The molecular descriptor is the final result of logic and mathematical procedure which transform chemical information encoded within a symbolic representation of a molecule into a useful member or the result of some standardized experiments. Attention is paid to the term "useful" with its double meanings. It means that the number can give more insights into the interpretation of the molecular properties and / or is able to take part in a model for the prediction of some interesting property of the molecules.
A fundamental concept of chemistry is that the structural characteristics of a molecule are responsible for its properties. Topological indices are a convenient means of translating chemical constitution into numerical values which can be used for correlation with physical properties in quantitative structure-property/activity relationship (QSPR/QSAR) studies. The use of graph invariant (topological indices) in QSPR and QSAR studies has become of major interest in recent years. Topological indices have found application in various areas of chemistry, physics, mathematics, informatics, biology, etc [1, 7, 26], but their most important use to date is in the non-empirical Quantitative Structure- Property Relationships (QSPR) and Quantitative Structure -Activity Relationships (QSAR) [5, 14, 19, 21, 23, 24, 27].
let
The terminal Wiener index
Thus if
Where
Where
which could be applied to all connected graphs, since then the above formula is used the definition of the hyper Wiener index.
We have used three distance based topological indices and four degree-distance based topological indices viz,Wiener Index (
S.No. | Alkane | bp(° |
mv( |
mr ( |
hv(kJ) | ct(° |
cp(atm) | st(dyne/cm) | mp(° |
---|---|---|---|---|---|---|---|---|---|
1 | Butane | -0.500 | 152.01 | 37.47 | -138.35 | ||||
2 | 2-methyl propane | -11.730 | 134.98 | 36 | -159.60 | ||||
3 | Pentane | 36.074 | 115.205 | 25.2656 | 26.42 | 196.62 | 33.31 | 16.00 | -129.72 |
4 | 2-methyl butane | 27.852 | 116.426 | 25.2923 | 24.59 | 187.70 | 32.9 | 15.00 | -159.90 |
5 | 2,2 dimethylpropane | 9.503 | 112.074 | 25.7243 | 21.78 | 160.60 | 31.57 | -16.55 | |
6 | Hexane | 68.740 | 130.688 | 29.9066 | 31.55 | 234.70 | 29.92 | 18.42 | -95.35 |
7 | 2-methylpentane | 60.271 | 131.933 | 29.9459 | 29.86 | 224.90 | 29.95 | 17.38 | -153.67 |
8 | 3-methyalpentane | 63.282 | 129.717 | 29.8016 | 30.27 | 231.20 | 30.83 | 18.12 | -118.00 |
9 | 2,2-methylbutane | 49.741 | 132.744 | 29.9347 | 27.69 | 216.20 | 30.67 | 16.30 | -99.87 |
10 | 2,3-dimethylbutane | 57.988 | 130.240 | 29.8104 | 29.12 | 227.10 | 30.99 | 17.37 | -128.54 |
11 | Heptanes | 98.427 | 146.540 | 34.5504 | 36.55 | 267.55 | 27.01 | 20.26 | -90.61 |
12 | 2-methylhexane | 90.052 | 147.656 | 34.5908 | 34.80 | 257.90 | 27.2 | 19.29 | -118.28 |
13 | 3-methylhexane | 91.850 | 145.821 | 34.4597 | 35.08 | 262.40 | 28.1 | 19.79 | -119.40 |
14 | 3-ethylpentane | 93.475 | 143.517 | 34.2827 | 35.22 | 267.60 | 28.6 | 20.44 | -118.60 |
15 | 2,2-dimethylpentane | 79.197 | 148.695 | 34.6166 | 32.43 | 247.70 | 28.4 | 18.02 | -123.81 |
16 | 2,3 -dimethylpentane | 89.784 | 144.153 | 34.3237 | 34.24 | 264.60 | 29.2 | 19.96 | -119.10 |
17 | 2,4-dimethylpentane | 80.500 | 148.949 | 34.6192 | 32.88 | 247.10 | 27.4 | 18.15 | -119.24 |
18 | 3,3-dimethylpentane | 86.064 | 144.530 | 34.3323 | 33.02 | 263.00 | 30 | 19.59 | -134.46 |
19 | Octane | 125.665 | 162.592 | 39.1922 | 41.48 | 296.20 | 24.64 | 21.76 | -56.79 |
20 | 2-methylheptane | 117.647 | 163.663 | 39.2316 | 39.68 | 288.00 | 24.8 | 20.60 | -109.04 |
21 | 3 -methylheptane | 118.925 | 161.832 | 39.1001 | 39.83 | 292.00 | 25.6 | 21.17 | -120.50 |
22 | 4-methylheptane | 117.709 | 162.105 | 39.1174 | 39.67 | 290.00 | 25.6 | 21.00 | -120.95 |
23 | 3-ethylhexane | 118.53 | 160.07 | 38.94 | 39.40 | 292.00 | 25.74 | 21.51 | |
24 | 2,2-dimethylhexane | 10.84 | 164.28 | 39.25 | 37.29 | 279.00 | 25.6 | 19.60 | -121.18 |
25 | 2,3-dimethylhexane | 115.607 | 160.39 | 38.98 | 38.79 | 293.00 | 26.6 | 20.99 | |
26 | 2,4-dimethylhexane | 109.42 | 163.09 | 39.13 | 37.76 | 282.00 | 25.8 | 20.05 | -137.50 |
27 | 2,5-dimethylhexane | 109.10 | 164.69 | 39.25 | 37.86 | 279.00 | 25 | 19.73 | -91.20 |
28 | 3,3 -dimethy lhexane | 111.96 | 160.87 | 39.00 | 37.93 | 290.84 | 27.2 | 20.63 | -126.10 |
29 | 3,4-dimethy lhexane | 117.72 | 158.81 | 38.84 | 39.02 | 298.00 | 27.4 | 21.64 | |
30 | 3 -ethyl-2-methylpentane | 115.65 | 158.79 | 38.83 | 38.52 | 295.00 | 27.4 | 21.52 | -114.96 |
31 | 3-ethyl-3-methylpentane | 118.25 | 157.02 | 38.71 | 37.99 | 305.00 | 28.9 | 21.99 | -90.87 |
32 | 2,2,3-trimethylpentane | 109.84 | 159.52 | 38.92 | 36.91 | 294.00 | 28.2 | 20.67 | -112.27 |
33 | 2,2,4-trimethylpentane | 99.23 | 165.08 | 39.26 | 35.13 | 271.15 | 25.5 | 18.77 | -107.38 |
34 | 2,3,3-trimethylpentane | 114.76 | 157.29 | 38.76 | 37.22 | 303.00 | 29 | 21.56 | -100.70 |
35 | 2,3,4-trimethylpentane | 113.46 | 158.85 | 38.86 | 37.61 | 295.00 | 27.6 | 21.14 | -109.21 |
36 | Nonane | 150.79 | 178.71 | 43.84 | 46.44 | 322.00 | 22.74 | 22.92 | -53.52 |
37 | 2-methyloctane | 143.26 | 179.77 | 43.87 | 44.65 | 315.00 | 23.6 | 21.88 | -80.40 |
38 | 3-methyloctane | 144.18 | 177.95 | 43.72 | 44.75 | 318.00 | 23.7 | 22.34 | -107.64 |
39 | 4-methyloctane | 142.48 | 178.15 | 43.76 | 44.75 | 318.30 | 23.06 | 22.34 | -113.20 |
40 | 3-ethylheptane | 143.00 | 176.41 | 43.64 | 44.81 | 318.00 | 23.98 | 22.81 | -114.90 |
41 | 4-ethylheptane | 175.68 | 43.49 | 44.81 | 318.30 | 23.98 | 22.81 | ||
42 | 2,2-dimethylheptane | 132.69 | 180.50 | 43.91 | 42.28 | 302.00 | 22.8 | 20.80 | -113.00 |
43 | 2,3-dimethylheptane | 140.50 | 176.65 | 43.63 | 43.79 | 315.00 | 23.79 | 22.34 | -116.00 |
44 | 2,4-dimethylheptane | 133.50 | 179.12 | 43.73 | 42.87 | 306.00 | 22.7 | 23.30 | |
45 | 2,5-dimethylheptane | 136.00 | 179.37 | 43.84 | 43.87 | 307.80 | 22.7 | 21.30 | |
46 | 2,6- dimethylheptane | 135.21 | 180.91 | 43.92 | 42.82 | 306.00 | 23.7 | 20.83 | -102.90 |
47 | 3,3- dimethylheptane | 137.300 | 176.897 | 43.6870 | 42.66 | 314.00 | 24.19 | 22.01 | |
48 | 3,4- dimethylheptane | 140.600 | 175.349 | 43.5473 | 43.84 | 322.70 | 22.80 | ||
49 | 3,5- dimethylheptane | 136.000 | 177.386 | 43.6379 | 42.98 | 312.30 | 23.59 | 21.77 | |
50 | 4,4- dimethylheptane | 135.200 | 176.897 | 43.6022 | 42.66 | 317.80 | 24.18 | 22.01 | |
51 | 3-ethyl-2-methylhexane | 138.000 | 175.445 | 43.6550 | 43.84 | 322.70 | 24.77 | 22.80 | |
52 | 4-ethyl-2-methylhexane | 133.800 | 177.386 | 43.6472 | 42.98 | 330.30 | 25.56 | 21.77 | |
53 | 3 -ethyl- 3-methylhexane | 140.600 | 173.077 | 43.2680 | 44.04 | 327.20 | 25.66 | 23.22 | |
54 | 2,2,4- trimethylhexane | 126.540 | 179.220 | 43.7638 | 40.57 | 301.00 | 23.39 | 20.51 | -120.00 |
55 | 2,2,5- trimethylhexane | 124.084 | 181.346 | 43.9356 | 40.17 | 296.60 | 22.41 | 20.04 | -105.78 |
56 | 2,3,3- trimethylhexane | 137.680 | 173.780 | 43.4347 | 42.23 | 326.10 | 25.56 | 22.41 | -116.80 |
57 | 2,3,4- trimethylhexane | 139.000 | 173.498 | 43.4917 | 42.93 | 324.20 | 25.46 | 22.80 | |
58 | 2,3,5- trimethylhexane | 131.340 | 177.656 | 43.6474 | 41.42 | 309.40 | 23.49 | 21.27 | -127.80 |
59 | 3,3,4- trimethylhexane | 140.460 | 172.055 | 43.3407 | 42.28 | 330.60 | 26.45 | 23.27 | -101.20 |
60 | 3,3-diethylpentane | 146.168 | 170.185 | 43.1134 | 43.36 | 342.80 | 26.94 | 23.75 | -33.11 |
61 | 2,2-dimethyl-3-ethylpentane | 133.830 | 174.537 | 43.4571 | 42.02 | 322.60 | 25.96 | 22.38 | -99.20 |
62 | 2,3-dimethyl-3-ethylpentane | 142.000 | 170.093 | 42.9542 | 42.55 | 338.60 | 26.94 | 23.87 | |
63 | 2,4-dimethyl-3-ethylpentane | 136.730 | 173.804 | 43.4037 | 42.93 | 324.20 | 25.46 | 22.80 | -122.20 |
64 | 2,2,3,3-tetramethylpentane | 140.274 |
169.495 | 43.2147 | 41.00 | 334.50 | 27.04 | 23.38 | -99.0 |
65 | 2,2,3,4- tetramethylpentane | 133.016 | 173.557 | 43.4359 | 41.00 | 319.60 | 25.66 | 21.98 | -121.09 |
66 | 2,2,4,4- tetramethylpentane | 122.284 | 178.256 | 43.8747 | 38.10 | 301.60 | 24.58 | 20.37 | -66.54 |
67 | 2,3,3,4- tetramethylpentane | 141.551 | 169.928 | 43.2016 | 41.75 | 334.50 | 26.85 | 23.31 | -102.12 |
S.No. | Alkane | |||||||
---|---|---|---|---|---|---|---|---|
1 | Butane | 10 | 3 | 28 | 19 | 12 | 12 | 46 |
2 | 2-methyl propane | 9 | 6 | 20 | 13 | 36 | 54 | 27 |
3 | Pentane | 20 | 8 | 60 | 44 | 16 | 16 | 146 |
4 | 2-methyl butane | 18 | 8 | 52 | 36 | 42 | 54 | 90 |
5 | 2,2 dimethylpropane | 16 | 8 | 44 | 28 | 96 | 192 | 52 |
6 | Hexane | 35 | 5 | 110 | 82 | 20 | 20 | 371 |
7 | 2-methylpentane | 32 | 10 | 96 | 73 | 52 | 66 | 254 |
8 | 3-methyalpentane | 31 | 10 | 94 | 69 | 46 | 52 | 217 |
9 | 2,2-methylbutane | 26 | 15 | 82 | 57 | 102 | 168 | 142 |
10 | 2,3-dimethylbutane | 29 | 16 | 84 | 61 | 96 | 144 | 161 |
11 | Heptanes | 56 | 6 | 182 | 146 | 24 | 24 | 812 |
12 | 2-methylhexane | 52 | 12 | 166 | 130 | 62 | 78 | 604 |
13 | 3-methylhexane | 50 | 12 | 161 | 122 | 55 | 62 | 506 |
15 | 3-ethylpentane | 48 | 12 | 150 | 144 | 48 | 48 | 408 |
16 | 2,2-dimethylpentane | 49 | 16 | 142 | 106 | 120 | 192 | 370 |
17 | 2,3 -dimethylpentane | 46 | 15 | 154 | 109 | 108 | 144 | 352 |
18 | 2,4-dimethylpentane | 48 | 16 | 150 | 114 | 120 | 180 | 426 |
19 | 3,3-dimethylpentane | 44 | 14 | 136 | 98 | 104 | 144 | 296 |
20 | Octane | 84 | 7 | 280 | 231 | 28 | 28 | 1596 |
21 | 2-methylheptane | 79 | 14 | 263 | 211 | 72 | 90 | 1261 |
22 | 3 -methylheptane | 76 | 14 | 248 | 212 | 64 | 72 | 1072 |
23 | 4-methylheptane | 75 | 14 | 224 | 193 | 64 | 72 | 1011 |
24 | 3-ethylhexane | 72 | 14 | 232 | 190 | 56 | 56 | 822 |
25 | 2,2-dimethylhexane | 71 | 21 | 228 | 179 | 138 | 216 | 845 |
26 | 2,3 -dimethylhexane | 71 | 22 | 291 | 275 | 118 | 156 | 766 |
27 | 2,4-dimethylhexane | 71 | 23 | 231 | 179 | 125 | 168 | 803 |
28 | 2,5 -dimethylhexane | 74 | 24 | 240 | 191 | 144 | 216 | 962 |
29 | 3,3-dimethylhexane | 67 | 21 | 212 | 163 | 113 | 150 | 649 |
30 | 3,4-dimethylhexane | 68 | 22 | 216 | 168 | 108 | 131 | 668 |
31 | 3-ethyl-2-methylpentane | 67 | 22 | 215 | 163 | 108 | 130 | 607 |
32 | 3-ethyl-3-methylpentane | 64 | 21 | 239 | 129 | 102 | 120 | 514 |
33 | 2,2,3 -trimethylpentane | 63 | 27 | 196 | 147 | 198 | 318 | 495 |
34 | 2,2,4-trimethylpentane | 66 | 32 | 194 | 152 | 228 | 330 | 606 |
35 | 2,3,3-trimethylpentane | 60 | 27 | 242 | 200 | 194 | 314 | 458 |
36 | 2,3,4-trimethylpentane | 65 | 32 | 198 | 155 | 192 | 288 | 551 |
37 | Nonane | 120 | 8 | 422 | 365 | 32 | 32 | 2892 |
38 | 2-methyloctane | 114 | 16 | 391 | 327 | 82 | 102 | 2388 |
39 | 3-methyloctane | 110 | 16 | 310 | 268 | 73 | 82 | 2076 |
40 | 4-methyloctane | 108 | 16 | 353 | 295 | 73 | 82 | 1920 |
41 | 3-ethylheptane | 105 | 16 | 331 | 271 | 72 | 72 | 1604 |
42 | 4-ethylheptane | 102 | 16 | 239 | 190 | 68 | 68 | 1452 |
43 | 2,2-dimethylheptane | 104 | 24 | 343 | 378 | 156 | 240 | 1718 |
44 | 2,3-dimethylheptane | 102 | 25 | 336 | 264 | 133 | 174 | 1548 |
45 | 2,4-dimethylheptane | 102 | 26 | 342 | 268 | 148 | 190 | 1524 |
46 | 2,5-dimethylheptane | 110 | 27 | 344 | 269 | 147 | 198 | 1646 |
47 | 2,6- dimethylheptane | 108 | 28 | 344 | 280 | 168 | 252 | 1926 |
48 | 3,3- dimethylheptane | 98 | 24 | 320 | 277 | 138 | 184 | 1340 |
49 | 3,4- dimethylheptane | 98 | 25 | 320 | 392 | 122 | 147 | 1298 |
50 | 3,5- dimethylheptane | 100 | 26 | 320 | 264 | 128 | 156 | 1396 |
51 | 4,4- dimethylheptane | 96 | 24 | 314 | 248 | 136 | 184 | 1218 |
52 | 3-ethyl-2-methylhexane | 96 | 25 | 315 | 248 | 122 | 146 | 1146 |
53 | 4-ethyl-2-methylhexane | 98 | 26 | 303 | 249 | 126 | 148 | 1244 |
54 | 3 -ethyl- 3-methylhexane | 92 | 24 | 295 | 228 | 114 | 130 | 992 |
55 | 2,2,4- trimethylhexane | 94 | 36 | 301 | 238 | 237 | 378 | 1108 |
56 | 2,2,5- trimethylhexane | 98 | 38 | 322 | 270 | 270 | 474 | 1328 |
57 | 2,3,3- trimethylhexane | 90 | 32 | 289 | 256 | 210 | 318 | 936 |
58 | 2,3,4- trimethylhexane | 92 | 36 | 295 | 238 | 199 | 273 | 992 |
59 | 2,3,5- trimethylhexane | 96 | 38 | 317 | 251 | 228 | 342 | 1188 |
60 | 3,3,4- trimethylhexane | 87 | 34 | 278 | 214 | 201 | 278 | 838 |
61 | 3,3-diethylpentane | 88 | 24 | 134 | 96 | 96 | 96 | 796 |
62 | 2,2-dimethyl-3-ethylpentane | 88 | 32 | 279 | 213 | 208 | 304 | 814 |
63 | 2,3-dimethyl-3-ethylpentane | 86 | 34 | 266 | 197 | 186 | 250 | 740 |
64 | 2,4-dimethyl-3-ethylpentane | 90 | 36 | 291 | 224 | 200 | 276 | 870 |
65 | 2,2,3,3-tetramethylpentane | 82 | 44 | 223 | 170 | 316 | 560 | 628 |
66 | 2,2,3,4- tetramethylpentane | 86 | 47 | 273 | 209 | 327 | 564 | 758 |
67 | 2,2,4,4- tetramethylpentane | 86 | 40 | 280 | 216 | 316 | 530 | 850 |
68 | 2,3,3,4- tetramethylpentane | 84 | 47 | 264 | 200 | 28 | 464 | 729 |
We have tested the following linear regression model
where P = physical property, TI = topological index.
Using (3.1), we have obtained the following different linear models for each degree based topological index, which are listed below.
By inspection of the data given in tables 3 to 9, It is possible to draw numbers of conclusion for the given distance and degree-distance based TIs.
Statical parameters for the linear QSPR model for Wiener index.
Physical Properties | N | a | b | r | s | F |
---|---|---|---|---|---|---|
Boiling point | 70 | 20.8432 | 1.2203 | 0.921 | 14.3278 | 388.436 |
Molar volume | 67 | 113.868 | 0.6412 | 0.970 | 4.32084 | 1037.804 |
Molar refraction | 67 | 24.7432 | 0.1944 | 0.962 | 1.45880 | 795.781 |
Heats of vaporization | 67 | 23.710 | 0.1998 | 0.964 | 1.45328 | 846.841 |
Critical temperature | 70 | 179.262 | 1.4606 | 0.899 | 19.8772 | 285.433 |
Critical Pressure | 70 | 34.1143 | -0.1025 | 0.921 | 1.2167 | 380.698 |
Surface tension | 66 | 16.126748 | 0.0634 | 0.815 | 1.14383 | 126.812 |
Melting point | 52 | -129.02 | 0.2909 | 0.317 | 25.87537 | 5.585 |
Statical parameters for the linear QSPR model for terminal Wiener index.
Physical Properties | N | a | b | r | s | F |
---|---|---|---|---|---|---|
Boiling point | 70 | 68.2472 | 1.9072 | 0.574 | 30.3815 | 33.333 |
Molar volume | 67 | 139.62 | 1.002 | 0.606 | 14.17194 | 37.698 |
Molar refraction | 67 | 32.25 | 0.3178 | 0.644 | 4.06101 | 46.075 |
Heats of vaporization | 67 | 37.616 | 0.055 | 0.443 | 4.87876 | 15.910 |
Critical temperature | 70 | 230.099 | 2.5196 | 0.620 | 35.5665 | 42.39 |
Critical Pressure | 70 | 29.5512 | -0.1327 | 0.475 | 2.7503 | 19.816 |
Surface tension | 66 | 19.1536 | 0.088 | 0.481 | 1.73103 | 19.315 |
Melting point | 52 | 579.080 | -32.214 | 0.096 | 27.1532 | 0.461 |
Statical parameters for the linear QSPR model for hyper Wiener index.
Physical Properties | N | a | b | r | s | F |
---|---|---|---|---|---|---|
Boiling point | 70 | 69.8172 | 0.04586 | 0.722 | 25.6758 | 73.879 |
Molar volume | 67 | 140.3322 | 0.02365 | 0.759 | 11.59154 | 88.511 |
Molar refraction | 67 | 33.2598 | 0.001937 | 0.555 | 1.64346 | 28.430 |
Heats of vaporization | 67 | 31.82212 | 0.007513 | 0.789 | 3.34131 | 107.499 |
Critical temperature | 70 | 245.468 | 0.04589 | 0.809 | 1.1358 | 129.100 |
Critical Pressure | 70 | 30.4719 | -0.00433 | 0.636 | 34.9872 | 6.078 |
Surface tension | 66 | 19.1519 | 0.0019 | 0.555 | 1.64346 | 28.430 |
Melting point | 52 | -120.603 | 0.013596 | 0.318 | 25.86514 | 5.629 |
Statical parameters for the linear QSPR model for Degree distance index.
Physical Properties | N | a | b | r | s | F |
---|---|---|---|---|---|---|
Boiling point | 70 | 32.2663 | 0.3432 | 0.863 | 18.7367 | 198.428 |
Molar volume | 67 | 119.529 | 0.182 | 0.919 | 7.03409 | 315.874 |
Molar refraction | 67 | 37.81 | 0.00714 | 0.897 | 2.34677 | 267.614 |
Heats of vaporization | 67 | 37.144 | 0.00732 | 0.897 | 2.40325 | 268.443 |
Critical temperature | 70 | 196.428 | 0.3932 | 0.809 | 26.6334 | 128.863 |
Critical Pressure | 70 | 33.418 | -0.0298 | 0.890 | 1.4243 | 259.425 |
Surface tension | 66 | 17.121 | 0.0162 | 0.716 | 1.37956 | 67.174 |
Melting point | 52 | -122.787 | 0.0641 | 0.232 | 26.53927 | 2.839 |
Statical parameters for the linear QSPR model for Gutman index.
Physical Properties | N | a | b | r | s | F |
---|---|---|---|---|---|---|
Boiling point | 70 | 38.62 | 0.3983 | 0.858 | 19.0533 | 189.648 |
Molar volume | 67 | 201.965 | -0.20958 | 0.892 | 8.05741 | 252.709 |
Molar refraction | 67 | 28.02 | 0.061 | 0.874 | 2.58307 | 209.543 |
Heats of vaporization | 67 | 26.978 | 0.0632 | 0.882 | 2.56979 | 226.624 |
Critical temperature | 70 | 203.4429 | 0.4577 | 0.807 | 26.7911 | 126.553 |
Critical Pressure | 70 | 20.218 | -0.034733 | 0.889 | 1.4332 | 255.359 |
Surface tension | 66 | 17.37 | 0.0190 | 0.711 | 1.38853 | 65.486 |
Melting point | 52 | -119.40 | 0.0616 | 0.187 | 26.80008 | 1.815 |
Statical parameters for the linear QSPR model for Ashwini index.
Physical Properties | N | a | b | r | s | F |
---|---|---|---|---|---|---|
Boiling point | 70 | 135.6962 | -0.1870 | 0.420 | 33.644 | 14.578 |
Molar volume | 67 | 148.45 | 0.1095 | 0.492 | 15.51334 | 20.706 |
Molar refraction | 67 | 35.573 | 0.034 | 0.519 | 4.53808 | 23.949 |
Heats of vaporization | 67 | 39.95 | -0.00823 | 0.288 | 5.21235 | 5.885 |
Critical temperature | 70 | 237.8298 | 0.3766 | 0.459 | 40.2596 | 18.155 |
Critical Pressure | 70 | 23.4180 | -0.01427 | 0.381 | 2.8901 | 11.523 |
Surface tension | 66 | 19.970 | 0.0078 | 0.320 | 1.87121 | 7.299 |
Melting point | 52 | -113.0059 | 0.03 | 0.561 | 4.90731 | 22.913 |
Statical parameters for the linear QSPR model for SM index.
Physical Properties | N | a | b | r | s | F |
---|---|---|---|---|---|---|
Boiling point | 70 | 97.968 | 0.069 | 0.292 | 35.4737 | 6.3828 |
Molar volume | 67 | 74.47 | 0.46 | 0.378 | 16.4949 | 10.809 |
Molar refraction | 67 | 10.394 | 0.152 | 0.400 | 4.8866 | 12.352 |
Heats of vaporization | 67 | 37.749 | 0.00587 | 0.158 | 5.37507 | 1.658 |
Critical temperature | 70 | 268.506 | 0.0956 | 0.326 | 42.8387 | 8.093 |
Critical Pressure | 70 | 27.68 | -0.00582 | 0.288 | 2.9931 | 6.145 |
Surface tension | 66 | 20.486 | 0.00266 | 0.198 | 1.93590 | 2.6614 |
Melting point | 52 | -109.163 | -0.00016 | 0.339 | 5.1208 | 8.7442 |
First, the famous and much studied distance based Topological index viz, Wiener index found to be more suitable tool to predict the physical properties of alkanes.The Wiener Index shows good correlation with almost all physical properties of alkanes which are listed in table 3 except molar volume and surface tension of alkanes.The correlation coefficient value lies between 0.815 to 0.970. The QSPR study reveals that Wiener Index is more suitable to predict heats of vapourization and molar volumes of alkanes with correlation coefficient value r=0.964, and r = 0.0.970 respectively.
In addition the result for Terminal Wiener index revealed that the recent advocated idea of using Terminal Wiener index did not pass the test. This important details seems to have ignored in recent paper [9], on Terminal Wiener index.
Recently introduced distance based topological invariant viz, Hyper Wiener index found to be adequate for any structure-property correlation, except for critical temperatures of alkanes with correlation coefficient value r=0.809.
The QSPR study of degree-distance index in tables 6 reveals that the degree-distance index is an useful topological invariant. It shows good correlation with almost all physical properties which are listed in Table 6, except surface tension and melting points of alkanes. The correlation coefficient values lies between 0. 809 to 0.919. The degree-distance index is more suitable to predict the molar volume and heats of vaporization with
The multiplicative version of degree-distance index is known as Gutman Index. By observing the results in table 7,One can say that the Gutman index has less predictive ability compared to degree-distance index. Further the correlation of Gutman index with physical properties of alkanes is very less and correlation coefficient value lies between 0.187 to 0.892.
The another degree-distance based topological index viz, Ashwini index. The predicting power of Ashwini index with physical properties of alkanes is too less. The correlation coefficient value of Ashwini index lies between 0.288 to 0.519.
Motivated by Gutman index and Ashwini index, Here we introduce a new degree-distance based topological invariant viz, SM Index. The QSPR study of SNM Index in table-9 shows good predicting power for alkanes.
From practical point of view, topological indices for which the absolute value of the correlation coefficient is less than 0.8 can be characterized useless. Thus the QSPR study of these distance and degree-distance based topological indices with physical properties of alkanes helps us to characterize useful topological indices indices with absolute values of correlation coefficients lies between 0.8 to 0.970.