Abstract
This review describes the first-principles calculation of chiroptical properties such as optical rotation, electronic and vibrational circular dichroism, and Raman optical activity. Recent years have witnessed a flurry of activity in this area, especially in the advancement of density-functional and coupled cluster methods, with two ultimate goals: the elucidation of the fundamental relationship between chiroptical properties and detailed molecular structure, and the development of a suite of computational tools for the assignment of the absolute configurations of chiral molecules. The underlying theory and the basic principles of such calculations are given for each property, and a number of representative applications are discussed.
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References
Eliel EL, Wilen SH (1994). Stereochemistry of organic compounds. Wiley, New York
Friedman L, Miller JG (1971). Science 172:1044
Wnendt S, Zwingenberger K (1997). Nature 385:303
Lee TJ, Scuseria GE (1995) In: Langhoff SR. (ed). Quantum mechanical electronic structure calculations with chemical accuracy. Kluwer, Dordrecht, pp. 47–108
Helgaker T, Jørgensen P, Olsen J (2000) Molecular electronic structure theory. Wiley, New York
Helgaker T, Ruden TA, Jørgensen P, Olsen J, Klopper W (2004). J Phys Org Chem 17:913
Snatzke G (1979). Angew Chem Int Ed Engl 18:363
Rinderspacher BC, Schreiner PR (2004). J Phys Chem A 108:2867
Goddard WA (1985). Science 227:917
Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University, New York
Bartlett RJ (1995) In: Yarkony DR (eds) Modern electronic structure theory, vol 2 of Advanced series in physical chemistry. World Scientific, Singapore, Chap16, pp. 1047–1131
Crawford TD, Schaefer HF (2000) In: Lipkowitz KB, Boyd DB (eds) Reviews in Computational Chemistry, vol 14, Chap. 2. VCH Publishers, New York, pp 33–136
Møller C, Plesset MS (1934). Phys Rev 46:618
Bartlett RJ (1981). Annu Rev Phys Chem 32:359
Becke AD (1993). J Chem Phys 98:5648
Lee C, Yang, Parr RG (1988). Phys Rev B 37:785
Pulay P (1983). Chem Phys Lett 100:151
Sæbø S, Pulay P (1993). Ann Rev Phys Chem 44:213
Hampel C, Werner H-J (1996). J Chem Phys 104:6286
Schütz M (2002). Phys Chem Chem Phys 4:3941
Russ NJ, Crawford TD (2004). Chem Phys Lett 400:104
Barron LD (2004) Molecular Light scattering and optical activity, 2nd edn. Cambridge University Press, Camridge
Caldwell DJ, Eyring H (1971) The theory of optical activity. Wiley, New York
Charney E (1979) The molecular basis of optical activity: optical rotatory dispersion and circular dichroism. Wiley, New York
Mason SF (1982) Molecular optical activity and the chiral discriminations. Cambridge University Press, Cambridge
Polavarapu PL (2002). Chirality 14:768
Stephens RJ, Devlin FJ, Cheeseman JR, Drisch MJ, Bortolini O, Besse P (2003). Chirality 15:S57
Stephens PJ, McCann DM, Cheeseman JR, Frisch MJ (2005). Chirality 17:S52
Polavarapu PL (1998) Vibrational spectra: principles and applications with emphasis on optical activity, vol 85 of studies in physical and theoretical chemistry. Elsevier, Amsterdam
Stephens PJ, Devlin FJ (2000). Chirality 12:172
Freedman TB, Cao X, Dukor RK, Nafie (2003). Chirality 15:743
Nafie LA (1997). Ann Rev Phys Chem 48:357
Barron LD, Hecht L, McColl IH, Blanch EW (2004). Mol Phys 102:731
Wagnière GH (1999). Chem Phys 245:165
Coriani S, Jørgensen P, Rizzo A, Ruud K, Olsen J (1999). Chem Phys Lett 300:61
Coriani S, Pecul M, Rizzo A, Jørgensen P, Jaszunski M (2002). J Chem Phys 117:6417
Rizzo A, Kallay M, Gauss J, FPawlowski, Jørgensen P, Hättig C (2004). J Chem Phys 121:9461
Ekstrom U, Norman P, Rizzo A (2005). J Chem Phys 122:074321
Kirkwood J, Albrecht AC, Fischer P, Buckingham AD (2002) In: Hicks J (ed) Chirality: physical chemistry, vol 810 of ACS symposium series Chap. 10. Oxford University Press, Oxford, pp 130–144
Stephens PJ (1970). J Chem Phys 52:3489
Stephens PJ (1976). Adv Chem Phys 35:197
Buckingham AD (2004). Chem Phys Lett 398:1
Rosenfeld L (1928). Z Physik 52:161
Jørgensen P, Simons J (1981) Second quantization-based methods in quantum chemistry. Academic, New York
Linderberg J, öhrn Y (2004) Propagators in quantum chemistry, 2nd edn. Wiley, New Jersey
Rowe DJ (1968). Rev Mod Phys 40:153
Casida ME (1995) In: Chong DP (ed) Recent advances in density functional methods, vol 1. World Scientific, Singapore
Bauernschmitt R, Ahlrichs R (1996). Chem Phys Lett 256:454
Grimme S (2001). Chem Phys Lett 339:380
Ruud K, Helgaker T (2002). Chem Phys Lett 352:533
Furche F (2001). J Chem Phys 114:5982
Autschbach J, Patchkovskii S, Ziegler T, van Gisbergen S, Baerends EJ (2002). J Chem Phys 117:581
Polavarapu PL (1997). Mol Phys 91:551
Amos RD (1982). Chem Phys Lett 87:23
Cheeseman JR, Frisch MJ, Devlin FJ, Stephens PJ (2000). J Phys Chem A 104:1039
Stephens PJ, Devlin FJ, Cheeseman JR, Frisch MJ (2001). J Phys Chem A 105:5356
Amos RD, Alberts IL, Andrews JS, Colwell SM, Handy NC, Jayatilaka D, Knowles PJ, Kobayashi R, Laidig KE, Laming G, Lee AM, Maslen PE, Murray CW, Rice JE, Simandiras ED, Stone AJ, Su M-D, Tozer DJ (1995) CADPAC: The Cambridge Analytic Derivatives Package Issue 6, Cambridge. A suite of quantum chemistry programs
Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2003) GAUSSIAN-03. Gaussian, Inc., Pittsburg
Ahlrichs R, Bärand M, Baron H-P, Bauernschmitt R, Böcker S, Deglmann P, Ehrig M, Eichkorn K, Elliott S, Furche F, Haase F, Häser M, Horn H, Hättig C, Huber C, Huniar U, Kattannek M, Köhn A, Kölmel C, Kollwitz M, May K, Ochsenfeld C, Ohm H, Patzelt H, Rubner O, Schäfer A, Schneider U, Sierka M, Treutler O, Unterreiner B, von Arnim M, Weigend F, Weis P, Weiss H (2002) Turbomole v5.6
Crawford TD, Sherrill CD, Valeev EF, Fermann JT, King RA, Leininger ML, Brown ST, Janssen CL, Seidl ET, Kenny JP, Allen WD (2003) PSI 3.2
DALTON, a molecular electronic structure program, Release 2.0 (2005) see http://www.kjemi.uio.no/software/dalton/dalton.html
Amsterdam Density Functional program, Theoretical Chemistry, Vrije Universiteit, Amsterdam, http://www.scm.com
Grimme S, Furche F, Ahlrichs R (2002). Chem Phys Lett 361:321
Koch H, Jørgensen P (1990). J Chem Phys 93:3333
Christiansen O, Jørgensen P, Hättig C (1998). Int J Quantum Chem 68:1
Pedersen TB, Koch K (1997). J Chem Phys 106:8059
Ruud K, Stephens PJ, Devlin FJ, Taylor PR, Cheeseman JR, Frisch MJ (2003). Chem Phys Lett 373:606
Helgaker T, Jensen HJAa, Jørgensen P, Olsen J, Ruud K, Ågren H, Auer AA, Bak KL, Bakken V, Christiansen O, Coriani S, Dahle P, Dalskov EK, Enevoldsen T, Fernandez B, Hättig C, Hald K, Halkier A, Heiberg H, Hettema H, Jonsson D, Kirpekar S, Kobayashi R, Koch H, Mikkelsen KV, Norman P, Packer MJ, Pedersen TB, Ruden TA, Sanchez A, Saue T, Sauer SPA, Schimmelpfennig B, Sylvester-Hvid KO, Taylor PR, Vahtras O (2005) Dalton, a molecular electronic structure program, Release 2.0
Tam MC, Russ NJ, Crawford TD (2004). J Chem Phys 121:3550
Crawford TD, Owens LS, Tam MC, Schreiner PR, Koch H (2005). J Am Chem Soc 127:1368
Kongsted J, Pedersen TB, Strange M, Osted A, Hansen AE, Mikkelsen KV, Pawlowski F, Jørgensen P, Hättig C (2005). Chem Phys Lett 401:385
Koch H, Christiansen O, Jørgensen P, Olsen J (1995). Chem Phys Lett 244:75
Pedersen TB, Koch H, Hättig C (1999). J Chem Phys 110:8318
London F (1937). J Phys Radium 8:397
Helgaker T, Jørgensen P (1991). J Chem Phys 95:2595
Ditchfield R (1974). Mol Phys 27:789
Wolinski K, Hinton JF, Pulay P (1990). J Am Chem Soc 112:8251
Gauss J, Stanton JF (1995). J Chem Phys 103:3561
Bak KL, Hansen AE, Ruud K, Heglaker T, Olsen J, Jørgensen P (1995). Theor Chim Acta 90:441
Helgaker T, Ruud K, Bak KL, Jørgensen P, Olsen J (1994). Faraday Discuss 99:165
The lack of equivalence between the length- and velocity-gauge representations of the Rosenfeld tensor for truncated coupled cluster models arises because of the lack of variational optimization of the underlying molecular orbitals, and, thus the same problem will arise for perturbation theory and multireference configuration interaction models. This problem has been addressed by Pedersen and Koch, who, in Ref. [73], developed a gauge-invariant form of coupled cluster theory through the optimized coupled cluster (OCC) approach
Pedersen TB, Koch H, Boman L, de Meras AMJS (2004). Chem Phys Lett 393:319
Polavarapu PL, Chakraborty DK (1998). J Am Chem Soc 120:6160
Polavarapu PL, Chakraborty DK (1999). Chem Phys 240:1
Kondru RK, Wipf P, Beratan DN (1998). J Am Chem Soc 120:2204
Perry TL, Dickerson A, Kahn AA, Kondru RK, Beratan DN, Wipf P, Kelly M, Hamann MT (2001). Tetrahedron 57:1483
Ribe S, Kondru RK, Beratan DN, Wipf P (2000). J Am Chem Soc 122:4608
Goldsmith M-R, Jayasuriya N, Beratan DN, Wipf P (2003). J Am Chem Soc 125:15696
Kondru RK, Wipf P, Beratan DN (1998). Science 282:2247
Stephens PJ, Devlin FJ, Cheeseman JR, Frisch MJ, Rosini C (2002). Org Lett 4:4595
Polavarapu PL (2002). Angew Chem Int Ed 41:4544
Hecht L, Costante J, Polavarapu PL, Collet A, Barron LD (1997). Angew Chem Int Ed 36:885
Schreiner PR, Fokin AA, Lauenstein O, Okamoto Y, Wakita T, Rinderspacher C, Robinson GH, Vohs JK, Campana CF (2002). J Am Chem Soc 124:13348
Giorgio E, Viglione RG, Zanasi R, Rosini C (2004). J Am Chem Soc 126:12968
Norman P, Ruud K, Helgaker T (2004). J Chem Phys 120:5027
Wiberg KB, Vaccaro PH, Cheeseman JR (2003). J Am Chem Soc 125:1888
Wiberg KB, Wang YG, Vaccaro PH, Cheeseman JR, Trucks G, Frisch MJ (2004). J Phys Chem A 108:32
Wiberg KB, Wang Y-G, Vaccaro PH, Cheeseman JR, Luderer MR (2005). J Phys Chem A 109:3405
Kumata Y, Furukawa J, Fueno T (1970). Bull Chem Soc Japan 43:3920
Mennucci B, Tomasi J, Cammi R, Cheeseman JR, Frisch MJ, Devlin FJ, Gabriel S, Stephens PJ (2002). J Phys Chem A 106:6102
Christiansen O, Koch H, Jørgensen P (1998). Chem Phys Lett 243:409
de Meijere A, Khlebnikov AF, Kostikov RR, Kozhushkov SI, Schreiner PR, Wittkopp A, Yufit DS (1999). Angew Chem Int Ed 38:3474
de Meijere A, Khlebnikov AF, Kostikov RR, Kozhushkov SI, Schreiner PR, Wittkopp A, Rinderspacher C, Menzel H, Yufit DS, Howard JAK (2002). Chem Eur J 8:828
Koch H, de Merás AMJS, Pedersen TB (2003). J Chem Phys 118:9481
Pedersen TB, de Merás AMJS, Koch H (2004). J Chem Phys 120:8887
Müller T, Wiberg KB, Vaccaro PH (2000). J Phys Chem A 104:5959
Müller T, Wiberg KB, Vaccaro PH, Cheeseman JR, Frisch MJ (2002). J Opt Soc Am B 19:125
Giorgio E, Rosini C, Viglione RG, Zanasi R (2003). Chem Phys Lett 376:452
Ruud K, Zanasi R (2005). Angew Chem Int Ed Engl 44:3594
Ruud K, Taylor PR, Åstrand P-O (2001). Chem Phys Lett 337:217
Hansen AE, Bouman TD (1980). Adv Chem Phys 44:545
Rauk A (1998) In: Schleyer PVR (ed) Encyclopedia of computational chemistry. Wiley, New York
Foresman JB, Head-Gordon M, Pople JA, Frisch MJ (1992). J Phys Chem 96:135
Tamm I (1945). J Phys USSR 9:449
Dancoff SM (1950). Phys Rev 78:382
Pople JA (1953). Trans Faraday Soc 49:1375
Del Bene JE, Ditchfield R, Pople JA (1971). J Chem Phys 55:2236
Grimme S, Harren J, Sobanski A, Vögtle F (1998). Eur J Org Chem 1491
Stanton JF, Gauss J, Ishikawa N, Head-Gordon M (1995). J Chem Phys 103:4160
Tozer DJ, Amos RD, Handy NC, Roos BO, Serrano-Andrés L (1999). Mol Phys 97:859
Dreuw A, Weisman JL, Head-Gordon M (2003). J Chem Phys 119:2943
Tozer DJ, Handy NC (2000). Phys Chem Chem Phys 2:2117
Hamprecht FA, Cohen AJ, Tozer DJ, Handy NC (1998). J Chem Phys 109:6264
Burcl R, Amos RD, Handy NC (2002). Chem Phys Lett 355:8
Pecul M, Ruud K, Helgaker T (2004). Chem Phys Lett 388:110
Rauk A (1984). J Am Chem Soc 106:6517
Hansen AE, Bouman TD (1985). J Am Chem Soc 107:4828
Carnell M, Peyerimhoff SD, Breest A, Godderz KH, Ochmann P, Hormes J (1991). Chem Phys Lett 180:477
Grimme S, Peyerimhoff SD, Bartram S, Vögtle F, Breest A, Hormes J (1993). Chem Phys Lett 213:32
Carnell M, Grimme S, Peyerimhoff SD (1994). Chem Phys 179:385
Carnell M, Peyerimhoff SD (1994). Chem Phys 183:37
Grimme S (1996). Chem Phys Lett 259:128
Pulm F, Schramm J, Hormes J, Grimme S, Peyerimhoff SD (1997). Chem Phys 224:143
Furche F, Ahlrichs R, Wachsmann C, Weber E, Sobanski A, Vögtle F, Grimme S (2000). J Am Chem Soc 122:1717
Autschbach J, Ziegler T, van Gisbergen SJA, Baerends EJ (2002). J Chem Phys 116:6930
Autschbach J, Jorge FE, Ziegler T (2003). Inorg Chem 42:2867
Neugebauer J, Baerends EJ, Nooijen M, Autschbach J (2005). J Chem Phys 122:234305
Pecul M, Marchesan D, Ruud K, Coriani S (2005). J Chem Phys 122:024106
Diedrich C, Grimme S (2003). J Phys Chem A 107:2524
Waletzke M, Grimme S (2000). Phys Chem Chem Phys 2:2075
Grimme S, Waletzke M (1999). J Chem Phys 111:5645
Stephens PJ, McCann DM, Devlin FJ, Cheeseman JR, Frisch MJ (2004). J Am Chem Soc 126:7514
Stephens PJ, McCann DM, Butkus E, Stoncius S, Cheeseman JR, Frisch MJ (2004). J Org Chem 69:1948
Stanton JF, Bartlett RJ (1993). J Chem Phys 98:7029
Christiansen O, Halkier A, Koch H, Jørgensen P, Helgaker T (1998). J Chem Phys 108:2801
Pedersen TB, Koch H, Ruud K (1999). J Chem Phys 110:2883
Pedersen TB, Hansen AE (1995). Chem Phys Lett 246:1
Pedersen TB, Koch H (2000). J Chem Phys 112:2139
Yamaguchi Y, Osamura Y, Goddard JD, Schaefer HF (1994) A new dimension to quantum chemistry: analytic derivative methods in ab initio molecular electronic structure theory, No. 29 in international series of monographs on chemistry. Oxford University Press, New York
Wilson EB, Decius JC, Cross PC (1980) Molecular vibrational: the theory of infrared and raman vibrational spectra. Dover, New York
Barron LD, Buckingham AD (2001). Acc Chem Res 34:781
Stephens PJ (1985). J Phys Chem 89:748
Buckingham AD, Fowler PW, Galwas PA (1987). Chem Phys 112:1
Buckingham AD (1994). Faraday Discuss 99:1
Stephens PJ (1987). J Phys Chem 91:1712
Stevens RM, Pitzer RM, Lipscomb WN (1963). J Chem Phys 38:550
Koch H, Jensen HJAa, Jørgensen P, Helgaker T, Scuseria GE, Schaefer HF (1990). J Chem Phys 92:4924
Gauss J, Stanton JF (1997). Chem Phys Lett 276:70
Stanton JF, Gauss J (1997) In: Bartlett RJ (ed) Recent advances in coupled-cluster methods. World Scientific Publishing, Singapore, pp 49–79
Gauss J, Stanton JF (1995). J Chem Phys 103:3561
Raghavachari K, Trucks GW, Pople JA, Head-Gordon M (1989). Chem Phys Lett 157:479
Bartlett RJ, Watts JD, Kucharski SA, Noga J (1990). Chem. Phys. Lett. 165:513 erratum: 167:609
Noga J, Bartlett RJ, Urban M (1987). Chem Phys Lett 134:126
Lowe MA, Segal GA, Stephens PJ (1986). J Am Chem Soc 108:248
Lowe MA, Stephens PJ, Segal GA (1986). Chem Phys Lett 123:108
Amos RD, Handy NC, Jalkanen KJ, Stephens PJ (1987). Chem Phys Lett 133:21
Morokuma K, Sugeta H (1987). Chem Phys Lett 134:23
Amos RD, Handy NC, Palmieri P (1990). J Chem Phys 93:5796
Stephens PJ, Jalkanene KJ, Devlin FJ, Chabalowski CF (1993). J Phys Chem 97:6107
Stephens PJ, Chabalowski CF, Devlin FJ, Jalkanen KJ (1994). Chem Phys Lett 225:247
Amos RD, Jalkanen KJ, Stephens PJ (1988). J Phys Chem 92:5571
Yang DY, Rauk A (1992). J Chem Phys 97:6517
Bak KL, Jørgensen P, Helgaker T, Ruud K, Jensen HJAa (1993). J Chem Phys 98:8873
Bak KL, Jørgensen P, Helgaker T, Ruud K (1994). Faraday Discuss 99:121
Stephens PJ, Devlin FJ, Ashvar CS, Chabalowski CF, Frisch MJ (1994). Faraday Discuss 99:103
Cheeseman JR, Frisch MJ, Devlin FJ, Stephens PJ (1996). Chem Phys Lett 252:211
Bak KL, Bludský O, Jørgensen P (1995). J Chem Phys 103:10548
Cappelli C, Corni S, Mennucci B, Cammi R, Tomasi J (2002). J Phys Chem A 106:12331
He J, Petrovich A, Polavarapu PL (2004). J Phys Chem A 108:1671
He J, Petrovic AG, Polavarapu PL (2004). J Phys Chem A 108:20451
Blanch EW, Hecht L, Syme CD, Volpetti V, Lomonossoff G, Nielsen K, Barron LD (2002). J Gen Virology 83:2593
Blanch EW, McColl IH, Hecht L, Nielsen K, Barron LD (2004). Vib Spectrosc 35:87
Barron LD, Buckingham AD (1971). Mol Phys 20:1111
Vibrational ROA CIDs are defined as the difference in scattering intensity of right and left circularly polarized light, arbitrarily opposite to that of VCD and ECD, which make use of rotatory strengths as a difference in left and right circularly polarized light absorption
Barron LD, Borgaard MP, Buckingham AD (1973). J Am Chem Soc 95:603
Placzek G (1934) In: Marx E (ed) Handbuch der Radiologie. Akademische, Leipzig, No. 2, p 205
Quinet O, Champagne B, Kirtman B (2001). J Comp Chem 22:1920
Jayatilaka D, Maslen PE, Amos RD, Handy NC (1992). Mol Phys 75:271
Bose PK, Barron LD, Polavarapu PL (1989). Chem Phys Lett 155:423
Bose PK, Polavarapu PL, Barron LD, Hecht L (1990). J Phys Chem 94:1734
Polavarapu PL (1990). J Phys Chem 94:8106
Polavarapu PL (1993). J Phys Chem 97:1793
Pecul M, Rizzo A (2003). Mol Phys 101:2073
Dunning TH (1989). J Chem Phys 90:1007
Kendall RA, Dunning TH, Harrison RJ (1992). J Chem Phys 96:6796
Woon DE, Dunning TH (1994). J Chem Phys 100:2975
Zuber G, Hug W (2004). J Phys Chem A 108:2108
Hehre WJ, Ditchfield R, Pople JA (1972). J Chem Phys 56:2257
Hariharan PC, Pople JA (1973). Theor Chim Acta 28:213
Bouř P (1998). Chem Phys Lett 288:363
Bouř P (2001). J Comp Chem 22:426
Ruud K, Helgaker T, Bouř P (2002). J Phys Chem A 106:7448
Bouř P, Kapitán J, Baumruk V (2001). J Phys Chem A 105:6362
Jalkanen KJ, Nieminen RM, Frimand K, Bohr J, Bohr H, Wade RC, Tajkhorshid E, Suhai S (2001). Chem Phys 265:125
Bouř P, Sychrovský V, Maloň P, Hanzlíková J, Baumruk V, Pospíšek J, Buděšínský M (2002). J Phys Chem A 106:7321
Pecul M, Rizzo A, Leszczynski J (2002). J Phys Chem A 106:11008
Hug W (2001). Chem Phys 264:53
Hug W, Zuber G, de Meijere A, Khlebnikov AE, Hansen H-J (2001). Helv Chim Acta 84:1
Zuber G, Hug W (2004). Helv Chim Acta 87:2208
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Crawford, T.D. Ab initio calculation of molecular chiroptical properties. Theor Chem Acc 115, 227–245 (2006). https://doi.org/10.1007/s00214-005-0001-4
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DOI: https://doi.org/10.1007/s00214-005-0001-4