Excited-State Polarizabilities: A Combined Density Functional Theory and Information-Theoretic Approach Study
Abstract
:1. Introduction
2. Results
3. Discussion
4. Materials and Methods
4.1. Information-Theoretic Approach Quantities
4.2. Computational Details
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Index | αiso | SS | IF | SGBP | rR2 | rR3 | IG | G1 | G2 | G3 | Vol | Θiso |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 175.68 | 96.35 | 4343.89 | 746.75 | 112.64 | 117.78 | 1.38 | −35.34 | 24.07 | 139.78 | 1715.75 | −87.39 |
2 | 200.87 | 20.66 | 13,967.27 | 973.91 | 146.61 | 151.68 | 1.36 | −34.93 | 23.70 | 141.74 | 2073.70 | −103.29 |
3 | 237.32 | 142.90 | 5692.80 | 1016.86 | 154.03 | 161.91 | 2.10 | −50.98 | 35.00 | 196.05 | 2441.40 | −115.43 |
4 | 182.97 | 97.74 | 4793.46 | 801.56 | 120.76 | 126.07 | 1.45 | −34.44 | 22.49 | 147.78 | 1855.73 | −91.79 |
5 | 197.76 | 107.94 | 5045.63 | 855.45 | 129.06 | 135.01 | 1.60 | −39.10 | 25.75 | 159.82 | 1886.74 | −95.32 |
6 | 175.11 | 92.94 | 4917.98 | 801.81 | 120.62 | 125.71 | 1.37 | −34.55 | 22.69 | 144.27 | 1765.67 | −93.87 |
7 | 188.87 | 81.70 | 6524.29 | 855.22 | 128.61 | 133.70 | 1.37 | −34.93 | 22.13 | 142.27 | 1959.26 | −100.99 |
8 | 197.51 | 20.60 | 13,967.06 | 973.87 | 146.60 | 151.67 | 1.36 | −34.95 | 23.67 | 141.84 | 1850.09 | −101.48 |
9 | 194.07 | 102.37 | 4928.42 | 829.28 | 124.78 | 130.18 | 1.46 | −36.68 | 23.12 | 151.22 | 1897.41 | −106.85 |
10 | 189.36 | 106.46 | 4595.48 | 800.72 | 120.93 | 126.64 | 1.53 | −39.13 | 25.97 | 150.98 | 1931.31 | −93.18 |
11 | 194.81 | 107.96 | 5045.77 | 855.48 | 129.06 | 135.02 | 1.60 | −39.13 | 23.71 | 159.81 | 1994.38 | −95.26 |
12 | 191.68 | 81.72 | 6524.35 | 855.23 | 128.60 | 133.66 | 1.36 | −34.98 | 22.67 | 142.29 | 1957.16 | −105.11 |
13 | 200.29 | 20.66 | 13,967.37 | 973.93 | 146.60 | 151.67 | 1.36 | −35.01 | 22.86 | 141.85 | 1980.91 | −111.96 |
14 | 198.88 | 102.42 | 4928.71 | 829.32 | 124.77 | 130.16 | 1.45 | −36.79 | 23.62 | 151.19 | 1696.49 | −112.11 |
15 | 190.18 | 106.46 | 4595.43 | 800.71 | 120.93 | 126.64 | 1.53 | −39.12 | 24.61 | 151.02 | 1842.17 | −94.41 |
16 | 191.22 | 96.42 | 6318.70 | 965.73 | 144.80 | 150.24 | 1.46 | −37.81 | 23.40 | 165.13 | 2064.71 | −117.92 |
17 | 255.95 | 135.18 | 5826.22 | 1017.73 | 153.69 | 160.90 | 1.92 | −52.71 | 36.65 | 192.16 | 2401.28 | −125.79 |
18 | 246.58 | 135.11 | 5826.00 | 1017.67 | 153.68 | 160.90 | 1.92 | −52.74 | 36.93 | 192.52 | 2494.60 | −119.81 |
19 | 277.67 | 146.79 | 6528.00 | 1126.45 | 170.10 | 178.13 | 2.14 | −56.48 | 38.53 | 212.18 | 2819.11 | −137.35 |
20 | 295.24 | 153.19 | 7225.20 | 1222.09 | 184.32 | 192.76 | 2.25 | −58.90 | 39.85 | 226.76 | 2761.18 | −154.13 |
21 | 268.01 | 146.71 | 6527.76 | 1126.38 | 170.10 | 178.12 | 2.14 | −56.47 | 39.11 | 212.53 | 2467.93 | −128.04 |
22 | 283.05 | 153.12 | 7225.00 | 1222.03 | 184.32 | 192.76 | 2.25 | −58.93 | 39.71 | 227.00 | 2913.80 | −139.45 |
23 | 205.46 | 91.83 | 6775.95 | 909.20 | 136.89 | 142.52 | 1.51 | −38.70 | 26.44 | 153.26 | 1963.41 | −110.94 |
24 | 205.03 | 106.53 | 6570.28 | 1019.70 | 153.09 | 159.11 | 1.61 | −41.55 | 26.57 | 176.20 | 2201.13 | −123.83 |
25 | 327.20 | 173.93 | 7308.31 | 1288.65 | 194.73 | 204.01 | 2.46 | −70.08 | 50.17 | 244.74 | 3066.91 | −156.33 |
26 | 320.10 | 190.84 | 7330.19 | 1328.47 | 201.30 | 211.70 | 2.76 | −74.61 | 52.80 | 255.30 | 3332.26 | −160.67 |
27 | 175.19 | 82.72 | 6640.05 | 966.86 | 144.50 | 149.36 | 1.31 | −32.94 | 20.03 | 158.50 | 3218.41 | −108.98 |
28 | 173.51 | 96.75 | 4012.72 | 706.25 | 106.66 | 111.88 | 1.39 | −37.76 | 26.11 | 130.76 | 1856.23 | −84.26 |
29 | 169.68 | 91.91 | 4453.45 | 747.21 | 112.55 | 117.54 | 1.33 | −36.02 | 24.66 | 137.43 | 1800.53 | −87.68 |
30 | 186.83 | 80.69 | 5927.71 | 800.75 | 120.52 | 125.45 | 1.31 | −36.59 | 25.86 | 133.70 | 2002.44 | −95.13 |
31 | 163.90 | 90.16 | 4002.93 | 692.24 | 104.49 | 109.37 | 1.29 | −36.26 | 25.07 | 129.50 | 1582.16 | −82.37 |
32 | 176.33 | 103.65 | 4822.91 | 815.19 | 123.03 | 128.93 | 1.58 | −41.53 | 28.16 | 148.35 | 1952.13 | −95.39 |
33 | 243.77 | 128.34 | 5902.42 | 1004.58 | 151.72 | 158.98 | 1.94 | −49.38 | 32.40 | 187.62 | 2418.28 | −113.49 |
34 | 204.56 | 113.06 | 5648.71 | 937.42 | 141.25 | 147.59 | 1.70 | −44.88 | 30.55 | 170.08 | 2071.58 | −114.39 |
35 | 116.08 | 68.78 | 3451.98 | 571.00 | 85.89 | 89.56 | 0.99 | −21.64 | 13.14 | 104.71 | 1404.36 | −66.08 |
36 | 135.67 | 74.85 | 4147.84 | 666.78 | 100.16 | 104.28 | 1.15 | −22.46 | 12.48 | 118.31 | 1405.54 | −78.67 |
R2 | 0.560 | 0.068 | 0.890 | 0.897 | 0.908 | 0.922 | 0.936 | 0.912 | 0.938 | 0.705 | 0.893 |
Index | αiso | SS | IF | rR2 | rR3 | G2 | G3 | Vol | Θiso |
---|---|---|---|---|---|---|---|---|---|
1 | 166.08 | 96.94 | 4345.68 | 112.73 | 118.02 | 23.88 | 138.16 | 1797.33 | −89.93 |
2 | 189.81 | 21.28 | 13,969.19 | 146.67 | 151.87 | 23.61 | 140.08 | 2016.04 | −114.26 |
3 | 224.23 | 143.51 | 5694.61 | 154.12 | 162.16 | 34.15 | 194.24 | 2493.81 | −126.71 |
4 | 174.81 | 98.36 | 4795.23 | 120.83 | 126.27 | 22.33 | 146.07 | 1709.27 | −96.38 |
5 | 187.84 | 108.57 | 5047.40 | 129.14 | 135.22 | 25.53 | 158.13 | 1977.08 | −101.96 |
6 | 166.88 | 93.55 | 4919.65 | 120.68 | 125.87 | 22.56 | 142.61 | 1732.69 | −97.69 |
7 | 182.88 | 82.29 | 6525.95 | 128.66 | 133.83 | 23.33 | 140.53 | 1814.22 | −105.58 |
8 | 188.20 | 21.19 | 13,968.88 | 146.65 | 151.80 | 22.97 | 140.28 | 1849.59 | −110.07 |
9 | 182.03 | 103.04 | 4930.44 | 124.83 | 130.34 | 24.17 | 149.51 | 1973.71 | −110.22 |
10 | 178.88 | 107.05 | 4597.05 | 121.02 | 126.88 | 26.58 | 149.31 | 1997.79 | −96.99 |
11 | 182.81 | 108.54 | 5047.21 | 129.14 | 135.22 | 25.57 | 158.15 | 1950.36 | −99.73 |
12 | 178.54 | 82.29 | 6526.00 | 128.69 | 133.90 | 23.14 | 140.43 | 1956.40 | −103.35 |
13 | 186.41 | 21.24 | 13,968.99 | 146.69 | 151.92 | 23.40 | 139.90 | 1829.44 | −105.81 |
14 | 185.73 | 102.96 | 4930.10 | 124.85 | 130.37 | 24.33 | 149.38 | 1967.61 | −111.23 |
15 | 179.03 | 107.06 | 4597.29 | 121.01 | 126.87 | 26.78 | 149.25 | 1905.76 | −94.93 |
16 | 178.64 | 96.95 | 6320.18 | 144.88 | 150.45 | 23.97 | 163.21 | 1970.62 | −111.79 |
17 | 240.42 | 135.77 | 5827.95 | 153.76 | 161.09 | 36.81 | 190.49 | 2259.46 | −117.96 |
18 | 253.40 | 135.66 | 5827.52 | 153.75 | 161.08 | 36.75 | 190.81 | 2360.15 | −120.97 |
19 | 260.31 | 147.38 | 6529.77 | 170.17 | 178.31 | 39.03 | 210.40 | 2749.56 | −124.40 |
20 | 280.48 | 153.76 | 7226.84 | 184.39 | 192.94 | 40.08 | 225.02 | 2771.27 | −136.33 |
21 | 267.99 | 147.29 | 6529.43 | 170.17 | 178.33 | 38.50 | 210.79 | 2513.32 | −128.47 |
22 | 327.99 | 153.50 | 7225.08 | 184.32 | 192.78 | 39.42 | 226.35 | 2727.21 | −138.46 |
23 | 190.90 | 92.40 | 6777.37 | 136.99 | 142.77 | 25.46 | 151.82 | 1979.58 | −110.61 |
24 | 191.30 | 107.05 | 6571.54 | 153.18 | 159.32 | 26.69 | 174.50 | 2133.33 | −119.08 |
25 | 331.10 | 174.16 | 7307.99 | 194.72 | 204.02 | 48.71 | 244.76 | 3175.10 | −168.67 |
26 | 309.58 | 191.50 | 7332.09 | 201.39 | 211.92 | 53.05 | 253.29 | 3230.21 | −164.60 |
27 | 190.21 | 83.28 | 6640.35 | 144.47 | 149.29 | 19.82 | 157.57 | 1816.70 | −115.25 |
28 | 218.02 | 97.17 | 4012.63 | 106.64 | 111.81 | 26.47 | 129.86 | 1682.95 | −83.82 |
29 | 212.42 | 92.41 | 4453.25 | 112.53 | 117.45 | 23.89 | 136.29 | 1811.12 | −88.93 |
30 | 173.32 | 81.32 | 5929.80 | 120.61 | 125.71 | 25.00 | 132.03 | 1756.26 | −92.75 |
31 | 170.34 | 90.61 | 4002.95 | 104.46 | 109.29 | 25.03 | 128.51 | 1684.98 | −83.54 |
32 | 178.67 | 104.22 | 4824.82 | 123.06 | 129.03 | 27.87 | 146.61 | 1942.93 | −94.35 |
33 | 301.59 | 128.75 | 5902.73 | 151.65 | 158.79 | 32.41 | 186.62 | 2379.78 | −111.36 |
34 | 202.06 | 113.48 | 5649.74 | 141.23 | 147.54 | 29.60 | 169.10 | 2107.86 | −113.38 |
35 | 148.12 | 69.41 | 3452.63 | 85.88 | 89.58 | 13.17 | 103.81 | 1270.25 | −67.10 |
36 | 129.10 | 74.99 | 4148.18 | 100.12 | 104.16 | 12.54 | 117.98 | 1486.28 | −83.28 |
R2 | 0.552 | 0.025 | 0.729 | 0.740 | 0.821 | 0.824 | 0.818 | 0.672 |
αiso@S0 | SS | IF | SGBP | rR2 | rR3 | |
R2 | 0.845 | 0.553 | 0.025 | 0.723 | 0.730 | 0.742 |
IG | G1 | G2 | G3 | Vol | Θiso | |
R2 | 0.819 | 0.844 | 0.827 | 0.820 | 0.674 | 0.689 |
R2 | SS | IF | SGBP | rR2 | rR3 | IG | G1 | G2 | G3 | Vol | Θiso |
---|---|---|---|---|---|---|---|---|---|---|---|
αiso@S0 | 0.560 | 0.068 | 0.890 | 0.897 | 0.909 | 0.925 | 0.938 | 0.912 | 0.940 | 0.923 | 0.887 |
αiso@S1 | 0.553 | 0.025 | 0.723 | 0.730 | 0.743 | 0.825 | 0.843 | 0.824 | 0.821 | 0.818 | 0.667 |
Index | αiso | SGBP | rR2 | rR3 | IG | G1 | G2 | G3 | Vol | Θiso |
---|---|---|---|---|---|---|---|---|---|---|
37 | 105.36 | 109.32 | 109.77 | 110.45 | 143.92 | 146.72 | 154.26 | 120.04 | 137.25 | 115.53 |
38 | 155.68 | 151.14 | 151.26 | 151.64 | 169.53 | 185.83 | 187.63 | 158.87 | 163.68 | 147.97 |
39 | 216.91 | 196.27 | 196.48 | 197.01 | 207.58 | 229.76 | 236.35 | 203.48 | 205.75 | 184.62 |
40 | 101.70 | 113.02 | 113.08 | 113.47 | 140.59 | 136.98 | 143.60 | 120.15 | 136.21 | 100.86 |
41 | 166.55 | 150.90 | 151.41 | 152.11 | 174.87 | 185.60 | 194.70 | 166.02 | 168.11 | 144.96 |
42 | 111.10 | 102.29 | 102.60 | 102.89 | 130.30 | 116.57 | 125.36 | 97.52 | 125.61 | 106.82 |
43 | 196.65 | 193.10 | 192.90 | 193.28 | 200.66 | 216.50 | 224.05 | 196.26 | 199.29 | 253.81 |
MUE a (%) | −2.38 | −2.22 | −1.88 | 14.82 | 17.96 | 22.97 | 2.17 | 11.36 | 0.18 | |
MSE b (%) | 6.64 | 6.61 | 6.56 | 16.05 | 17.96 | 22.97 | 7.58 | 12.83 | 10.89 |
Index | αiso | rR2 | rR3 | G2 | G3 | Vol | Θiso |
---|---|---|---|---|---|---|---|
37 | 118.81 | 113.52 | 113.85 | 152.35 | 120.93 | 116.81 | 114.30 |
38 | 192.21 | 153.15 | 153.33 | 189.82 | 159.90 | 158.02 | 132.22 |
39 | 290.76 | 196.25 | 196.61 | 235.54 | 204.05 | 179.41 | 170.00 |
40 | 117.99 | 116.65 | 116.65 | 139.41 | 121.02 | 119.35 | 100.33 |
41 | 148.92 | 153.43 | 154.11 | 194.56 | 165.60 | 167.43 | 159.88 |
42 | 111.22 | 106.39 | 105.78 | 122.68 | 97.10 | 128.12 | 107.88 |
43 | 205.36 | 192.73 | 192.65 | 215.87 | 196.92 | 197.54 | 227.59 |
MUE a (%) | −9.41 | −9.36 | 10.32 | −6.84 | −4.69 | −10.90 | |
MSE b (%) | 10.27 | 10.35 | 16.10 | 11.28 | 12.91 | 16.10 |
Ground-State (S0) | Excited-State (S1) | |||||
---|---|---|---|---|---|---|
Becke | Hirshfeld | Avg. | Becke | Hirshfeld | Avg. | |
Based on the original TS formula | ||||||
MUE (%) a | −26.44 | 7.92 | −9.26 | −24.94 | 8.93 | −8.01 |
MSE (%) b | 28.87 | 9.03 | 14.40 | 28.59 | 12.76 | 15.53 |
Based on the new TS formula | ||||||
MUE (%) a | −29.02 | 7.22 | −10.90 | −27.31 | 8.31 | −9.50 |
MSE (%) b | 31.45 | 8.33 | 16.04 | 30.95 | 12.61 | 17.02 |
Index | Excitation Energies | ||
---|---|---|---|
Conv. | Mod_1 c | Mod_2 d | |
37 | 4.28 | 2.24 | 2.25 |
38 | 3.52 | 2.67 | 2.55 |
39 | 3.53 | 2.64 | 2.51 |
40 | 4.55 | 3.00 | 3.45 |
41 | 4.12 | 3.13 | 3.33 |
42 | 3.71 | 3.30 | NA e |
43 | 4.28 | 5.14 | 5.65 |
MUE a | −0.84 | −0.76 | |
MSE b | 1.08 | 1.21 |
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Zhao, D.; He, X.; Ayers, P.W.; Liu, S. Excited-State Polarizabilities: A Combined Density Functional Theory and Information-Theoretic Approach Study. Molecules 2023, 28, 2576. https://doi.org/10.3390/molecules28062576
Zhao D, He X, Ayers PW, Liu S. Excited-State Polarizabilities: A Combined Density Functional Theory and Information-Theoretic Approach Study. Molecules. 2023; 28(6):2576. https://doi.org/10.3390/molecules28062576
Chicago/Turabian StyleZhao, Dongbo, Xin He, Paul W. Ayers, and Shubin Liu. 2023. "Excited-State Polarizabilities: A Combined Density Functional Theory and Information-Theoretic Approach Study" Molecules 28, no. 6: 2576. https://doi.org/10.3390/molecules28062576
APA StyleZhao, D., He, X., Ayers, P. W., & Liu, S. (2023). Excited-State Polarizabilities: A Combined Density Functional Theory and Information-Theoretic Approach Study. Molecules, 28(6), 2576. https://doi.org/10.3390/molecules28062576