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Azanaphthalenes
JOURNAL
OF MOLECULAR
SPECTROSCOPY
(1966)
25-33
19,
Azanaphthalenes Part I. Huckel Orbital S. C. WAIT, Department
Energy
of Chemistry,
levels,
JR.
wave functions
JOHN
ASD
Rensselaer
Calculations* W. WEsLEYt
Polytechnic
Institute,
and charge densities
Troy, New I7ark
are reported
for 74 aza-
naphthalenes. Calculations were performed using the Huckel method. Comparison of the lowest singlet-singlet transition w-ith that calculated by the Pariser-Parr method is given for 21 compounds. INTROl>UCTION
The prediction of spectral hransitions and chemical properties of heterocyclic molecules is receiving increasing attention. Recent works by Streitweiser (1)) Pullman and Pullman (Z), and a monograph edited by Lowdin and Pullman (3) summarize the current status of both a priori and semiempirical approaches to these problems. As part of a research program designed to study the spectral properties of heterocyclic molecules related to naphthalene, calculations of the energy levels and charge densities have been performed for naphthalene and all 74 azanaphthalenes which do not, have nitrogen atoms along the rent’ral bond. HUCKEL
ORBITAL
CALCULATIONS
The basis of the Huckel orbital m&hod is well known (l-3) and will not be repeated here. The assumptions made in the present work are (i) the Coulomb integrals, olc are the same for all carbon atoms, (ii) the Coulomb integrals for all the nitrogen atoms are given by o(N = (Ye+ 0.5p [the value 0.5 seems to be a good starting point in the calculat,ions and has been extensively used (1, ,$)I, (iii) the resonance integrals, &c , pCN , and PNN all have t’he same value. Symmetry factoring of the 10 X 10 energy matrix was not undertaken prior to solution of the eigen-problem on an IRM 709-O computer. The energy levels calculated are given in Table 1 and t,he charge densities are given in Table 2.l The numbering of the atoms is given in Fig. 1. For t,h(> sake of presenbing a syst’e* This investigation was supported in part by Public Health Service Research Grant! Number CA-07993 from the National Cancer Institute. t Participant in the National Science Foundation Research Participation for High School Teachers Program at Rensselaer Polytechnic Institute in 1965. 1Complete tables including orbital coefficients are available from the authors. 25
WAIT,
26
JR. AND
WESLEY
Table 1 Energy Levels by Huckel Orbital Calculation
*
-2.303
-2.267
-2.282
-2.251
-2.247
-2.229
-2.226
-2.243
-2.244
-1.618
-1.593
-1.549
-1.531
-1.507
-1.550
-1.577
-1.533
-1.522
-1.565
-1.303
-1.232
-1.290
-1.212
-1.229
-1.186
-1.141
-1.209
-1.222
-1.145
-l.coo
-1.000
-0.920
-0.919
-0.917
-1.OQO
-1.000
-0.912
-0.918
-1.000
-0.618
-0.527
-0.576
-0.454
-0.495
-0.414
-0.450
-0.498
-0.484
-0.460
0.618
0.703
0.646
0.714
0.732
0.764
0.807
0.738
0.727
0.812
1.000
I.000
1.078
1.081
1.078
1.000
l.COO
1.086
1.079
1.000
1.303
1.384
1.319
1.386
1.435
1.515
1.430
1.386
1.410
1.459
1.618
1.669
1.733
1.776
1.750
1.686
1.746
1.794
1.781
1.712
2.303
2.363
2.340
2.410
2.399
2.414
2.410
2.391
2.392
2.416
-123
-124
-125
-126
-127
-128
-135
-23
26
-27
-2.230
-2,266
-2.259 -2.260 -2.235 -2.214 -2.207 -2.225 -2.226 -2.211 -2.203
-1.482
-1.477
-1.464
-1.453
-1.468
-1.522
-1.471
-1.446
-1.500
-1.493
-1.279
-1.254
-1.284
-1.210
-1.180
-1.115
-1.158
-1.211
-1.131
-1.139
-0.794
-0.874
-0.837
-0.786
-0.916
-0.906
-0.870
-0.833
-0.915
-0.916
-0.559
-0.522
-0.547
-0.447
-0.353
-0.393
-0.417
-0.424
-0.388
-0.414
0.699
0.666
0.683
0.762
0.777
0.822
0.742
0.746
0.819
0.832
1.123
1.196
1.147
1.128
1.083
1.087
1.196
1.162
1.082
1.083
1.343
1.323
1.363
1.444
1.532
1.431
1.386
1.426
1.465
1.495
1.826
1.833
1.828
1.840
1.779
1.856
1.884
1.872
1.823
1.816
2.389
2.370
2.371
2.457
2.460
2.449
2.432
2.433
2.456
2.441
-136
137 138 ---------
145
146
235
236
1234
1236
1235
-2.221
-2.221
-2.206
-2.185
-2.201
-2.224
-2.241
-2.202
-2.206
-2.188
-1.433
-1.424
-1.485
-1.532
-1.488
-1.464
-1.391
-1.396
-1.382
-1.446
-1.208
-1.210
-1.138
-1.081
-1.169
-1.199
-1.255
-1.173
-1.154
-1.110
-0.836
-0.865
-0.911
-1.000
-0.910
-0.792
-0.747
-0.773
-0.747
-0.778
-0.473
-0.443
-0.436
-0.359
-0.384
-0.474
-0.515
-0.323
-0.414
-0.380
0.782
0.747
0.848
0.892
0.794
0.794
0.727
0.805
0.801
0.875
1.154
1.200
1.094
l.ooo
1.088
1.124
1.230
1.136
1.232
1.128
1.456
1.438
1.480
1.550
1.520
1.417
1.365
1.566
1.457
1.496
1.858
1.855
1.810
1.755
1.812
1.886
1.916
1.847
1.940
1.916
2.422
2.423
2.445
2.459
2.438
2.431
2.412
2.513
2.473
2.489
+ Ener ies in terms of Beta. The lowest energy levels are at the bottom of each co9urn for a given molecule.
27
AZANAPHTHALENES
Table 1 (Continued)
1238
1245
-2.207
-2.192
-2.167
-2.184
-1.349
-1.427
-1.457
-1.S98
1237
1246 ---e
1248
1256
-2.184
-2.168
-1.388
-1.450
1247
1267
1257
1258
-2.185
-2.181
-2.163
-2.204
-1.467
-1.427
-1.475
-1,388 -1.158
-1.203
-1.119
-1.071
-1.139
-1.168
-1.077
-1.038
-1.112
-1.063
-0.729
-0.786
-0.906
-0.862
-0.833
-0.914
-0.868
-0.830
-0.898
-0.745
-0.366
-0.304
-0.403 0.803
-0.410
-0.384
-0.308
-0.315
-0.330
-0.296
-0.330
0.784
0.881
0.907
0.799
0.820
0.899
0.829
0.861
0.900
1.251
1.136
1.094
1.200
1.167
1.084
1.197
1.163
1.088
1.233
1.454
1.496
1,554
1.532
1.555
1.586
1.431
1.500
1.551
1.427
1.935
1.902
1.858
1.890
1.883
1.837
1.953
1.918
1.873
1.971
2.474
2.493
2.496
2.478
2.478
2.498
2.480
2.474
2.491
2.463
1268
1278 ---------1357
1358
1367
1458
1467
2367
45678
35678 -2.170
-2.185
-2.191
-2.177
-2.158
-2.199
-2.137
-2.178
-2.220
-2.154
-1.412
-1.419
-1.391
-1.455
-1.345
-1.500
-1.428
-1.281
-1.385
-1.307
-1.100
-1.126
-1.135
-1.077
-1.197
-1.000
-1.147
-1.252
-1,OM)
-1.139
-0.864
-0.822
-0.861
-0.910
a.747
-1.000
-0.790
-0.655
-0.771
-0.728
-0.357
-0.331
-0.372
-0.332
-0.438
-0.281
-0.368
-0,500
-0.273
-0.292
0.848
0.831
0.845
0.919
0.826
1.000
0.864
0.781
0.939
0.837
1.204
1.169
1,215
1.103
1.232
1.000
1.126
1.307
1.139
1.252
1.480
1.483
1,520
1.583
1.461
1.637
1.532
1.375
1.600
1.572
1.908
1,919
1,890
1.842
1.951
1.780
1.918
2.000
1.921
1.948
2.479
2.488
2.467
2.484
2.456
2.500
2.470
2.444
2.543
2.527
34568 34567 ----~--~~~
34678
34578
24670
24578
24568
24567
23678
23578
-2.143
-2.170
-2.165
-2.142
-2.160
-2.137
-2.137
-2.163
-2.183
-2.159
-1.377
-1.334
-1.381
-1.394
-1.328
-1.360
-1.356
-1.317
-1.272
-1.315
-1.062
-1.097
-1.036
-1.006
-1.110
-1.071
-1.059
-1.100
-1.153
-1.134
-0.819
-0.729
-0.744
-0.862
-0.728
-0.829
-0.860
-0.746
-0.654
-0.745
-0.249
-0.320
-0.322
-0.267
-0.346
-0.287
-0.263
-0.355
-0.395
-0.305
0.920
0.884
0.891
0.909
0.900
0.969
0.918
0.934
0.855
0.877
1.170
1.252
1.233
1.204
1.254
1.167
1.219
1.232
1.309
1.234
1.592
1.500
1.500
1.556
1.527
1.602
1.597
1.527
1.465
1.556
1.944
1.995
2.010
1.960
1.983
1.928
1.923
1.977
2.030
1.987
2.524
2.519
2.513
2.522
2.508
2.516
2.518
2.512
2.490
2.503
WAIT, JR. AND WESLEY
28
Table 1 (Continued)
14678
14578
345678
245678
235678
234678
234578
234568
234567
145678
-2.140
-2.116
-2.127
-2.121
-2.143
-2.141
-2.117
-2.118
-2.146
-2.099
-1.404
-1.424
-1.306
-1.266
-1.191
-1.271
-1.304
-1.284
-1.212
-1.359
-1.046
-1.000
-1.005
-1.055
-1.131
-1.029
-1.006
-1.044
-1.090
-0.972
-0.778
-0.897
-0.728
-0.727
-0.651
-0.653
-0.744
-0.727
-0.650
-0.769
-0.295
-0.229
-0.218
-0.244
-0.275
-0.310
-0.240
-0.234
-0.312
-0.201 1.058
0.944
0.998
0.973
0.960
1.313
1.315
1.234
1.255
1.309
1.140
1.580
1.531
1.602
1.607
1.531
1.659
1.995
2.046
2.073
2.027
2.020
2.065
1.961
2.564
2.559
2.546
2.540
2.550
2.552
2.545
2.573
134568 ----
2345678
1345678
12345678
-2.091
-2,091
-2.099
-2.072
-2.050
-1.335
-1.328
-1.180
-1.245
-1.118
-0.953
-1.am
-1.005
-0.951
-0.940
-0.860
-0.811
-0.649
-0.727
-0.647
-0.171
-0.183
-0.207
-0.148
-0.118
l.ooO
1,047
1.023
1.069
1.118
1.228
1.170
1.316
1.256
1.318
1.650
1.672
1.625
1.681
1.697
1.972
1.964
2.092
2.043
2.118
2.559
2.560
2.585
2.594
2.623
0.969
l.OQO
0.947
0.982
0.905
11136
1.106
1.252
1.254
1.587
1.647
1.601
1.622
1.947
1.882
2.020
2.525
2.532
matic set of results, all molecules are numbered in the same manner regardless of the preferred order. The energy levels in Table 1 are presented as illustrated below for 1,2_diazanaphthalene. 12 -2.251 -1.531 - 1.212 -0.919 -0.454 0.714 1.081 1.386 1.776 2.410
Highest energy unoccupied orbital
Occupied orbitals in the ground state Lowest energy occupied orbital
Table 2 * Charge Densities from Huckel Orbital Calculation
2
-12
-13
-17
1
1.000
1.216
1.000
0.896 1.198 1.100 0.841 0.902 0.899 0.881 0.895
l.OOC
1.008 0.947 0.950 1.206 0.902 0.993
0.895
-14
-15
-16
Naphthalene
-18
1.119 1.223 1.151 1.205 1.219 1.201 1.226 0.883
1.009 0.993 1.011
1.000
0.932
1.000
0.988 1.003 0.991
1.000
1.003 0.984 0.987 1.003 0.907 0.899 1.201 0.949
l.ooO
0.984
1.000
1.013 0.984 0.998 1.016 1.002 0.945
1.021 0.909
l.COO
0.957 1.004 0.957 0.934 0.958 0.958
0.932 0.961 0.912
1.000
1.002 0.976 0.977 1.005 0.958
1.009 0.930 0.030
1.151 0.945 0.917 0.935 0.922
0.973 1.002
1.000 0.983 0.969
1.205 0.885 0.997 0.922
0.987 0.993
0.930
1.011
1.183 0.883
0.958 1.005 0.977
1.226
1.003
-23
-26
0.899
0.898
1.151
1,183 1.198 1.043 1.108 1.103
1.084 1.099 1.086 0.844 0.950 0.936 0.951
1.191
27 --
123
124 -
125 -
126 --
127
128
-135
0.880 1.119 1.049 1.107 1.122 1.102 1.132 1.213
1.151
0.946
0.899
0.993 1.012 0.039
1.159 0.951
0.921 0.941 0.927
0.842
0.986
0.898
1.005 1.208 0.885 l.ooO 0.923
1.191
0.983
1.183 0.930 0.986 0.969 0.002
0.930 1.151 0.849 0.935
1.012 0.976
1.186 0.934 0.996 0.898
0.983
0.946 1.198 0.969 0.986
0.992 0.930
0.906
0.993 0.880 0.999 0.986
0.929
0.980
0.900
0.980
0.980 0.952 0.980
-136
-137
1.007 0.937 0.958 0.958 0.934
138 -
145 -
0.931 0.934
146 -
235
1.182 0.870 0.977
1.007 0.891 1.214 0.948 0.961 0.914
0.900 0.954
236
1234
1.226
1.209 1.233 1.140 1.154 0,890 0.902
0.825
0.841 0.826 0.906 0.886
1.206
1.191 1.208 0.888
0.902
0.816
0.831 0.822
1.163
1.136 0.912 0.885
0.869
0.982 0.907
1.217 0.897 1.203 0.883 0.909
1.152
1.201
0.948
1.169 0.869 0.996 0.933 0.992
1.024
0.912
0.910
0.937 0.889
1.009
0.981
1.228 0.934 0.959
1236
1235
1.058 1.122 1.109
1.135 1.051 1.026 1.046
1.134 1.150 1.051 1.151 1.136
0.915
1.011 0.884
0.934
0.978 0.962
1.187 0.881
1.058 0.824
1.183 0.969
0.851
0.872 1.193 1.186 0.882
0.929 0.969 0.915 0.977
1.011 0.920 0.995 0.989
1.008 0.932
0.934 0.981
0.913 0.937
1.007 0.914 0.961
0.955 0.933
0.935 0.983 0.933 0.984 0.936
See Figure 1 and text for numbering of atoms in molecules.
WAIT,JR.
30
AND
WESLEY
Table 2 (Continued) 1246
1247
1248
1256
1257
1258
1267
1237
1238 --
1.104 1.043
1.131 1.039 1.051 1.032 1.063 1.109 1.091 1.121 1.105 1.027 1.111 1.090 1.107 1.093 1.085 1.102 1.088 1.084
1.137
1.152 0.835 0.849 0.834 0.852 0.935 0.921 0.938 0.934
0.839
0.830 1.171 1.142 1.162 1.147 0.934 0.954 0.940 0.924
0.985
0.910 1.220 0.898 1.014 0.936 1.109 1.216 1.142 0.891
1245
0.932
0.995 0.865 1.170 0.917 0.978 1.085 0.828 0.887 1.138
1.169
0.866 0.995 0.933 1.186 0.879 0.935 1.190 0.883 1.134
0.894
1.215 0.918 0.995 0.878 1.204 0.934 0.824 1.149 0.897
0.940
0.892 0.959 0.936 0.961 0.916 0.936 0.962 0.916 0.937
0.957
0.981 0.887 0.934 0.909 0.931 0.936 0.911 0.935 0.957.
1268
1278 1357 ----w-e--
1.135
1.116 1.199 1.224 1.210 1.153 1.139 0.888 0.921 0.998
1358
1367
1458
1467
2367
45678 35678
1.071
1.082 0.844 0.829 0.825 0.889 0.886 1.133 0.978 0.917
0.951
0.939 1.177 1.194 1.190 0.889 0.886 1.133 0.863 1.170
0.910
0.928 0.843 0.831 0.818 1.153 1.139 0.888 1.206 0.881
0.818
0.928 1.199 1.126 0.876 1.153 0.902 0.888 1.071 1.040
1.194
0.939 0.844 0.905 1.152 0.889 1.137 1.133 1.036 1.051
0.824
1.082 1,177 0.872 1.118 0.889 1.137 1.133 1.054 1.034
1.222
1.116 0.843 1.166 0.914 1.153 0.902 0.888 1.048 1.059
0.892
0.916 0.938 0.891 0.911 0.915 0.937 0.958 0.933 0.912
0.982
0.955 0.938 0.963 0.985 0.915 0.937 0.958 0.891 0.937
34568
34567 34678 34578 24678 24578 24568 24567 23678 23578 Pm-------
0.942
0.913 0.937 0.921 0.826 0.813 0.829 0.807 0.899 0.885
0.923
0,937 0.921 0.938 1.177 1.193 1.179 1.193 1.118 1.137
1.084
1.069 1.085 1.070 0.828 0.812 0.827 0.811 1.136 1.121
1.103
1.118 1.094 1.123 1.201 1.227 1.212 1.222 0.878 0.903
1.044
1.117 0.833 1.156 0.852 1.174 1.065 1.134 0.826 1.145
1.089
1.025 1.136 0.833 1.122 0.820 1.077 1.010 1.135 0.834
0.837 1.150
1.140 1.029 1.093 1.046 1.110 0.852 1.151 1.026 1.090 0.827 1.111 1.037 1.095 1.023 1.131 0.816 1.107 1.035
0.910
0.958 0.915 0.937 0.940 0.962 0.934 0.985 0.914 0.939
0.918
0.895 0.938 0.891 0.913 co.865 0.894 0.869 0.959 0.910
31
AZANAPHTHALENEY
Table 2 (Continued)
1467n
14578 --
345678
245670 --
235678
234678 234778 --------
234560
234567
145676
1.151
1.138
0.924
0.813
0.888
0.835
0.822
0.039
0.816
1.141
('.869
0.885
0.923
1.179
1.121
1.122
1.139
1.125
1.138
0.868
0.087
0.869
1.068
0.811
1.121
1.029
1.012
1.029
1.010
0.868
1.129
1.155
1.106
1.214
0.888
1.098
1.124
1.107
1,120
1.141
0.041
1.160
1.053
1.073
1.043
0.835
1,158
1.047
1.120
1.06a
1.139
0.838
1.034
1.019
1.034
1.122
0.820
1.074
1.010
1.039
1.030
1.096
1.037
1.054
1.034
1.029
1.093
0.837
1.138
1.039
1.122
1.052
1.046
1.031
1.043
1.098
1.024
1.134
0.816
1.060
0.894
0.917
0.913
0.936
0.913
0.916
0.940
0.912
0,961
0.692
0.938
0.889
0.894
0.869
0.913
0.916
0.869
0.897
0.872
0.892
134578
134568
2345678
1345678
12345678
1.144
1.163
0.822
1.148
1.063
0.836
0.821
1.125
0.820
1.020
1.076
1.091
1.011
1.074
1.020
1;051
1.032
1.110
1.034
1.043
1.144
1.032
1.056'
1.041
1.043
0.836
1.091
1.019
1.037
1.020
1.076
0.821
1.037
1.021
1.020
1.051
1.163
1.032
1.060
1.043
0.892
0.866
0.915
0.869
0.073
0.092
0.919
0.873
0.896
0.073
The entries, k, in Table 1 can t’hen be converted to energy using the relation E = cx + A$. Since both cx and /3 are negative, the most positive value of 1;corresponds t’o the lowest orbital energy. The charge densities in Tablr 2 start with aton 1 :lt the top and end with atom 10 at t,hc bottom. DISCXMSION
Analysis of the results from several viewpoints can be undert,aken. It sl~oulcl be emphasized first, however, that, although Huckel orbital calculations providr a reasonable starting point, further and more refined calculations are needed to draw quantitat.ive conclusions. Such Aculations, including the effect of the lone pair electrons on the nitrogen atoms, arc being undertaken. Favini ri al. (4) have reported calculations for 31 azines including 21 azanaphthalent~s using the Pariser-Pan and Pople method. The energies of the lowest l7r - IT2 electronic transitions calculated by Favini et al. (4) are compared with those from the present work in Table 3. The value of p was chosen as -3.32( e\-. 10 l!mke the Huckel orbital calculation for 1-azanaphthalene agree
32
WAIT,
JR. AND
WESLEY
8
1
7
2
FIG. 1. Numbering
of atoms in azanaphthalenes. TABLE
LOWEST % +
A = Calc - True
Favini et al. (4)
A = Calc - True
Exptl.
4.085 e.v. 4.058 3.879 4.075 3.912 4.171 4.105 4.022 4.224 4.174
0.125 0.148 0.030 0.089 -0.010 0.146 0.170 0.075 0.199 0.084 0.021 -0.435 -0.155
0.125 0.156 0.060 0.134 0.079 0.052 0.225 0.111 0.061 0.110 0.242
3.960 e.v. 3.910 3.849 3.986 3.922 4.025
4.085 3.752 3.909 4.171 4.168 3.952 4.151 3.909 4.155 4.254
4.085 e.v. 4.066 3.909 4.120 4.001 4.077 4.160 4.058 4.086 4.200 4.306 3.817 4.145 4.441
Wesley* Wait 1 2 12 13 14 15 16 17 18 23 27 124 135 136 137 138 145 146 1358 1458
3
b* TRANSITIONS FOR AZANAPHTHALENES
-0.437 0.246 -0.125 0.126 -0.116 0.037 0.393
4.047 4.163 3.973 3.988 4.074 3.844
-0.3io 0.081 -0.167 0.125 0.086 -0.052 -0.037 -0.044 -0.017
3.935 3.947 4.025 4.090 4.064 4.187 4.064 4.608 3.922 4.077 4.025 4.025 4.118 3.861
* fl = 3.321 e.v.
with the more refined calculation for this molecule. It is seen that for the monoand di-azanaphthalenes, the agreement with experiment of the simple Huckel orbital calculation is as good as that obtained by Favini. HoweT*er, the Huckel calculation becomes worse for the triazines. This is most likely d!>e to differences in flCN, pee , and &N which were neglected in the present Cal:: J~tions. It
:c3
AZANAPHTHALEIWS
however, t#hat the Huckcl calculations are, at’ least, qualital~ivcly useful ill I)rrdict,ing electronic sl)ectra of these hcterocyclic systems. The charge densities in Table 2 are of some value in l)redicting t,he positions of electrophilic and nucleophilic attack on t)he het)erocyclic molecules Certainly, without consideration of the at,tacking species and the environment, i.e., solvent, accurate predictions cannot bc made. However, t,hc isolat’ed molecule approximation has found relatively wide acceptance in recent years (2) and in 1hc absence of more complete information is a useful approximat’ion. Det,ailcd discussion and comparison of reactivities is beyond the scope of this paper. Spectroscopic investigations of the electronic transitions of the axanal)hth:tICIICS in the vapor phase are in progress in this laboratory, and the results will bc used to obtain bet,ter semiempirical calculations for t’hcse nitrogen hatcrocycles. is :~~)p:wwt,
'lh assistarrce of the gratefully ackuoaledged. RECEIVED:
Selkember
Reusselacr
Polyiwhrlic
Itrstitlltr
completer
laboratory
staff
is
21, 1965 REFERENCES
1. A. RTREITWIESER, JR., “ Molecular Orbital Theory.” Wiley, New York, 1961. 2. B. PVLLMAN AND A. PTLLMAN, “Quantum Biochemistry. ” Iuterscieuce, New York, 1963. S. “Molecular Orbital5 in Chemistry, Physirs, aud Biology,” (I’. 0. Lowdiu and B. Pullmarl, eds.). Academic Press, Kew York, 1964. 4. (:. FAVINI, I. ~‘ANDONI, AND M. ~IMONETT.~, Thwr~t. Chim. ilcta (kkd.) 3,45 (1965).
OF MOLECULAR
SPECTROSCOPY
(1966)
25-33
19,
Azanaphthalenes Part I. Huckel Orbital S. C. WAIT, Department
Energy
of Chemistry,
levels,
JR.
wave functions
JOHN
ASD
Rensselaer
Calculations* W. WEsLEYt
Polytechnic
Institute,
and charge densities
Troy, New I7ark
are reported
for 74 aza-
naphthalenes. Calculations were performed using the Huckel method. Comparison of the lowest singlet-singlet transition w-ith that calculated by the Pariser-Parr method is given for 21 compounds. INTROl>UCTION
The prediction of spectral hransitions and chemical properties of heterocyclic molecules is receiving increasing attention. Recent works by Streitweiser (1)) Pullman and Pullman (Z), and a monograph edited by Lowdin and Pullman (3) summarize the current status of both a priori and semiempirical approaches to these problems. As part of a research program designed to study the spectral properties of heterocyclic molecules related to naphthalene, calculations of the energy levels and charge densities have been performed for naphthalene and all 74 azanaphthalenes which do not, have nitrogen atoms along the rent’ral bond. HUCKEL
ORBITAL
CALCULATIONS
The basis of the Huckel orbital m&hod is well known (l-3) and will not be repeated here. The assumptions made in the present work are (i) the Coulomb integrals, olc are the same for all carbon atoms, (ii) the Coulomb integrals for all the nitrogen atoms are given by o(N = (Ye+ 0.5p [the value 0.5 seems to be a good starting point in the calculat,ions and has been extensively used (1, ,$)I, (iii) the resonance integrals, &c , pCN , and PNN all have t’he same value. Symmetry factoring of the 10 X 10 energy matrix was not undertaken prior to solution of the eigen-problem on an IRM 709-O computer. The energy levels calculated are given in Table 1 and t,he charge densities are given in Table 2.l The numbering of the atoms is given in Fig. 1. For t,h(> sake of presenbing a syst’e* This investigation was supported in part by Public Health Service Research Grant! Number CA-07993 from the National Cancer Institute. t Participant in the National Science Foundation Research Participation for High School Teachers Program at Rensselaer Polytechnic Institute in 1965. 1Complete tables including orbital coefficients are available from the authors. 25
WAIT,
26
JR. AND
WESLEY
Table 1 Energy Levels by Huckel Orbital Calculation
*
-2.303
-2.267
-2.282
-2.251
-2.247
-2.229
-2.226
-2.243
-2.244
-1.618
-1.593
-1.549
-1.531
-1.507
-1.550
-1.577
-1.533
-1.522
-1.565
-1.303
-1.232
-1.290
-1.212
-1.229
-1.186
-1.141
-1.209
-1.222
-1.145
-l.coo
-1.000
-0.920
-0.919
-0.917
-1.OQO
-1.000
-0.912
-0.918
-1.000
-0.618
-0.527
-0.576
-0.454
-0.495
-0.414
-0.450
-0.498
-0.484
-0.460
0.618
0.703
0.646
0.714
0.732
0.764
0.807
0.738
0.727
0.812
1.000
I.000
1.078
1.081
1.078
1.000
l.COO
1.086
1.079
1.000
1.303
1.384
1.319
1.386
1.435
1.515
1.430
1.386
1.410
1.459
1.618
1.669
1.733
1.776
1.750
1.686
1.746
1.794
1.781
1.712
2.303
2.363
2.340
2.410
2.399
2.414
2.410
2.391
2.392
2.416
-123
-124
-125
-126
-127
-128
-135
-23
26
-27
-2.230
-2,266
-2.259 -2.260 -2.235 -2.214 -2.207 -2.225 -2.226 -2.211 -2.203
-1.482
-1.477
-1.464
-1.453
-1.468
-1.522
-1.471
-1.446
-1.500
-1.493
-1.279
-1.254
-1.284
-1.210
-1.180
-1.115
-1.158
-1.211
-1.131
-1.139
-0.794
-0.874
-0.837
-0.786
-0.916
-0.906
-0.870
-0.833
-0.915
-0.916
-0.559
-0.522
-0.547
-0.447
-0.353
-0.393
-0.417
-0.424
-0.388
-0.414
0.699
0.666
0.683
0.762
0.777
0.822
0.742
0.746
0.819
0.832
1.123
1.196
1.147
1.128
1.083
1.087
1.196
1.162
1.082
1.083
1.343
1.323
1.363
1.444
1.532
1.431
1.386
1.426
1.465
1.495
1.826
1.833
1.828
1.840
1.779
1.856
1.884
1.872
1.823
1.816
2.389
2.370
2.371
2.457
2.460
2.449
2.432
2.433
2.456
2.441
-136
137 138 ---------
145
146
235
236
1234
1236
1235
-2.221
-2.221
-2.206
-2.185
-2.201
-2.224
-2.241
-2.202
-2.206
-2.188
-1.433
-1.424
-1.485
-1.532
-1.488
-1.464
-1.391
-1.396
-1.382
-1.446
-1.208
-1.210
-1.138
-1.081
-1.169
-1.199
-1.255
-1.173
-1.154
-1.110
-0.836
-0.865
-0.911
-1.000
-0.910
-0.792
-0.747
-0.773
-0.747
-0.778
-0.473
-0.443
-0.436
-0.359
-0.384
-0.474
-0.515
-0.323
-0.414
-0.380
0.782
0.747
0.848
0.892
0.794
0.794
0.727
0.805
0.801
0.875
1.154
1.200
1.094
l.ooo
1.088
1.124
1.230
1.136
1.232
1.128
1.456
1.438
1.480
1.550
1.520
1.417
1.365
1.566
1.457
1.496
1.858
1.855
1.810
1.755
1.812
1.886
1.916
1.847
1.940
1.916
2.422
2.423
2.445
2.459
2.438
2.431
2.412
2.513
2.473
2.489
+ Ener ies in terms of Beta. The lowest energy levels are at the bottom of each co9urn for a given molecule.
27
AZANAPHTHALENES
Table 1 (Continued)
1238
1245
-2.207
-2.192
-2.167
-2.184
-1.349
-1.427
-1.457
-1.S98
1237
1246 ---e
1248
1256
-2.184
-2.168
-1.388
-1.450
1247
1267
1257
1258
-2.185
-2.181
-2.163
-2.204
-1.467
-1.427
-1.475
-1,388 -1.158
-1.203
-1.119
-1.071
-1.139
-1.168
-1.077
-1.038
-1.112
-1.063
-0.729
-0.786
-0.906
-0.862
-0.833
-0.914
-0.868
-0.830
-0.898
-0.745
-0.366
-0.304
-0.403 0.803
-0.410
-0.384
-0.308
-0.315
-0.330
-0.296
-0.330
0.784
0.881
0.907
0.799
0.820
0.899
0.829
0.861
0.900
1.251
1.136
1.094
1.200
1.167
1.084
1.197
1.163
1.088
1.233
1.454
1.496
1,554
1.532
1.555
1.586
1.431
1.500
1.551
1.427
1.935
1.902
1.858
1.890
1.883
1.837
1.953
1.918
1.873
1.971
2.474
2.493
2.496
2.478
2.478
2.498
2.480
2.474
2.491
2.463
1268
1278 ---------1357
1358
1367
1458
1467
2367
45678
35678 -2.170
-2.185
-2.191
-2.177
-2.158
-2.199
-2.137
-2.178
-2.220
-2.154
-1.412
-1.419
-1.391
-1.455
-1.345
-1.500
-1.428
-1.281
-1.385
-1.307
-1.100
-1.126
-1.135
-1.077
-1.197
-1.000
-1.147
-1.252
-1,OM)
-1.139
-0.864
-0.822
-0.861
-0.910
a.747
-1.000
-0.790
-0.655
-0.771
-0.728
-0.357
-0.331
-0.372
-0.332
-0.438
-0.281
-0.368
-0,500
-0.273
-0.292
0.848
0.831
0.845
0.919
0.826
1.000
0.864
0.781
0.939
0.837
1.204
1.169
1,215
1.103
1.232
1.000
1.126
1.307
1.139
1.252
1.480
1.483
1,520
1.583
1.461
1.637
1.532
1.375
1.600
1.572
1.908
1,919
1,890
1.842
1.951
1.780
1.918
2.000
1.921
1.948
2.479
2.488
2.467
2.484
2.456
2.500
2.470
2.444
2.543
2.527
34568 34567 ----~--~~~
34678
34578
24670
24578
24568
24567
23678
23578
-2.143
-2.170
-2.165
-2.142
-2.160
-2.137
-2.137
-2.163
-2.183
-2.159
-1.377
-1.334
-1.381
-1.394
-1.328
-1.360
-1.356
-1.317
-1.272
-1.315
-1.062
-1.097
-1.036
-1.006
-1.110
-1.071
-1.059
-1.100
-1.153
-1.134
-0.819
-0.729
-0.744
-0.862
-0.728
-0.829
-0.860
-0.746
-0.654
-0.745
-0.249
-0.320
-0.322
-0.267
-0.346
-0.287
-0.263
-0.355
-0.395
-0.305
0.920
0.884
0.891
0.909
0.900
0.969
0.918
0.934
0.855
0.877
1.170
1.252
1.233
1.204
1.254
1.167
1.219
1.232
1.309
1.234
1.592
1.500
1.500
1.556
1.527
1.602
1.597
1.527
1.465
1.556
1.944
1.995
2.010
1.960
1.983
1.928
1.923
1.977
2.030
1.987
2.524
2.519
2.513
2.522
2.508
2.516
2.518
2.512
2.490
2.503
WAIT, JR. AND WESLEY
28
Table 1 (Continued)
14678
14578
345678
245678
235678
234678
234578
234568
234567
145678
-2.140
-2.116
-2.127
-2.121
-2.143
-2.141
-2.117
-2.118
-2.146
-2.099
-1.404
-1.424
-1.306
-1.266
-1.191
-1.271
-1.304
-1.284
-1.212
-1.359
-1.046
-1.000
-1.005
-1.055
-1.131
-1.029
-1.006
-1.044
-1.090
-0.972
-0.778
-0.897
-0.728
-0.727
-0.651
-0.653
-0.744
-0.727
-0.650
-0.769
-0.295
-0.229
-0.218
-0.244
-0.275
-0.310
-0.240
-0.234
-0.312
-0.201 1.058
0.944
0.998
0.973
0.960
1.313
1.315
1.234
1.255
1.309
1.140
1.580
1.531
1.602
1.607
1.531
1.659
1.995
2.046
2.073
2.027
2.020
2.065
1.961
2.564
2.559
2.546
2.540
2.550
2.552
2.545
2.573
134568 ----
2345678
1345678
12345678
-2.091
-2,091
-2.099
-2.072
-2.050
-1.335
-1.328
-1.180
-1.245
-1.118
-0.953
-1.am
-1.005
-0.951
-0.940
-0.860
-0.811
-0.649
-0.727
-0.647
-0.171
-0.183
-0.207
-0.148
-0.118
l.ooO
1,047
1.023
1.069
1.118
1.228
1.170
1.316
1.256
1.318
1.650
1.672
1.625
1.681
1.697
1.972
1.964
2.092
2.043
2.118
2.559
2.560
2.585
2.594
2.623
0.969
l.OQO
0.947
0.982
0.905
11136
1.106
1.252
1.254
1.587
1.647
1.601
1.622
1.947
1.882
2.020
2.525
2.532
matic set of results, all molecules are numbered in the same manner regardless of the preferred order. The energy levels in Table 1 are presented as illustrated below for 1,2_diazanaphthalene. 12 -2.251 -1.531 - 1.212 -0.919 -0.454 0.714 1.081 1.386 1.776 2.410
Highest energy unoccupied orbital
Occupied orbitals in the ground state Lowest energy occupied orbital
Table 2 * Charge Densities from Huckel Orbital Calculation
2
-12
-13
-17
1
1.000
1.216
1.000
0.896 1.198 1.100 0.841 0.902 0.899 0.881 0.895
l.OOC
1.008 0.947 0.950 1.206 0.902 0.993
0.895
-14
-15
-16
Naphthalene
-18
1.119 1.223 1.151 1.205 1.219 1.201 1.226 0.883
1.009 0.993 1.011
1.000
0.932
1.000
0.988 1.003 0.991
1.000
1.003 0.984 0.987 1.003 0.907 0.899 1.201 0.949
l.ooO
0.984
1.000
1.013 0.984 0.998 1.016 1.002 0.945
1.021 0.909
l.COO
0.957 1.004 0.957 0.934 0.958 0.958
0.932 0.961 0.912
1.000
1.002 0.976 0.977 1.005 0.958
1.009 0.930 0.030
1.151 0.945 0.917 0.935 0.922
0.973 1.002
1.000 0.983 0.969
1.205 0.885 0.997 0.922
0.987 0.993
0.930
1.011
1.183 0.883
0.958 1.005 0.977
1.226
1.003
-23
-26
0.899
0.898
1.151
1,183 1.198 1.043 1.108 1.103
1.084 1.099 1.086 0.844 0.950 0.936 0.951
1.191
27 --
123
124 -
125 -
126 --
127
128
-135
0.880 1.119 1.049 1.107 1.122 1.102 1.132 1.213
1.151
0.946
0.899
0.993 1.012 0.039
1.159 0.951
0.921 0.941 0.927
0.842
0.986
0.898
1.005 1.208 0.885 l.ooO 0.923
1.191
0.983
1.183 0.930 0.986 0.969 0.002
0.930 1.151 0.849 0.935
1.012 0.976
1.186 0.934 0.996 0.898
0.983
0.946 1.198 0.969 0.986
0.992 0.930
0.906
0.993 0.880 0.999 0.986
0.929
0.980
0.900
0.980
0.980 0.952 0.980
-136
-137
1.007 0.937 0.958 0.958 0.934
138 -
145 -
0.931 0.934
146 -
235
1.182 0.870 0.977
1.007 0.891 1.214 0.948 0.961 0.914
0.900 0.954
236
1234
1.226
1.209 1.233 1.140 1.154 0,890 0.902
0.825
0.841 0.826 0.906 0.886
1.206
1.191 1.208 0.888
0.902
0.816
0.831 0.822
1.163
1.136 0.912 0.885
0.869
0.982 0.907
1.217 0.897 1.203 0.883 0.909
1.152
1.201
0.948
1.169 0.869 0.996 0.933 0.992
1.024
0.912
0.910
0.937 0.889
1.009
0.981
1.228 0.934 0.959
1236
1235
1.058 1.122 1.109
1.135 1.051 1.026 1.046
1.134 1.150 1.051 1.151 1.136
0.915
1.011 0.884
0.934
0.978 0.962
1.187 0.881
1.058 0.824
1.183 0.969
0.851
0.872 1.193 1.186 0.882
0.929 0.969 0.915 0.977
1.011 0.920 0.995 0.989
1.008 0.932
0.934 0.981
0.913 0.937
1.007 0.914 0.961
0.955 0.933
0.935 0.983 0.933 0.984 0.936
See Figure 1 and text for numbering of atoms in molecules.
WAIT,JR.
30
AND
WESLEY
Table 2 (Continued) 1246
1247
1248
1256
1257
1258
1267
1237
1238 --
1.104 1.043
1.131 1.039 1.051 1.032 1.063 1.109 1.091 1.121 1.105 1.027 1.111 1.090 1.107 1.093 1.085 1.102 1.088 1.084
1.137
1.152 0.835 0.849 0.834 0.852 0.935 0.921 0.938 0.934
0.839
0.830 1.171 1.142 1.162 1.147 0.934 0.954 0.940 0.924
0.985
0.910 1.220 0.898 1.014 0.936 1.109 1.216 1.142 0.891
1245
0.932
0.995 0.865 1.170 0.917 0.978 1.085 0.828 0.887 1.138
1.169
0.866 0.995 0.933 1.186 0.879 0.935 1.190 0.883 1.134
0.894
1.215 0.918 0.995 0.878 1.204 0.934 0.824 1.149 0.897
0.940
0.892 0.959 0.936 0.961 0.916 0.936 0.962 0.916 0.937
0.957
0.981 0.887 0.934 0.909 0.931 0.936 0.911 0.935 0.957.
1268
1278 1357 ----w-e--
1.135
1.116 1.199 1.224 1.210 1.153 1.139 0.888 0.921 0.998
1358
1367
1458
1467
2367
45678 35678
1.071
1.082 0.844 0.829 0.825 0.889 0.886 1.133 0.978 0.917
0.951
0.939 1.177 1.194 1.190 0.889 0.886 1.133 0.863 1.170
0.910
0.928 0.843 0.831 0.818 1.153 1.139 0.888 1.206 0.881
0.818
0.928 1.199 1.126 0.876 1.153 0.902 0.888 1.071 1.040
1.194
0.939 0.844 0.905 1.152 0.889 1.137 1.133 1.036 1.051
0.824
1.082 1,177 0.872 1.118 0.889 1.137 1.133 1.054 1.034
1.222
1.116 0.843 1.166 0.914 1.153 0.902 0.888 1.048 1.059
0.892
0.916 0.938 0.891 0.911 0.915 0.937 0.958 0.933 0.912
0.982
0.955 0.938 0.963 0.985 0.915 0.937 0.958 0.891 0.937
34568
34567 34678 34578 24678 24578 24568 24567 23678 23578 Pm-------
0.942
0.913 0.937 0.921 0.826 0.813 0.829 0.807 0.899 0.885
0.923
0,937 0.921 0.938 1.177 1.193 1.179 1.193 1.118 1.137
1.084
1.069 1.085 1.070 0.828 0.812 0.827 0.811 1.136 1.121
1.103
1.118 1.094 1.123 1.201 1.227 1.212 1.222 0.878 0.903
1.044
1.117 0.833 1.156 0.852 1.174 1.065 1.134 0.826 1.145
1.089
1.025 1.136 0.833 1.122 0.820 1.077 1.010 1.135 0.834
0.837 1.150
1.140 1.029 1.093 1.046 1.110 0.852 1.151 1.026 1.090 0.827 1.111 1.037 1.095 1.023 1.131 0.816 1.107 1.035
0.910
0.958 0.915 0.937 0.940 0.962 0.934 0.985 0.914 0.939
0.918
0.895 0.938 0.891 0.913 co.865 0.894 0.869 0.959 0.910
31
AZANAPHTHALENEY
Table 2 (Continued)
1467n
14578 --
345678
245670 --
235678
234678 234778 --------
234560
234567
145676
1.151
1.138
0.924
0.813
0.888
0.835
0.822
0.039
0.816
1.141
('.869
0.885
0.923
1.179
1.121
1.122
1.139
1.125
1.138
0.868
0.087
0.869
1.068
0.811
1.121
1.029
1.012
1.029
1.010
0.868
1.129
1.155
1.106
1.214
0.888
1.098
1.124
1.107
1,120
1.141
0.041
1.160
1.053
1.073
1.043
0.835
1,158
1.047
1.120
1.06a
1.139
0.838
1.034
1.019
1.034
1.122
0.820
1.074
1.010
1.039
1.030
1.096
1.037
1.054
1.034
1.029
1.093
0.837
1.138
1.039
1.122
1.052
1.046
1.031
1.043
1.098
1.024
1.134
0.816
1.060
0.894
0.917
0.913
0.936
0.913
0.916
0.940
0.912
0,961
0.692
0.938
0.889
0.894
0.869
0.913
0.916
0.869
0.897
0.872
0.892
134578
134568
2345678
1345678
12345678
1.144
1.163
0.822
1.148
1.063
0.836
0.821
1.125
0.820
1.020
1.076
1.091
1.011
1.074
1.020
1;051
1.032
1.110
1.034
1.043
1.144
1.032
1.056'
1.041
1.043
0.836
1.091
1.019
1.037
1.020
1.076
0.821
1.037
1.021
1.020
1.051
1.163
1.032
1.060
1.043
0.892
0.866
0.915
0.869
0.073
0.092
0.919
0.873
0.896
0.073
The entries, k, in Table 1 can t’hen be converted to energy using the relation E = cx + A$. Since both cx and /3 are negative, the most positive value of 1;corresponds t’o the lowest orbital energy. The charge densities in Tablr 2 start with aton 1 :lt the top and end with atom 10 at t,hc bottom. DISCXMSION
Analysis of the results from several viewpoints can be undert,aken. It sl~oulcl be emphasized first, however, that, although Huckel orbital calculations providr a reasonable starting point, further and more refined calculations are needed to draw quantitat.ive conclusions. Such Aculations, including the effect of the lone pair electrons on the nitrogen atoms, arc being undertaken. Favini ri al. (4) have reported calculations for 31 azines including 21 azanaphthalent~s using the Pariser-Pan and Pople method. The energies of the lowest l7r - IT2 electronic transitions calculated by Favini et al. (4) are compared with those from the present work in Table 3. The value of p was chosen as -3.32( e\-. 10 l!mke the Huckel orbital calculation for 1-azanaphthalene agree
32
WAIT,
JR. AND
WESLEY
8
1
7
2
FIG. 1. Numbering
of atoms in azanaphthalenes. TABLE
LOWEST % +
A = Calc - True
Favini et al. (4)
A = Calc - True
Exptl.
4.085 e.v. 4.058 3.879 4.075 3.912 4.171 4.105 4.022 4.224 4.174
0.125 0.148 0.030 0.089 -0.010 0.146 0.170 0.075 0.199 0.084 0.021 -0.435 -0.155
0.125 0.156 0.060 0.134 0.079 0.052 0.225 0.111 0.061 0.110 0.242
3.960 e.v. 3.910 3.849 3.986 3.922 4.025
4.085 3.752 3.909 4.171 4.168 3.952 4.151 3.909 4.155 4.254
4.085 e.v. 4.066 3.909 4.120 4.001 4.077 4.160 4.058 4.086 4.200 4.306 3.817 4.145 4.441
Wesley* Wait 1 2 12 13 14 15 16 17 18 23 27 124 135 136 137 138 145 146 1358 1458
3
b* TRANSITIONS FOR AZANAPHTHALENES
-0.437 0.246 -0.125 0.126 -0.116 0.037 0.393
4.047 4.163 3.973 3.988 4.074 3.844
-0.3io 0.081 -0.167 0.125 0.086 -0.052 -0.037 -0.044 -0.017
3.935 3.947 4.025 4.090 4.064 4.187 4.064 4.608 3.922 4.077 4.025 4.025 4.118 3.861
* fl = 3.321 e.v.
with the more refined calculation for this molecule. It is seen that for the monoand di-azanaphthalenes, the agreement with experiment of the simple Huckel orbital calculation is as good as that obtained by Favini. HoweT*er, the Huckel calculation becomes worse for the triazines. This is most likely d!>e to differences in flCN, pee , and &N which were neglected in the present Cal:: J~tions. It
:c3
AZANAPHTHALEIWS
however, t#hat the Huckcl calculations are, at’ least, qualital~ivcly useful ill I)rrdict,ing electronic sl)ectra of these hcterocyclic systems. The charge densities in Table 2 are of some value in l)redicting t,he positions of electrophilic and nucleophilic attack on t)he het)erocyclic molecules Certainly, without consideration of the at,tacking species and the environment, i.e., solvent, accurate predictions cannot bc made. However, t,hc isolat’ed molecule approximation has found relatively wide acceptance in recent years (2) and in 1hc absence of more complete information is a useful approximat’ion. Det,ailcd discussion and comparison of reactivities is beyond the scope of this paper. Spectroscopic investigations of the electronic transitions of the axanal)hth:tICIICS in the vapor phase are in progress in this laboratory, and the results will bc used to obtain bet,ter semiempirical calculations for t’hcse nitrogen hatcrocycles. is :~~)p:wwt,
'lh assistarrce of the gratefully ackuoaledged. RECEIVED:
Selkember
Reusselacr
Polyiwhrlic
Itrstitlltr
completer
laboratory
staff
is
21, 1965 REFERENCES
1. A. RTREITWIESER, JR., “ Molecular Orbital Theory.” Wiley, New York, 1961. 2. B. PVLLMAN AND A. PTLLMAN, “Quantum Biochemistry. ” Iuterscieuce, New York, 1963. S. “Molecular Orbital5 in Chemistry, Physirs, aud Biology,” (I’. 0. Lowdiu and B. Pullmarl, eds.). Academic Press, Kew York, 1964. 4. (:. FAVINI, I. ~‘ANDONI, AND M. ~IMONETT.~, Thwr~t. Chim. ilcta (kkd.) 3,45 (1965).