Ag
Ag
Bu
Ag
Bu
Ag
131.2*
160.4
294.5
399.6
448.2
584.0
596.7
980.4
1036.0
1276.5
2191.8
2245.0
0.0
0.4
0.0
0.0
3.5
12.6
0.0
0.0
112.1
0.0
206.7
0.0
Raman
Intensity
0.0
0.0
8.0
0.2
0.0
0.0
20.3
10.6
0.0
45.3
0.0
498.6
Depolarization Ratio
0.74
0.75
0.45
0.75
0.40
0.73
0.22
0.74
0.68
0.32
0.72
0.29
*
out of plane bend
33
N6+ C2v 2Bg (B3LYP/aug-cc-pVDZ)
Structure
1.3288
119.32
1.3064
166.05
1.1268
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
Symm.
Frequency
IR Intensity
A1
A2
B2
B1
A2
A1
B2
B2
A1
A1
B2
A1
122.3*
217.1
283.9
381.4
389.5
530.7
769.1
840.9
844.6
1281.6
2138.7
2189.5
0.0
0.0
1.1
7.0
0.0
0.5
46.4
35.0
12.8
0.7
54.1
35.3
Raman
Intensity
9.5
0.0
1.0
0.1
0.3
2.7
12.3
0.5
10.7
13.8
91.8
172.2
Depolarization Ratio
0.57
0.75
0.75
0.75
0.75
0.08
0.75
0.75
0.05
0.30
0.75
0.16
*
in plane rocking
N6 D3h 1A1’ (B3LYP/aug-cc-pVDZ)
Structure
1.4840
1.5245
Vibrational frequencies
1
2
3
4
5
6
7
8
*
Symm.
Frequency
IR Intensity
E"
A1 "
E'
E'
E"
A1 '
A2 "
A1 '
589.3*
600.5
768.6
879.4
948.8
983.8
1043.9
1207.5
0.0
0.0
2.2
14.0
0.0
0.0
7.4
0.0
torsion around C3 axis
34
Raman
Intensity
0.1
0.0
4.0
5.8
2.5
37.7
0.0
25.3
Depolarization Ratio
0.75
0.75
0.75
0.75
0.75
0.09
0.75
0.12
N6 D3h 1A1’(EOM-CCSD/PBS//B3LYP/aug-cc-pVDZ)
Vertical Excitation Energies by EE-STEOM
Mult.
Singlet
Singlet
Singlet
Singlet
Singlet
Triplet
Triplet
Triplet
Triplet
Triplet
Symmetry
A1 ’
A2 ’
E’’
E’
E’’
E’
A1’’
A2’’
E’’
E’
Excitation energy (eV)
5.07
5.08
5.43
6.30
6.36
4.60
4.62
4.63
4.82
5.95
Osc. Strength
0
0
0
0.007
0
0
0
0
0
Vertical Ionization Potentials by IP-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
Symmetry
E’’
E’
A2’’
E’
A1 ’
IP (eV)
12.01
12.52
13.91
16.91
17.38
Vertical Electron Affinities by EA-EOM
Mult.
Doublet
Doublet
Doublet
Doublet
Doublet
Symmetry
A2’’
A2 ’
E’
A1 ’
A2’’
EA (eV)
0.10
0.94
1.25
1.56
2.34
35
N6 C2 book 1A (B3LYP/aug-cc-pVDZ)
Structure
1.4654
85.22
94.77
1.4997
1.2558
94.78
1.4653
109.86
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
36
Symm.
Frequency
IR Intensity
A
A
B
B
A
A
B
A
A
B
B
A
451.1*
468.4
498.7
604.2
741.9
821.7
901.9
981.1
1012.7
1108.6
1500.4
1575.0
0.0
4.6
4.8
121.3
0.0
2.8
0.0
0.0
1.3
8.3
14.9
1.9
Raman
Intensity
0.9
8.3
0.7
1.2
2.2
8.6
0.1
1.7
11.9
0.2
2.4
27.8
Depolarization Ratio
0.75
0.43
0.75
0.75
0.75
0.02
0.75
0.75
0.34
0.75
0.75
0.05
N6 D2 1A (B3LYP/aug-cc-pVDZ)
Structure
116.81
121.21
1.3185
1.3274
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
Symm.
Frequency
IR Intensity
B2
A
B3
A
B2
B3
A
B1
A
B1
B3
B2
146.9
292.6
294.6
682.9
735.3
858.0
1144.7
1109.5
1122.1
1150.4
1174.8
1369.1
0.0
0.0
8.2
0.0
6.8
9.2
0.0
0.8
0.0
1.9
0.1
2.8
Raman
Intensity
0.2
1.0
0.0
2.1
2.0
0.0
31.8
0.1
2.6
1.1
1.0
0.3
Depolarization Ratio
0.75
0.22
0.75
0.74
0.75
0.75
0.05
0.75
0.33
0.75
0.75
0.75
N6 C2h 1Ag (B3LYP/aug-cc-pVDZ)
Structure
171.59
109.25
1.4438
1.1402
1.2481
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
Symm.
Frequency
IR Intensity
Au
Bu
Ag
Au
Bg
Ag
Bu
Ag
Bu
Ag
Bu
Ag
63.0
163.4
284.5
467.4
505.4
597.9
639.6
888.5
1243.7
1300.7
2183.0
2242.0
0.2
2.5
0.0
8.2
0.0
0.0
39.9
0.0
118.5
0.0
1293.2
0.0
Raman
Intensity
0.0
0.0
14.3
0.0
0.5
21.5
0.0
23.8
0.0
37.4
0.0
159.1
Depolarization Ratio
0.70
0.74
0.50
0.49
0.75
0.19
0.44
0.53
0.49
0.21
0.75
0.29
Note : not a local minimum at higher level of theory
37
N6 C2h 1Ag (CCSD(T)/cc-pVDZ)
Structure
171.54
109.15
1.4672
1.1521
1.2614
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
Symm.
Frequency
IR Intensity
Au
Bu
Ag
Au
Bg
Ag
Bu
Ag
Bu
Ag
Bu
Ag
20.6i
158.7
276.4
456.6
504.6
584.1
631.4
882.4
1206.2
1266.4
2125.1
2182.3
0.7
2.2
0.0
12.2
0.0
0.0
27.2
0.0
97.2
0.0
1030.6
0.0
Raman
Intensity
Depolarization Ratio
N6 C2 1A (CCSD(T)/cc-pVDZ)
Structure
1.2621
1.1520
109.18
1.4675
171.44
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
38
Symm.
Frequency
IR Intensity
A
B
A
A
B
A
B
A
B
A
B
A
22.0
164.2
275.9
466.9
505.3
585.2
636.1
882.6
1202.2
1261.1
2126.0
2178.5
0.7
2.4
0.0
12.1
1.3
0.2
25.8
0.1
96.8
0.0
1000.7
4.2
Raman
Intensity
Depolarization Ratio
N6- C2 2A (B3LYP/aug-cc-pVDZ)
Structure
64.94
1.4577
106.81
1.5014
65.09
1.2676
1.4996
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
Symm.
Frequency
IR Intensity
A
B
A
A
B
B
A
A
B
A
B
A
177.8
341.6
350.6
520.4
565.8
693.4
739.2
771.2
779.6
856.9
1292.8
1546.8
0.3
2.1
0.0
4.4
62.5
306.2
3.0
0.2
301.2
0.0
1625.6
4.4
Raman
Intensity
62.1
1.0
183.5
6.7
4.1
10.2
19.8
32.7
1.9
22.0
8.2
28.3
Depolarization Ratio
0.36
0.75
0.30
0.65
0.75
0.75
0.44
0.13
0.75
0.26
0.75
0.64
N6- Cs 2A’ (B3LYP/aug-cc-pVDZ)
Structure
1.3453
126.03
1.1635
1.4405
105.04
1.2086
114.20
1.2231 174.10
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
Symm.
Frequency
IR Intensity
A"
A"
A"
A"
A"
A'
A'
A'
A'
A'
A'
A'
98.0*
169.3
320.0
392.9
415.2
511.3
661.4
882.4
1016.3
1283.2
1636.8
2145.5
0.0
5.4
1.4
4.7
4.8
5.6
109.0
32.9
192.9
11.0
390.5
936.9
Raman
Intensity
0.4
7.0
4.7
14.5
3.2
4.0
11.5
113.5
13.2
168.7
104.1
2.5
Depolarization Ratio
0.75
0.60
0.75
0.49
0.75
0.12
0.18
0.26
0.11
0.29
0.55
0.27
*
out of plane bend
39
N7+ C2v 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.3228
165.28
109.58
108.72
1.3009
1.1168
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
*
Symm.
Frequency
IR Intensity
A1
B1
A2
B2
A1
A2
B1
A1
B2
B2
A1
A1
B2
B2
A1
129.6*
194.7
218.4
259.3
452.5
505.5
537.8
543.5
718.0
868.8
1054.0
1326.3
1329.7
2310.6
2316.0
0.1
1.1
0.0
0.7
2.8
0.0
2.0
0.0
4.1
279.3
7.7
3.5
828.6
227.0
28.2
out of plane bend
40
Raman
Intensity
9.3
0.0
0.0
0.0
0.2
1.6
0.0
19.8
5.8
4.0
33.1
41.8
0.4
64.4
726.5
Depolarization Ratio
0.55
0.75
0.75
0.75
0.21
0.75
0.75
0.22
0.75
0.75
0.42
0.23
0.75
0.75
0.28
N7 Cs 2A’trigonal (B3LYP/aug-cc-pVDZ)
Structure
1.510
91.4
1.521
90.0
1.472
101.1
1.516
91.2
99.3
1.416
1.573
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Symm.
Frequency
IR Intensity
A’
A’
A”
A”
A’
A”
A’
A”
A’
A”
A’
A”
A’
A’
A’
204.4
361.4
416.8
523.9
604.9
695.2
742.5
790.5
841.0
867.8
874.1
932.7
988.4
1067.2
1088.0
14.8
13.0
0.8
0.0
7.8
0.7
5.0
4.7
0.5
0.2
4.4
0.4
12.5
0.5
1.3
Raman
Intensity
26.0
1.1
0.0
0.1
9.3
0.4
3.4
4.6
2.8
2.0
8.9
7.2
16.0
0.8
14.2
Depolarization Ratio
0.22
0.56
0.75
0.75
0.25
0.75
0.58
0.75
0.75
0.75
0.22
0.75
0.02
0.25
0.08
41
N7 Cs 2A’(B3LYP/aug-cc-pVDZ)
Structure
61.4
1.424
1.479
59.3
105.5
92.9
1.455
109.2
1.462
92.7
1.475
1.482
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
42
Symm.
Frequency
IR Intensity
A”
A’
A”
A’
A”
A’
A’
A”
A’
A”
A’
A”
A’
A’
A’
352.6
411.0
574.3
624.4
644.4
679.3
711.3
730.3
764.4
780.0
791.0
870.1
998.9
1163.5
1200.4
1.3
2.6
4.7
1.0
19.3
0.3
0.3
2.3
0.7
0.6
1.8
0.6
1.8
4.8
0.3
Raman
Intensity
0.2
0.9
2.8
4.0
3.6
2.4
8.8
5.6
2.8
2.4
8.0
0.2
3.4
26.8
13.7
Depolarization Ratio
0.75
0.25
0.75
0.16
0.75
0.42
0.40
0.75
0.32
0.75
0.47
0.75
0.15
0.03
0.02
N7 C2v 2B1 (B3LYP/aug-cc-pVDZ)
Structure
105.48
1.3998
109.18
60.92
102.77
1.4582
1.5836
1.4783
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Symm.
Frequency
IR Intensity
B1
B2
A1
A2
B1
B2
B1
A2
A1
A2
A1
B2
A1
A1
B2
275.0
334.6
503.3
512.4
584.8
656.8
696.3
738.6
780.6
879.8
927.3
935.2
962.0
1092.3
1103.7
0.1
0.5
7.0
0.0
17.3
16.4
0.6
0.0
14.6
0.0
13.5
6.5
1.0
0.0
0.0
Raman
Intensity
0.3
1.6
11.5
0.0
0.8
0.1
5.5
0.3
28.8
1.8
3.0
1.2
2.9
24.4
0.4
Depolarization Ratio
0.75
0.75
0.38
0.75
0.75
0.75
0.75
0.75
0.20
0.75
0.30
0.75
0.11
0.07
0.75
43
N7 D2d 2A2 (B3LYP/aug-cc-pVDZ)
Structure
1.322
1.474
87.0
99.5
86.4
122.1
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
44
Symm.
Frequency
IR Intensity
E
B1
A1
E
B2
E
E
A1
B2
A1
B2
116.0
348.7
458.4
506.8
778.7
940.3
1028.0
1088.3
1103.3
1290.6
1364.7
2.7
0
0
15.4
3.3
26.5
3.6
0
155.5
0
93.4
Raman
Intensity
3.8
3.1
156.5
0.1
1.7
59.8
56.2
16.3
5.7
27.0
2.7
Depolarization Ratio
0.75
0.75
0.27
0.75
0.75
0.75
0.75
0.11
0.75
0.00
0.75
N7 C2 2B (B3LYP/aug-cc-pVDZ)
Structure
167.25
122.09
120.36
1.3608
1.2676
1.1439
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Symm.
Frequency
IR Intensity
A
A
B
B
B
A
A
B
A
A
B
A
B
B
A
53.2
146.3
173.9
222.0
384.4
385.9
431.2
611.9
866.3
871.4
955.0
1086.0
1105.9
2095.9
2153.0
0.0
0.1
3.4
0.6
5.0
0.2
0.9
9.8
3.0
46.2
22.0
17.7
68.8
245.3
259.8
Raman
Intensity
2.3
9.2
4.8
5.9
0.3
0.1
0.4
1.5
11.5
4.3
1.5
39.2
17.4
48.2
52.2
Depolarization Ratio
0.72
0.41
0.75
0.75
0.75
0.54
0.56
0.75
0.24
0.16
0.75
0.12
0.75
0.75
0.09
45
N7 C2v 2B1 (B3LYP/aug-cc-pVDZ)
Structure
1.257
170.6
104.7
1.140
112.0
1.368
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
46
Symm.
Frequency
IR Intensity
A1
B1
A2
B2
B1
A2
A1
A1
B2
B2
A1
B2
A1
B2
A1
128.4
133.2
169.1
255.0
431.3
432.0
458.0
559.0
705.6
1035.0
1039.8
1188.2
1260.0
2193.0
2220.0
0.1
0.0
0.0
1.2
6.1
0.0
1.8
0.6
24.6
30.6
11.0
219.8
10.0
1285.0
90.2
Raman
Intensity
11.3
0.0
2.1
1.2
0.1
0.5
18.4
6.2
1.2
1.4
75.0
0.1
123.3
28.7
270.6
Depolarization Ratio
0.60
0.75
0.75
0.75
0.75
0.75
0.24
0.13
0.75
0.75
0.42
0.75
0.28
0.75
0.29
N7 Cs 2A’(B3LYP/aug-cc-pVDZ)
Structure
1.2897
1.3381
109.49
126.50
1.4763
1.3730
109.11
120.30
119.46
1.1687
104.31
1.3284
1.2916
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Symm.
Frequency
IR Intensity
A’
A”
A”
A”
A’
A”
A”
A’
A’
A’
A’
A’
A’
A’
A’
121.4
200.5
217.1
289.9
581.8
666.4
752.1
863.3
1035.7
1071.7
1091.5
1143.6
1292.7
1411.6
1823.6
1.4
1.0
7.6
48.8
40.0
0.2
0.0
63.5
8.3
16.5
14.2
4.8
0.2
8.2
24.7
Raman
Intensity
0.1
1.2
7.2
9.9
1.7
0.0
0.0
31.5
0.1
1.4
2.8
0.3
16.1
0.3
30.0
Depolarization Ratio
0.75
0.75
0.34
0.22
0.72
0.75
0.75
0.22
0.46
0.74
0.18
0.34
0.10
0.31
0.21
47
N7- C2v 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.2228
174.46
115.78
102.70
1.4149
1.1694
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
48
Symm.
Frequency
IR Intensity
B1
A2
A1
B2
B1
A2
A1
A1
B2
A1
B2
B2
A1
B2
A1
78.9
108.3
126.2
247.8
272.6
302.8
426.8
549.5
700.7
929.1
937.0
1257.3
1301.2
2132.1
2143.4
2.9
0.0
1.5
25.0
14.4
0.0
2.0
2.4
179.1
3.1
140.1
126.8
15.4
1638.3
110.1
Raman
Intensity
0.0
6.7
11.7
7.4
3.2
30.5
37.3
58.5
1.5
380.2
0.1
0.1
602.3
0.3
207.8
Depolarization Ratio
0.75
0.75
0.66
0.75
0.75
0.75
0.31
0.39
0.75
0.33
0.75
0.75
0.30
0.75
0.25
N8 Oh 1A1g (B3LYP/aug-cc-pVDZ)
Structure
1.5218
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Symm.
Frequency
IR Intensity
B2u
A1u
Eg
B1g
A2u
Eu
Eg
B1g
Eu
B1u
A1g
A1g
B2g
B2u
525.5*
525.7
738.0
738.4
798.8
799.3
856.6
856.6
924.9
925.0
936.3
1033.3
1033.5
1132.5
0.0
0.0
0.0
0.0
10.5
10.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Raman
Intensity
0.0
0.0
0.5
0.5
0.0
0.0
2.9
2.9
0.0
0.0
54.2
13.5
13.5
0.0
Depolarization Ratio
0.00
0.00
0.75
0.75
0.20
0.75
0.75
0.75
0.00
0.00
0.00
0.75
0.75
0.60
*
torsion around C4 axis
49
N8 D2h 1A1g (B3LYP/aug-cc-pVDZ)
Structure
60.38
117.32
1.4621
59.23
1.4793
1.4536
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
50
Symm.
Frequency
IR Intensity
Au
B1u
B3g
Ag
B1g
B2g
B3u
B2g
Au
Ag
B1u
B2u
B2u
B1g
Ag
B3u
B3u
Ag
195.5*
344.4
490.8
532.3
642.8
661.1
666.9
706.8
716.4
727.8
731.3
733.8
785.1
873.2
922.9
1067.6
1187.5
1228.0
0.0
6.3
0.0
0.0
0.0
0.0
1.3
0.0
0.0
0.0
1.0
0.3
6.5
0.0
0.0
5.7
0.2
0.0
Raman
Intensity
0.0
0.0
8.7
15.2
3.0
5.1
0.0
7.2
0.0
16.7
0.0
0.0
0.0
7.4
14.2
0.0
0.0
43.8
Depolarization Ratio
0.00
0.00
0.75
0.22
0.75
0.75
0.75
0.75
0.48
0.33
0.71
0.42
0.70
0.75
0.02
0.00
0.75
0.02
N8 C2h ladder 1Ag (B3LYP/aug-cc-pVDZ)
Structure
95.43
84.57
104.82
90.00
1.4933
1.5296
1.4499
1.2552
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Symm.
Frequency
IR Intensity
Au
Bu
Au
Bg
Ag
Bu
Au
Bg
Ag
Ag
Bg
Au
Bu
Ag
Au
Bg
Bu
Ag
253.6*
304.9
429.4
444.4
447.0
740.4
762.7
790.6
817.1
853.8
900.3
938.5
958.4
1014.9
1103.8
1145.0
1543.8
1572.4
0.6
6.2
1.5
0.0
0.0
3.2
1.6
0.0
0.0
0.0
0.0
0.3
48.4
0.0
5.4
0.0
7.9
0.0
Raman
Intensity
0.0
0.0
0.0
3.1
9.4
0.0
0.0
1.1
9.9
19.1
1.3
0.0
0.0
5.9
0.0
0.5
0.0
27.6
Depolarization Ratio
0.00
0.00
0.00
0.75
0.34
0.00
0.00
0.75
0.10
0.14
0.75
0.00
0.68
0.66
0.58
0.75
0.66
0.06
*
torsion around C2 axis
51
N8 C2v ring 1A1 (B3LYP/aug-cc-pVDZ)
Structure
117.47
117.48
1.2410
1.4285
1.2409
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
52
Symm.
Frequency
IR Intensity
A2
A2
A1
A1
B1
B2
B2
B1
A2
A1
B2
B1
A2
A2
B2
B1
A1
A1
238.2
310.8
337.8
369.1
551.3
551.3
575.4
575.4
665.9
720.9
743.9
743.9
851.7
1035.3
1534.1
1534.4
1540.5
1604.8
0.0
0.0
0.0
2.3
6.3
6.4
13.5
13.6
0.0
0.0
14.2
14.1
0.0
0.0
3.2
3.2
0.0
11.4
Raman
Intensity
8.3
0.0
6.5
3.4
0.0
0.0
0.7
0.7
0.2
12.1
2.7
2.7
0.1
0.0
1.0
1.0
16.8
0.6
Depolarization Ratio
0.75
0.75
0.24
0.75
0.75
0.75
0.75
0.75
0.75
0.00
0.75
0.75
0.75
0.75
0.75
0.75
0.01
0.75
N8 C2v 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.1553
1.5713
1.1380
178.56
96.66
106.04
1.2474
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Symm.
Frequency
IR Intensity
B1
B2
A2
A1
B2
A1
A1
B1
A2
B1
B2
A1
B2
B2
A1
A1
B2
A1
55.1
83.2
107.7
112.2
277.4
314.6
388.8
505.5
549.6
557.1
599.4
735.9
815.4
1191.9
1249.5
1909.8
2174.8
2196.5
0.4
177.8
0.0
0.0
206.0
8.3
1.2
2.1
2.5
7.5
185.6
5.2
463.3
413.4
2.7
75.0
1109.6
48.6
Raman
Intensity
0.1
6.8
1.9
7.6
20.2
106.7
128.7
0.1
0.2
0.0
4.0
6.9
0.2
0.3
9.9
185.5
24.4
397.6
Depolarization Ratio
0.75
0.75
0.75
0.52
0.75
0.27
0.25
0.75
0.75
0.75
0.75
0.15
0.75
0.75
0.51
0.54
0.75
0.32
53
N8 C1 ZZE 1A (B3LYP/aug-cc-pVDZ)
Structure
172.62
1.2554
1.1361
168.41
1.1334
109.95
1.2614
1.2554
116.12
118.26
123.14
1.4152
1.2428
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
54
Symm.
Frequency
IR Intensity
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
57.7
96.9
141.0
211.5
307.0
475.6
511.5
541.5
593.6
603.4
804.3
827.6
935.9
1159.6
1238.8
1534.4
2197.2
2244.3
6.1
0.7
0.2
3.1
0.0
36.5
5.4
3.0
1.0
69.1
89.4
67.8
178.6
156.0
186.6
72.2
446.8
647.0
Raman
Intensity
2.1
6.4
4.8
3.5
7.4
5.6
1.0
1.3
9.3
16.6
6.7
1.7
7.4
18.6
5.9
21.7
77.9
183.0
Depolarization Ratio
0.65
0.67
0.65
0.23
0.40
0.47
0.75
0.52
0.16
0.41
0.47
0.71
0.28
0.10
0.18
0.18
0.48
0.26
N8 C2h ZEZ 1Ag (B3LYP/aug-cc-pVDZ)
Structure
1.1326
115.47
170.42
1.2546
114.89
1.2720
1.3893
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Symm.
Frequency
IR Intensity
Au
Bu
Ag
Bg
Au
Bu
Ag
Bg
Au
Bu
Ag
Bu
Ag
Bu
Ag
Ag
Bu
Ag
51.2
118.7
161.4
258.0
365.2
371.6
431.5
522.8
526.1
697.3
837.6
1017.3
1019.4
1062.1
1119.3
1473.4
2194.6
2229.9
0.5
1.4
0.0
0.0
0.1
6.8
0.0
0.0
8.8
173.0
0.0
37.8
0.0
537.1
0.0
0.0
979.0
0.0
Raman
Intensity
0.0
0.0
22.6
0.4
0.0
0.0
4.0
1.0
0.0
0.0
46.6
0.0
14.1
0.0
121.0
383.5
0.0
244.1
Depolarization Ratio
0.47
0.00
0.45
0.75
0.75
0.00
0.74
0.75
0.60
0.53
0.52
0.54
0.12
0.50
0.27
0.30
0.66
0.34
55
N8 Cs 1A’(B3LYP/aug-cc-pVDZ)
Structure
1.2527
114.25
1.2738
1.3986
108.92
115.80
110.04
1.2578
170.17
170.67
1.1324
1.1351
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
56
Symm.
Frequency
IR Intensity
A
A
A
A
A”
A’
A
A
A”
A’
A’
A’
A’
A’
A’
A’
A’
A’
92.6
98.4
200.2
205.6
358.9
383.8
464.6
518.6
528.2
637.9
793.9
982.7
1047.7
1093.0
1232.1
1513.9
2199.8
2238.2
0.0
1.3
0.4
0.8
0.2
7.4
14.5
3.0
4.6
40.8
52.2
19.5
230.2
50.5
253.2
1.1
630.0
467.4
Raman
Intensity
1.0
16.2
3.7
0.4
0.2
6.2
4.4
0.2
0.0
18.6
22.0
11.3
18.4
104.2
44.4
298.5
101.2
124.3
Depolarization Ratio
0.75
0.56
0.74
0.75
0.75
0.36
0.20
0.75
0.75
0.39
0.26
0.69
0.22
0.32
0.19
0.32
0.73
0.16
N8 D2h planar 1A1g (B3LYP/aug-cc-pVDZ)
Structure
141.33
109.33
113.92
1.3357
103.70
1.3244
1.3363
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Symm.
Frequency
IR Intensity
B3u
Au
B2u
B2g
Ag
B3u
B1g
B3g
B1u
B2u
Ag
B1u
Ag
B3g
Ag
B2u
B1u
B3g
252.5*
376.1
469.1
686.1
692.7
702.1
725.9
842.2
968.2
1022.8
1050.9
1110.5
1179.6
1180.3
1291.8
1316.8
1319.4
1400.1
10.4
0.0
0.7
0.0
0.0
0.1
0.0
0.0
6.2
72.1
0.0
3.6
0.0
0.0
0.0
7.1
10.7
0.0
Raman
Intensity
0.0
0.0
0.0
0.0
14.4
0.0
0.0
10.4
0.0
0.0
27.2
0.0
20.4
5.3
5.4
0.0
0.0
1.5
Depolarization Ratio
0.75
0.33
0.33
0.75
0.15
0.00
0.75
0.75
0.24
0.33
0.07
0.53
0.09
0.75
0.67
0.34
0.58
0.75
*
out of plane bend
57
N8 C2h EEE 1Ag (B3LYP/aug-cc-pVDZ)
Structure
1.2590
1.2505
109.96
170.38
108.23
1.3965
1.1344
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
*
Symm.
Frequency
IR Intensity
Au
Bu
Bg
Ag
Au
Bu
Ag
Au
Bg
Ag
Bu
Bu
Ag
Ag
Bu
Ag
Bu
Ag
67.1*
115.4
200.7
204.8
340.1
393.4
462.1
521.6
523.3
657.6
733.5
958.7
1091.4
1230.1
1230.2
1555.8
2216.4
2247.5
0.3
1.8
0.0
0.0
1.2
30.4
0.0
6.9
0.0
0.0
38.0
98.3
0.0
0.0
706.8
0.0
1811.2
0.0
out of plane bend
58
Raman
Intensity
0.0
0.0
0.1
29.5
0.0
0.0
5.0
0.0
0.6
40.9
0.0
0.0
279.4
106.2
0.0
393.4
0.0
374.4
Depolarization Ratio
0.58
0.00
0.75
0.46
0.56
0.00
0.09
0.75
0.75
0.40
0.00
0.43
0.34
0.25
0.50
0.33
0.48
0.32
N8 C2v EZE 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.2415
1.4156
1.1343
115.44
109.86
1.2562
171.47
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Symm.
Frequency
IR Intensity
B1
A1
A2
B2
A1
A2
B1
A2
A1
B2
B2
A1
B2
A1
B2
A1
B2
A1
76.2
113.2
130.2
228.5
285.5
521.7
538.6
583.6
589.8
616.2
716.9
878.3
957.2
1229.8
1235.4
1576.7
2218.0
2248.2
0.0
0.0
0.0
1.1
1.1
0.0
7.9
0.0
0.3
160.8
102.7
21.1
472.0
13.7
394.4
55.8
1822.4
1.7
Raman
Intensity
0.0
0.4
2.4
4.6
23.6
0.0
0.0
1.9
42.7
0.2
2.2
50.3
0.3
24.9
0.5
18.6
1.5
487.3
Depolarization Ratio
0.75
0.59
0.75
0.75
0.30
0.75
0.75
0.75
0.22
0.75
0.75
0.50
0.75
0.21
0.75
0.17
0.75
0.30
59
N8 Cs pentagonal 1A’ (B3LYP/aug-cc-pVDZ)
Structure
1.3217
1.3876
1.3074
1.2606
103.90
111.14
109.31
169.36
113.33
1.3451
109.32
103.92
126.64
1.3285
1.1329
1.3058
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
*
Symm.
Frequency
IR Intensity
A"
A'
A"
A'
A"
A'
A"
A"
A'
A'
A'
A'
A'
A'
A'
A'
A'
A'
44.0*
156.3
275.7
402.0
486.2
542.1
693.0
749.1
783.2
984.2
1070.5
1117.7
1147.1
1201.6
1236.4
1373.3
1406.9
2250.8
0.0
0.4
3.3
1.6
3.2
0.1
0.6
0.0
10.1
50.1
0.5
1.1
2.2
43.4
1.0
8.5
71.1
408.5
out of plane bend
60
Raman
Intensity
0.3
6.3
1.2
3.4
0.1
5.3
0.0
0.0
4.3
26.5
0.5
14.1
3.3
4.4
6.9
42.9
60.9
78.1
Depolarization Ratio
0.75
0.52
0.75
0.51
0.75
0.10
0.75
0.75
0.75
0.22
0.41
0.20
0.32
0.11
0.13
0.26
0.24
0.32
N8- C2h 2Bg (B3LYP/aug-cc-pVDZ)
Structure
1.2346
1.3443
115.31
172.73
1.1632
105.61
1.3948
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Symm.
Frequency
IR Intensity
Au
Bu
Au
Bg
Ag
Bg
Au
Bu
Ag
Ag
Bu
Bu
Ag
Bu
Ag
Ag
Bu
Ag
63.8
110.8
139.3
165.5
202.0
271.4
272.2
376.9
434.7
630.9
708.2
897.4
962.0
1198.3
1206.6
1281.6
2115.3
2144.6
0.1
2.7
4.2
0.0
0.0
0.0
13.7
20.2
0.0
0.0
144.4
63.1
0.0
45.9
0.0
0.0
2458.2
0.0
Raman
Intensity
0.0
0.0
0.0
0.3
32.2
71.9
0.0
0.0
4.3
267.0
0.0
0.0
1741.7
0.0
823.3
290.1
0.0
307.1
Depolarization Ratio
0.60
0.75
0.24
0.75
0.59
0.75
0.53
0.72
0.30
0.32
0.71
0.58
0.32
0.52
0.32
0.38
0.44
0.24
61
N8- C2h ZEZ 2Bg (B3LYP/aug-cc-pVDZ)
Structure
119.54
168.78
1.3326
1.1614
111.44
1.2568
1.3807
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
62
Symm.
Frequency
IR Intensity
Au
Au
Bu
Bg
Ag
Au
Bg
Bu
Ag
Bu
Ag
Bu
Ag
Bu
Ag
Ag
Bu
Ag
18.3
90.7
117.7
153.4
168.2
276.7
299.8
364.7
420.2
655.6
827.6
982.3
994.9
1024.7
1047.5
1247.3
2057.7
2099.2
2.8
4.6
3.3
0.0
0.0
0.9
0.0
30.9
20.1
3.3
0.0
211.4
0.0
37.7
0.0
0.0
1634.6
0.0
Raman
Intensity
0.0
0.0
0.0
26.6
54.6
0.0
0.6
0.0
20.1
0.0
9.2
0.0
167.7
0.0
1357.5
5.4
0.0
12.6
Depolarization Ratio
0.74
0.62
0.75
0.75
0.43
0.68
0.75
0.70
0.61
0.45
0.52
0.45
0.39
0.36
0.31
0.23
0.65
0.36
N9+ C2v rings 1A1 (B3LYP/aug-cc-pVDZ)
Structure
128.72
115.05
123.09
121.86
104.96
1.4724
111.23
1.3304
1.4213
1.2410
1.3061
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Symm.
Frequency
IR Intensity
A2
B1
B2
B1
A1
B2
A1
A2
B1
A2
A1
B2
B2
A1
A1
A1
B2
A1
B2
A1
B2
116.0
178.6
328.8
382.8
433.8
526.7
532.4
599.4
722.2
725.7
757.0
810.3
1018.3
1045.5
1108.2
1170.4
1180.9
1281.2
1371.6
1505.2
1551.7
0.0
5.0
5.4
8.3
64.0
1.9
0.3
0.0
0.2
0.0
7.7
0.0
1.0
8.4
94.6
23.0
7.0
0.3
2.0
13.1
0.1
Raman
Intensity
0.1
0.0
0.0
0.8
4.1
2.2
6.5
0.0
0.0
0.0
7.7
0.0
2.7
14.4
44.8
12.3
1.6
2.4
0.0
11.4
0.4
Depolarization Ratio
0.75
0.75
0.75
0.75
0.09
0.75
0.72
0.75
0.75
0.75
0.66
0.75
0.75
0.08
0.14
0.12
0.75
0.06
0.75
0.06
0.75
63
N9+ C2v 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.3174
1.3281
108.23
164.92
105.15
109.83
1.2985
1.1170
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
64
Symm.
Frequency
IR Intensity
A1
B1
A2
B2
B1
A2
A1
A1
B2
B1
A2
B2
A1
B2
A1
B2
B2
A1
A1
B2
A1
93.8
107.8
144.5
189.3
288.8
299.6
304.7
433.9
525.4
526.1
545.3
694.0
715.3
869.7
936.1
1196.9
1325.7
1350.9
1393.7
2298.9
2305.6
1.0
0.0
0.0
3.8
2.4
0.0
2.8
0.0
17.2
1.6
0.0
91.8
1.4
1088.2
9.6
1718.3
11.0
0.2
5.8
389.4
33.3
Raman
Intensity
12.2
0.1
0.0
0.0
0.0
2.4
0.5
30.1
5.0
0.1
0.9
0.1
42.1
21.0
105.4
0.1
0.2
9.0
232.9
133.5
1691.4
Depolarization Ratio
0.52
0.75
0.75
0.75
0.75
0.75
0.29
0.21
0.75
0.75
0.75
0.75
0.37
0.75
0.35
0.75
0.75
0.18
0.31
0.75
0.29
N9 C2v rings 2B1 (B3LYP/aug-cc-pVDZ)
Structure
127.80
111.77
125.00
105.36
123.24
1.2935
111.35
1.3246
1.3500
1.3775
1.3168
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Symm.
Frequency
IR Intensity
B1
A2
B1
B2
A1
B2
A2
A2
A1
B1
B2
A1
B2
A1
B2
A1
A1
B2
A1
B2
A1
104.1
187.6
363.3
421.0
549.3
578.5
591.5
692.4
695.4
718.2
823.4
884.3
951.1
1050.5
1065.8
1138.7
1179.1
1212.4
1260.1
1377.8
1394.4
3.0
0.0
13.3
1.3
0.5
10.4
0.0
0.0
17.2
0.4
37.4
27.0
12.1
0.2
0.1
2.2
15.1
0.0
0.2
0.5
23.5
Raman
Intensity
0.0
0.1
0.3
0.2
8.9
14.1
0.0
0.0
8.6
0.0
0.1
39.0
0.3
5.2
3.9
12.0
9.7
0.4
19.0
1.2
19.2
Depolarization Ratio
0.75
0.75
0.75
0.75
0.17
0.75
0.75
0.75
0.72
0.75
0.75
0.10
0.75
0.09
0.75
0.21
0.75
0.75
0.10
0.75
0.42
65
N9 C2v 2A2 (B3LYP/aug-cc-pVDZ)
Structure
1.3058
169.80
1.2632
106.97
111.33
108.28
1.1355
1.3682
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
66
Symm.
Frequency
IR Intensity
B1
A1
A2
B2
A2
A1
B1
A1
B1
A2
B2
A1
A2
B2
B2
A1
A1
B2
A1
B2
A1
88.3
95.3
124.1
186.8
267.2
300.5
309.0
439.9
483.5
489.8
532.8
703.8
718.8
1008.6
1044.9
1133.7
1210.0
1239.1
1356.9
2197.6
2222.2
0.2
0.1
0.0
0.4
0.0
1.8
0.1
0.1
5.8
0.0
17.2
47.4
3.9
167.9
211.0
9.8
6.4
353.5
2.2
1906.9
99.9
Raman
Intensity
0.1
1.2
2.2
1.7
0.0
25.4
0.0
11.7
0.1
0.7
0.1
3.8
37.4
0.0
18.4
3.5
246.2
2.5
1.0
53.1
681.1
Depolarization Ratio
0.75
0.56
0.75
0.75
0.75
0.35
0.75
0.12
0.75
0.75
0.75
0.75
0.42
0.75
0.75
0.59
0.29
0.75
0.38
0.75
0.30
N9- C2 1A (B3LYP/aug-cc-pVDZ)
Structure
172.72
118.77
111.07
113.90
1.2973
1.4371
1.2403
1.1536
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Symm.
Frequency
IR Intensity
A
A
B
B
A
A
B
A
B
A
B
B
A
B
A
A
B
B
A
B
A
32.6
81.3
125.7
150.3
287.3
299.1
318.0
437.2
448.3
454.5
464.4
756.7
763.8
853.1
960.0
1176.9
1191.6
1310.6
1311.4
2112.9
2146.1
0.0
0.7
2.2
2.0
0.8
1.7
2.5
1.0
7.2
0.0
11.5
127.4
45.6
44.3
0.7
29.7
6.2
461.2
32.3
278.6
729.4
Raman
Intensity
2.4
13.6
0.8
22.1
2.0
14.5
1.5
22.3
1.6
1.5
0.1
22.8
3.8
26.3
135.8
411.7
78.2
2.3
47.1
50.3
20.8
Depolarization Ratio
0.75
0.34
0.75
0.75
0.56
0.29
0.75
0.64
0.75
0.03
0.75
0.75
0.51
0.75
0.31
0.16
0.75
0.75
0.52
0.75
0.61
67
N9- C2v 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.2285
173.55
1.2933
113.24
1.1572
105.89
113.12
1.4400
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
68
Symm.
Frequency
IR Intensity
B1
A2
A1
B2
A1
A2
B1
A1
A2
B1
B2
B2
A1
B2
A1
B2
A1
A1
B2
B2
A1
58.6
92.0
95.6
185.9
275.1
284.8
341.4
394.3
450.2
451.7
557.2
644.9
712.9
861.4
996.6
1269.6
1274.9
1327.2
1382.9
2142.2
2166.2
0.6
0.0
0.1
15.7
2.5
0.0
0.8
0.3
0.0
9.4
94.0
45.8
3.3
49.2
1.8
55.3
10.7
4.6
890.0
2695.6
117.7
Raman
Intensity
0.0
10.2
4.3
4.1
114.8
5.5
0.8
41.0
4.8
0.2
2.6
1.1
135.9
0.1
762.7
0.0
755.5
291.3
2.8
7.8
1.3
Depolarization Ratio
0.75
0.75
0.72
0.75
0.38
0.75
0.75
0.49
0.75
0.75
0.75
0.75
0.39
0.75
0.28
0.75
0.29
0.38
0.75
0.75
0.65
N9- Cs 1A’(B3LYP/aug-cc-pVDZ)
Structure
1.3356
1.3375
1.2269
109.62 104.27
1.3158
128.96
109.89
113.90
1.1593
106.70
111.79
1.3452
104.43
1.3282
172.98
1.4140
1.3389
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Symm.
Frequency
IR Intensity
A”
A”
A’
A’
A’
A”
A’
A’
A”
A”
A’
A’
A’
A’
A’
A’
A’
A’
A’
A’
A’
63.0
103.6
135.3
282.2
309.9
397.4
462.1
613.0
714.5
729.8
842.6
951.2
1005.8
1054.0
1098.8
1137.8
1235.8
1284.1
1341.6
1398.4
2164.4
0.8
0.1
3.4
4.8
4.9
4.5
1.5
52.8
1.4
0.4
13.2
35.2
2.0
55.0
5.5
68.1
0.5
22.4
5.2
474.3
1127.8
Raman
Intensity
5.1
3.0
6.2
22.6
0.2
3.0
3.0
3.8
0.0
0.1
34.5
154.9
86.6
88.0
11.0
10.7
15.4
252.4
81.9
34.2
1.0
Depolarization Ratio
0.75
0.75
0.75
0.35
0.75
0.75
0.19
0.65
0.75
0.75
0.41
0.35
0.37
0.18
0.74
0.70
0.06
0.30
0.34
0.30
0.74
69
N10+ C1 2A (B3LYP/aug-cc-pVDZ)
Structure
1.2768
117.47
1.3743
112.41
1.1277
168.96
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
70
Symm.
Frequency
IR Intensity
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
52.4
82.8
83.0
152.7
152.8
213.2
314.3
392.4
392.4
445.1
448.3
448.4
507.2
689.4
689.4
825.9
1084.6
1084.7
1209.2
1259.8
1259.9
2244.2
2244.3
2251.9
1.3
0.0
0.0
0.6
0.6
0.9
3.4
0.6
0.6
8.1
1.2
1.2
0.0
0.2
0.2
0.1
19.4
19.4
3.4
340.8
340.0
390.5
389.1
14.0
Raman
Intensity
0.8
6.7
6.7
6.5
6.5
11.8
0.4
4.4
4.4
0.0
1.1
1.2
18.2
5.7
5.7
2.0
21.4
21.4
1.4
39.9
40.0
105.8
105.8
506.6
Depolarization Ratio
0.74
0.75
0.75
0.75
0.75
0.10
0.04
0.75
0.75
0.75
0.75
0.75
0.08
0.75
0.75
0.00
0.75
0.75
0.01
0.75
0.75
0.75
0.75
0.11
N10+ C1 chain 2A (B3LYP/aug-cc-pVDZ)
Structure
1.3019
166.64
1.3295
109.63
1.2571
1.3325
112.65
116.38
116.35
112.68
1.2570
1.1210
1.1210
1.3296
109.64
166.64
1.3019
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Symm.
Frequency
IR Intensity
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
39.8
73.5
147.8
153.2
177.7
184.2
241.3
275.9
373.3
437.7
472.0
507.3
521.1
654.1
693.4
970.3
975.6
1101.1
1179.1
1268.8
1310.8
1492.4
2279.9
2289.1
1.6
1.0
0.1
22.2
0.0
0.0
7.7
1.2
0.0
0.0
158.5
0.0
17.6
0.4
0.0
78.4
0.0
0.0
1577.2
55.6
421.7
352.1
971.6
0.0
Raman
Intensity
0.0
0.0
31.8
0.1
2.9
1.2
0.0
0.0
49.6
3.6
0.0
19.3
0.0
0.0
343.7
0.0
8.1
34.9
0.0
55.6
421.7
0.0
0.0
1924.7
Depolarization Ratio
0.37
0.67
0.42
0.44
0.74
0.36
0.73
0.44
0.30
0.44
0.37
0.36
0.57
0.28
0.32
0.69
0.75
0.60
0.24
0.31
0.31
0.34
0.32
0.32
71
N10 C2v 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.4132
57.56
1.4611
120.47
1.5675
110.53
1.4620
117.07
1.4971
92.02
1.5325
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
72
Symm.
Frequency
IR Intensity
A2
B1
A1
B1
B2
B2
A1
A2
B1
A1
A2
A2
A1
A2
B1
B2
A1
B1
B2
B2
A2
A1
B2
A1
274.0
319.7
416.4
426.9
520.2
529.5
607.1
607.2
627.4
664.4
726.5
750.9
759.6
807.3
807.7
810.0
860.1
873.3
909.3
980.0
1040.8
1042.3
1064.7
1121.4
0.0
0.2
23.2
12.7
0.0
1.3
12.9
0.0
1.4
7.5
0.0
0.0
0.2
0.0
1.3
0.6
1.3
0.1
0.1
1.4
0.0
1.2
0.9
2.8
Raman
Intensity
0.4
0.6
11.2
1.8
4.6
1.3
3.5
2.2
1.0
5.6
5.8
1.0
31.2
0.0
0.8
1.2
18.4
1.2
0.0
0.0
0.1
7.2
0.0
19.4
Depolarization Ratio
0.75
0.75
0.61
0.75
0.75
0.75
0.58
0.75
0.75
0.51
0.75
0.75
0.04
0.75
0.75
0.75
0.00
0.75
0.75
0.75
0.75
0.34
0.75
0.01
N10 D5h 1A1’(B3LYP/aug-cc-pVDZ)
Structure
1.5207
1.4984
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Symm.
Frequency
IR Intensity
E2’’
A1’’
E2 ’
E1’’
E2’’
A2’’
E2 ’
A1 ’
E1 ’
E1’’
E2 ’
E1 ’
A1 ’
E2’’
470.3
642.5
664.9
713.2
715.6
719.2
773.0
839.4
854.9
874.7
954.0
962.1
1017.0
1049.6
0.0
0.0
0.0
0.0
0.0
10.9
0.0
0.0
3.5
0.0
0.0
1.5
0.0
0.0
Raman
Intensity
0.0
0.0
0.6
2.8
0.0
0.0
6.2
53.2
0.0
1.3
0.3
0.0
18.8
0.0
Depolarization Ratio
0.75
0.74
0.75
0.75
0.75
0.75
0.75
0.02
0.33
0.75
0.75
0.28
0.35
0.75
73
N10 Cs 1A’7-ring (B3LYP/aug-cc-pVDZ)
Structure
1.486
1.498
87.2
117.3
114.0
1.452
1.565
1.437
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
74
Symm.
Frequency
IR Intensity
A’’
A’
A’’
A’
A’
A’’
A’
A‘
A‘’
A‘
A‘’
A‘
A‘’
A‘’
A‘
A‘’
A‘
A‘’
A‘
A‘’
A‘
A’
A’
A’
174.0
279.8
440.9
489.0
524.7
540.0
589.8
622.6
648.9
708.4
721.9
742.8
754.4
786.1
815.1
913.0
927.2
967.7
971.2
992.9
995.6
1076.6
1082.0
1214.4
0.6
3.4
0.4
2.8
2.6
0.5
4.2
0.1
0.1
0.8
0.4
12.2
16.2
0.2
3.3
0.8
5.2
0.4
7.1
0.2
0.5
1.4
0.7
0.6
Raman
Intensity
0.2
1.0
1.1
5.3
7.5
3.0
6.5
9.3
1.3
7.8
8.8
3.4
1.6
1.3
14.0
1.3
3.2
0.6
0.4
1.3
1.3
28.6
1.4
21.7
Depolarization Ratio
0.75
0.43
0.75
0.59
0.11
0.75
0.43
0.32
0.75
0.55
0.75
0.73
0.75
0.75
0.01
0.75
0.73
0.75
0.72
0.75
0.42
0.01
0.42
0.02
N10 C2 1A (B3LYP/aug-cc-pVDZ)
Structure
1.489
1.510
1.447
60.4
1.494
1.430
1.542
1.509
1.415
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Symm.
Frequency
IR Intensity
A
A
B
B
A
A
B
A
B
A
B
B
A
A
A
B
B
B
A
A
A
B
A
B
302.7
411.6
492.7
505.6
605.7
622.5
627.1
705.0
715.4
736.6
738.5
778.6
779.0
785.8
854.2
861.4
883.8
934.9
946.1
971.5
987.7
1054.9
1074.1
1094.5
0.0
0.1
3.9
6.5
5.8
0.6
12.5
2.5
0.0
0.0
6.2
1.0
1.4
0.2
0.0
2.4
2.5
3.5
8.7
0.4
0.3
0.7
0.9
5.1
Raman
Intensity
0.2
1.0
0.0
0.2
7.9
14.3
0.0
6.3
5.6
7.0
2.1
7.0
16.0
0.6
2.2
2.6
1.0
0.5
2.0
2.8
4.9
0.7
29.8
0.2
Depolarization Ratio
0.42
0.71
0.75
0.75
0.75
0.21
0.75
0.09
0.75
0.24
0.75
0.75
0.04
0.75
0.75
0.75
0.75
0.75
0.41
0.09
0.05
0.75
0.01
0.75
75
N10 C2v 1A1 (B3LYP/aug-cc-pVDZ)
Structure
1.429
1.494
93.2
103.0
1.495
1.464
106.0
108.5
59.7
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
76
Symm.
Frequency
IR Intensity
A2
A1
B1
A2
B2
A1
B1
B2
A1
A2
A1
B2
A2
A1
B1
A1
A
A
B2
B1
A2
A1
B2
A1
189.1
232.3
368.4
490.8
529.7
538.0
583.4
677.2
702.6
712.5
753.2
779.7
799.5
833.1
849.1
878.3
889.0
896.7
1005.5
1014.8
1047.2
1064.8
1194.0
1199.2
0.0
1.2
1.4
0.0
4.1
0.0
0.0
1.5
1.0
0.0
1.2
4.9
0.0
0.1
1.6
3.5
9.6
0.7
4.0
0.8
0.0
0.4
0.4
0.8
Raman
Intensity
0.1
1.3
0.9
0.3
0.9
5.7
8.3
12.5
7.8
6.2
17.8
0.0
5.6
1.6
0.0
4.1
0.1
0.1
0.0
0.3
1.6
6.2
0.2
49.9
Depolarization Ratio
0.75
0.26
0.75
0.75
0.75
0.20
0.75
0.75
0.08
0.75
0.17
0.75
0.75
0.61
0.75
0.24
0.75
0.75
0.75
0.75
0.75
0.06
0.75
0.03
N10 C1 1A (B3LYP/aug-cc-pVDZ)
Structure
1.136
1.460
108.6
104.8
171.5
1.256
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Frequency
IR Intensity
27.4
28.8
41.9
139.3
214.1
214.4
405.7
405.8
484.1
505.4
535.9
536.2
542.5
684.8
685.4
870.0
871.4
910.3
1188.8
1189.0
1242.0
2207.4
2207.6
2228.1
0.1
0.1
0.1
0.2
1.0
1.1
3.1
3.0
4.6
0.2
2.9
2.8
0.0
34.8
33.6
70.3
71.0
0.2
158.7
158.7
45.1
550.8
552.4
237.9
Raman
Intensity
7.6
7.6
4.4
5.9
2.2
2.2
2.1
2.1
0.3
31.8
0.3
0.3
0.2
8.8
8.6
18.0
17.8
8.1
0.6
0.6
10.9
83.4
82.9
137.5
Depolarization Ratio
0.75
0.75
0.72
0.42
0.75
0.75
0.75
0.75
0.15
0.03
0.75
0.75
0.74
0.75
0.75
0.75
0.75
0.10
0.75
0.75
0.00
0.75
0.75
0.06
77
N10 C3 1A (B3LYP/aug-cc-pVDZ)
Structure
1.4612
1.4674
106.59
103.54
1,2297
111.60
106.21
1.4610
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
78
Symm.
Frequency
IR Intensity
E
A
E
A
E
A
A
E
E
A
E
A
A
E
E
A
200.3
372.3
467.7
492.9
543.7
551.2
670.6
713.2
780.2
830.6
899.0
966.8
993.2
1061.9
1601.2
1622.5
2.3
3.5
34.6
0.0
18.3
0.0
7.3
16.1
0.0
0.6
10.7
0.0
0.0
4.6
20.3
20.2
Raman
Intensity
2.2
8.6
0.6
0.0
6.3
0.0
13.4
1.7
0.3
13.0
0.9
0.0
0.4
0.4
0.6
27.9
Depolarization Ratio
0.75
0.25
0.75
0.05
0.75
0.00
0.00
0.75
0.75
0.00
0.75
0.23
0.60
0.75
0.75
0.05
N10 C1 1A n5-ring (B3LYP/aug-cc-pVDZ)
Structure
104.6
1.293
109.1
1.333
1.128
118.7
1.382
1.364
111.6
114.9
1.338
109.5
168.3
1.254
115.6
1.290
1.294
104.2
1.362
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Frequency
IR Intensity
30.7
104.8
117.4
207.9
262.3
373.8
409.0
506.2
538.7
674.6
697.4
748.6
897.7
939.7
953.3
1048.6
1081.6
1100.5
1183.9
1248.7
1352.4
1411.1
1519.1
2228.5
30.7
104.8
117.4
207.9
262.3
373.8
409.0
506.2
538.7
674.6
697.4
748.6
897.7
939.7
953.3
1048.6
1081.6
1100.5
1183.9
1248.7
1352.4
1411.1
1519.1
2228.5
Raman
Intensity
0.0
2.1
1.7
0.5
0.2
0.2
0.3
8.7
4.6
112.9
0.3
0.0
226.2
51.3
1.8
149.1
45.6
1.9
19.0
53.1
10.1
10.2
63.5
340.6
Depolarization Ratio
0.75
0.58
0.74
0.35
0.75
0.72
0.75
0.20
0.26
0.33
0.72
0.75
0.30
0.14
0.40
0.41
0.58
0.24
0.61
0.63
0.25
0.36
0.31
0.34
79
N10 Cs 1A’(B3LYP/aug-cc-pVDZ)
Structure
1.3334
1.2919
104.71
1.3824
1.2503
118.68
110.71
109.16
1.3657
109.48
1.3783
104.30
1.2690
108.61
128.96
109.62
169.45
1.3396
1.1300
1.3657
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
80
Symm.
Frequency
IR Intensity
A”
A”
A’
A”
A’
A’
A’
A’
A’
A”
A”
A”
A’
A’
A’
A’
A’
A’
A’
A’
A’
A’
A’
A’
46.7
104.8
162.2
184.4
247.3
391.4
402.5
476.0
529.1
697.3
704.0
748.9
823.8
900.5
1035.7
1086.1
1097.3
1188.7
1199.1
1250.1
1352.7
1417.3
1566.1
1149.6
0.0
0.6
2.2
1.0
0.4
3.2
0.0
30.3
3.0
0.3
4.5
0.0
63.9
144.6
35.1
26.7
7.4
138.3
220.8
99.7
34.4
3.2
77.3
713.0
Raman
Intensity
0.4
9.3
0.9
0.2
5.6
2.0
1.2
6.2
0..3
0.0
18.9
0.0
19.2
74.4
22.2
4.0
48.6
108.9
33.9
37.1
278.8
7.2
458.6
236.3
Depolarization Ratio
075
0.54
0.75
0.75
0.55
0.06
0.75
0.35
0.75
0.75
0.33
0.75
0.31
0.26
0.45
0.33
0.25
0.37
0.17
0.64
0.26
0.40
0.32
0.32
N10 D2d 1A1 (B3LYP/aug-cc-pVDZ)
Structure
104.15
1.3528
1.3756
109.52
123.66
1.3418
1.2843
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Symm.
Frequency
IR Intensity
B1
E
A1
E
E
A2
B1
A1
B2
E
B2
A1
E
B2
A1
B2
E
A1
66.1
108.4
428.9
434.4
675.1
738.8
763.4
853.4
874.6
1052.2
1086.6
1095.1
1135.7
1140.0
1258.6
1306.7
1432.9
1512.2
0.0
3.6
0.0
0.4
0.0
0.0
0.0
0.0
54.8
0.5
52.6
0.0
1.4
2.5
0.0
8.5
5.9
0.0
Raman
Intensity
3.5
1.4
12.1
0.0
0.1
0.0
0.0
10.7
0.3
2.0
1.1
21.3
0.1
0.0
18.2
6.5
0.2
85.8
Depolarization Ratio
0.75
0.75
0.22
0.75
0.75
0.13
0.75
0.12
0.75
0.75
0.75
0.11
0.75
0.75
0.08
0.75
0.75
0.20
81
N10- D2h 2B3u (B3LYP/aug-cc-pVDZ)
Structure
102.38
1.3245
103.04
1.3178
111.11
1.3644
1.3302
Vibrational frequencies
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
82
Symm.
Frequency
IR Intensity
Au
B3u
B2g
B2u
Ag
B3g
B3u
B2g
Au
B1g
B1u
B2u
B3g
Ag
B3g
B1u
B2u
B1u
B2u
Ag
B1u
Ag
B3g
Ag
60.2
122.4
181.5
187.3
431.0
454.8
531.6
536.7
694.2
704.5
857.5
933.0
966.0
998.3
1078.8
1079.8
1082.0
1125.7
1142.3
1172.1
1212.1
1212.8
1313.6
1580.5
0.0
7.0
0.0
0.8
0.0
0.0
5.4
0.0
0.0
0.0
238.5
22.7
0.0
0.0
0.0
113.3
1.2
40.2
111.5
0.0
3.7
0.0
0.0
0.0
Raman
Intensity
0.0
0.0
0.3
0.0
73.8
18.0
0.0
1.9
0.0
0.0
0.0
0.0
64.9
46.3
33.8
0.0
0.0
0.0
0.0
44.4
0.0
134.0
89.3
226.9
Depolarization Ratio
0.09
0.75
0.75
0.54
0.29
0.75
0.75
0.75
0.22
0.75
0.35
0.37
0.75
0.13
0.75
0.70
0.50
0.38
0.74
0.50
0.35
0.13
0.75
0.36
Absolute and Relative Electronic Energies
Symm.
N2 +
N2
N3 +
N3 +
N3
N3 N3 N3 N4 +
N4
N4
N4
N4
N4
N4 N4 N5 +
N5 +
N5 +
N5
N5 N5 N5 N6 +
N6 +
N6 +
N6
N6
N6
N6
N6 N6 N7 +
N7
N7
N7
N7
N7
N7
N7
N7 -
D∞ h
D∞ h
D∞ h
D3h
D∞ h
C2v
D3h
D∞ h
D2h
C2v
D2d
Td
D2h
C2h
D2h
C2h planar
D3h
D2d
C2v
D2d
D5h
D2d
D3h
C2h
C2h planar
C2v
D3h
C2 book
D2
C2h
C2
Cs
C2v
Cs trigonal
Cs 2a’
C2v
D2d
C2
C2v 2B1
Cs
C2v
Electronic Energy
(Hartree)
-108.9618387
-109.5428265
-163.6959494
-163.7113127
-164.1646313
-164.1484239
-164.1490584
-164.2636758
-218.417642
-218.7456892
-218.7947152
-218.8071775
-218.8083236
-218.8638079
-218.9100606
-218.9155753
-272.9557462
-273.1399788
-273.3220783
-273.4599408
-273.4886156
-273.5199278
-273.7950941
-327.8754231
-328.0422025
-328.0259405
-328.1452071
-328.2808122
-328.3378906
-328.376902
-328.3169611
-328.4277673
-382.8027423
-382.8444877
-382.8942315
-382.9012522
-382.9391571
-383.0713444
-383.0926083
-383.1155117
-383.1502583
Relative Energy
(kcal mol-1)
364.6
0.0
356.3
346.6
62.2
72.3
71.9
0.0
312.5
106.6
75.8
68.0
67.3
32.5
3.5
0.0
526.7
411.1
296.8
210.3
192.3
172.7
0.0
346.6
241.9
252.1
177.3
92.2
56.4
31.9
69.5
0.0
218.1
191.9
160.7
156.3
132.5
49.5
36.2
21.8
0.0
83
Symm.
N8
N8
N8
N8
N8
N8
N8
N8
N8
N8
N8
N8
N8 N8 N9 +
N9 +
N9
N9
N9 N9 N9 N10+
N10+
N10
N10
N10
N10
N10
N10
N10
N10
N10
N10
N10-
84
Oh
D2h
C2h ladder
C2v ring
C2v
C1 ZZE
C2h ZEZ
Cs
D2h planar
C2h EEE
C2v EZE
Cs pentagonal
C2h
C2h ZEZ
C2v rings
C2v
C2v rings
C2v
C2
C2v
Cs
C1
C1 chain
C2v
D5h
Cs 7-ring
C2
C2v
C3
C1 C3-like
C1 N5 ring
Cs
D2d
D2h
Electronic Energy
(Hartree)
-437.501925
-437.5647199
-437.6709384
-437.7811599
-437.8106544
-437.8370619
-437.8406469
-437.8445796
-437.8474594
-437.8499492
-437.8515448
-437.8684041
-437.8861288
-437.886331
-492.1849952
-492.2606899
-492.5170542
-492.5603617
-492.6445501
-492.6559203
-492.6857145
-546.9662818
-546.9736078
-546.9492043
-546.9528884
-546.9818793
-547.0238618
-547.0468873
-547.2419122
-547.2753055
-547.3297971
-547.3347569
-547.3502493
-547.4195383
Relative Energy
(kcal mol-1)
241.2
201.8
135.2
66.0
47.5
30.9
28.7
26.2
24.4
22.8
21.8
11.2
0.1
0.0
314.2
266.7
105.8
78.7
25.8
18.7
0.0
284.4
279.8
295.1
292.8
274.6
248.3
233.8
111.5
90.5
56.3
53.2
43.5
0.0
Heats of Formation (Direct method)
Symm.
N2
N3
N3 N3 N3 N4
N4
N4
N4
N4
N4 N4 N5
N5 N5 N6
N6
N6
N6
N6 N6 N7
N7
N7
N7
N7
N7
N7
N7 -
Description
D∞ h linear
D∞ h linear
C2v
D3h
D∞ h
C2v
butterfly
D2d
puckered ring
Td
tetrahedron
D2h
rectangle
C2h
linear E
D2h
rectangular
C2h
planar
D2d
D3h
bipyramid
D5h
pentagon
D3h
prism
C2
Book
D2
Twisted 6-ring
C2h
linear E
C2
linked triangles
Cs
chain (W-like)
Cs trigonal
Cs 2A’
C2v
log carrier
D2d
C2
linear ZZ
C2v 2B1
Cs
5-ring + chain
C2v
chain (W-like)
Electronic and
Thermal
Enthalpies
(Hartree)
-109.533594
-164.151467
-164.137515
-164.138027
-164.249409
-218.730393
-218.778917
-218.789892
-218.789855
-218.846737
-218.892177
-218.899292
-273.438591
-273.467253
-273.76942
-328.117214
-328.251513
-328.309463
-328.346304
-328.291329
-328.399466
-382.813472
-382.862886
-382.870344
-382.906138
-383.037366
-383.057369
-383.080314
-383.116003
∆H f
(kcal mol-1)
0.0
93.8
102.5
102.2
32.3
211.8
181.3
174.4
174.5
138.8
110.3
105.8
248.7
230.7
41.1
304.1
219.8
183.5
160.4
194.9
127.0
348.5
317.5
312.8
290.3
208.0
195.4
181.0
158.6
Isp
(s)
0
395.9
414.0
413.3
232.4
515.2
476.8
467.6
467.7
417.1
371.8
364.2
499.4
481.0
203.0
504.1
428.6
391.6
366.1
403.5
325.8
499.6
476.9
473.3
456.0
386.0
374.2
360.1
337.1
85
Symm.
N8
N8
N8
N8
N8
N8
N8
N8
N8
N8
N8
N8
N8 N8 N9
N9
N9 N9 N9 N10
N10
N10
N10
N10
N10
N10
N10
N10
N10
N10-
86
Description
Oh
cube
D2h
linked butterflies
C2h
ladder
C2v
8-ring (~D2d)
C2v
W-shape
C1
linear ZZE
C2h
linear ZEZ
Cs
linear ZEE
D2h
8N-pentalene
C2h
linear EEE
C2v
linear EZE
Cs
5-ring + chain
C2h
chain
C2h
ZEZ
C2v
ann. 5,6-rings
C2v
linear EEEE
C2
twisted W
C2v
chain
Cs
5-ring + chain
C2v
log carrier
D5h
prism
Cs 7-ring
C2
C2v
C1 C3-like
C1 N5-ring
C3
cap
Cs
5-ring + EE chain
D2d
linked 5-rings
D2h
two 5-rings
perpendicular
Electronic and
Thermal
Enthalpies
(Hartree)
-437.462235
-437.528306
-437.630591
-437.741496
-437.770227
-437.795911
-437.799618
-437.803286
-437.804109
-437.80826
-437.80992
-437.82524
-437.847229
-437.847614
-492.470881
-492.514436
-492.599421
-492.610201
-492.638218
-546.902183
-546.903006
-546.933852
-546.975286
-546.998285
-547.223217
-547.276300
-547.280799
-547.295231
-547.366753
∆H f
(kcal mol-1)
Isp
(s)
422.7
381.2
317.0
247.4
229.4
213.3
211.0
208.7
208.1
205.5
204.5
194.9
181.1
180.8
271.0
243.7
190.4
183.6
166.0
481.7
481.1
461.8
435.8
421.4
280.2
246.9
514.7
488.8
445.7
393.8
379.2
365.6
363.6
361.6
361.2
358.9
358.0
349.5
336.9
336.7
388.6
368.5
325.7
319.8
304.1
491.4
491.2
481.2
467.4
459.6
374.8
351.8
244.1
235.0
190.1
349.8
343.3
308.8
Heats of Formation (Quasi-isodesmic method)
Symm.
N2 +
N3 +
N3 +
N3 N3 N3 N4 +
N4 N4 N5 +
N5 +
N5 +
N5 N5 N5 N6 +
N6 +
N6 +
N6 N6 N7 +
N7 N8 N8 N9 +
N9 +
N9 N9 N9 N10+
N10+
N10-
D∞ h
D∞ h
D3h
C2v
D3h
D∞ h
D2h
D2h
C2h
D3h
D2d
C2v
D5h
D2d
D3h
C2h
C2h
C2v
C2
Cs
C2v
C2v
C2h
C2h
C2v
C2v
C2
C2v
Cs
C1
C1
D2h
Electronic
∆H f
and Thermal (kcal mol-1)
Enthalpies
(Hartree)
linear
-108.953227 348.4
linear
-163.6836
371.4
triangle
-163.698884 361.8
-164.137515 100.2
triangle
-164.138027
99.9
linear
-164.249409
30.0
rectangle
-218.400373 402.9
rectangle
-218.892177 107.9
planar
-218.899292
103.4
-272.936024
548.0
-273.116535
434.8
V-like
-273.296533
321.81
pentagon
-273.76942
38.7
-273.498245
38.7
bipyramid
-273.467253
228.3
linked triangles
-327.848745 456.6
planar
-328.012140 354.0
U-like
-327.996654 363.8
linked triangles
-328.291329 192.5
chain (W-like)
-328.399466 124.6
W-like
-382.766541 361.9
W-like
-383.116003 156.3
Chain
-437.847229 178.7
chain ZEZ
-437.847614 178.5
fused 5-ring + 6-ring -492.138314 463.7
chain
-492.213996 416.2
twisted W
-492.599421 188.0
chain
-492.610201 181.2
5-ring + chain
-492.638218 163.7
propeller-like
-546.913656 458.5
linear
-546.922489 452.9
log carrier
-547.366753 187.8
Description
Isp
(s)
934.6
787.8
777.6
409.2
408.5
223.8
710.6
367.8
360.1
741.3
660.3
568.1
197.0
197.0
478.5
617.7
543.9
551.3
401.1
322.7
509.2
334.6
334.7
334.4
508.2
481.5
323.6
317.8
301.9
479.4
476.5
306.8
1
A value of 351.1 kcal mol-1 was obtained with the G2 method by K. O. Christe, W. W. Wilson, J. A. Sheehy and J.
A. Boatz, Angew. Chem. Int. Ed. 1999, 38, 2004.
87
Quasi-isodesmic reactions2
x− 1
[NH4]+ +
N2 à Nx+ + 2 H2
2
x− 1
N2 à Nx- + H2
[NH2]- +
2
2
∆Hf(NH4+) = 150.6 kcal mol-1
∆H f(NH2-) = 27.0 kcal mol-1
Experimental heats of formation are from H.H. Michels, J. A. Montgomery Jr., K. O. Christe and D. A. Dixon, J.
Phys. Chem. 1995, 99, 187.
88
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Acknowledgements
This work was supported by the AFSOR-DARPA under grant number F49620-98-1-0477.
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