Theoretical approaches to the calculation of raman optical activity spectra

Chirality

Volumn 21, Issue 1 E, 2009, Pages

  Ruud, Kenneth ^a   Thorvaldsen, Andreas J ^a  

^a UNIVERSITY OF TROMSØ   (Norway)

Author keywords

Ab initio calculations; Chiral molecules; Raman optical activity

Indexed keywords

FORECASTING; OPTICAL ROTATION; RAMAN SPECTROMETRY; REVIEW;

FORECASTING; OPTICAL ROTATION; SPECTRUM ANALYSIS, RAMAN;

EID: 77951796932     PISSN: 08990042     EISSN: 1520636X     Source Type: Journal    
DOI: 10.1002/chir.20777     Document Type: Conference Paper

References (120)

1. Barron LD. Molecular light scattering and optical activity, 2nd ed. Cambridge: Cambridge University Press; 2004.
2. Barron LD, Buckingham AD. Rayleigh and Raman scattering from optically active molecules. Mol Phys 1971;20:1111-1119.
3. Barron LD, Bogaard MP, Buckingham AD. Raman scattering of circularly polarized light by optically active molecules. J Am Chem Soc 1973;95:603-605.
4. Hug W, Kint S, Bailey GF, Scherer JR. Raman circular intensity differential spectroscopy. Spectra of (2)-a-pinene and (1)-a-phenylethylamine. J Am Chem Soc 1975;97:5589-5590.
5. Haesler J, Schindelholz I, Riguet E, Bochet CG, Hug W. Absolute configuration of chirally deuterated neopentane. Nature 2007;446:526- 529.
6. Bell AF, Hecht L, Barron LD. Vibrational Raman optical activity of DNA and RNA. J Am Chem Soc 1998;120:5820-5821.
7. Barron LD, Hecht L, Bell AF, Wilson G. Recent developments in Raman optical activity of biopolymers. Appl Spectrosc 1996;50:619- 629.
8. Polavarapu PL, Deng Z. Structural determinations using vibrational Raman optical activity: from a single peptide group to b-turns. Faraday Discuss 1994;99:151-163.
9. Buckingham AD. Introductory lecture. The theoretical background to vibrational optical activity. Faraday Discuss 1994;99:1-12.
10. Hug W, Hangartner G. A novel high-throughput Raman spectrometer for polarization difference measurements. J Raman Spectrosc 1999;30:841-852.
11. Hug W. Virtual enantiomers as the solution of optical activity's deterministic offset problem. Appl Spectrosc 2003;57:1-13.
12. Sasagane K, Aiga F, Itoh R. Higher-order response theory based on the quasienergy derivatives: The derivation of the frequency-dependent polarizabilities and hyperpolarizabilities. J Chem Phys 1993;99:3738-3778.
13. Christiansen O, Jørgensen P, Hättig C. Response functions from Fourier component variational perturbation theory applied to a timeaveraged quasienergy. Int J Quantum Chem 1998;68:1-52.
14. Thorvaldsen AJ, Ruud K, Kristensen K, Jørgensen P, Coriani S. A density matrix-based quasienergy formulation of the Kohn-Sham density functional response theory using perturbation- and time-dependent basis sets. J Chem Phys 2008;129:214108.
15. Pecul M, Ruud K. Ab initio calculation of vibrational Raman optical activity. Int J Quantum Chem 2005;104:816-829.
16. Polavarapu PL. Quantum mechanical predictions of chiroptical vibrational properties. Int J Quantum Chem 2006;106:1809-1814.
17. Nafie LA. Vibrational optical activity. Appl Spectrosc 1996;50:14A- 26A.
18. Nafie LA. Infrared and Raman vibrational optical activity: theoretical and experimental aspects. Ann Rev Phys Chem 1997;48:357-386.
19. Hug W. Raman optical activity spectroscopy. In: Chalmers JM, Griffiths PR, editors. Handbook of vibrational spectroscopy, Vol. 1. New York: John Wiley; 2002. p 745-758.
20. Freedman TB, Nafie LA. Vibrational optical activity calculations using infrared and Raman atomic polar tensors. J Chem Phys 1983;78:27-31.
21. London F. Théorie quantique des courants interatomiques dans les combinaisons aromatiques. J Phys Radium 1937;8:397-409.
22. Dalton J. An ab initio electronic structure program. Release 2.0. Available at: http://www.kjemi.uio.no/software/dalton/dalton.html; accessed March 1 2005.
23. 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, Bakken V, 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. Gaussian 03, Revision C.02. Wallingford; Gaussian, Inc.; 2004.
24. Ahlrichs R, Bär M, Häser M, Horn H, Kölmel C. Electronic structure calculations on workstation computers: The program system turbomole. Chem Phys Lett 1989;162:165-169.
25. Luber S, Reiher M. Raman optical activity spectra of chiral transition metal complexes. Chem Phys 2008;346:212-223.
26. 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 MD, Tozer DJ. CADPAC: The Cambridge analytic derivatives package issue 6. Cambridge; 1995.
27. Polavarapu PL. Ab initio vibrational Raman and Raman optical activity spectra. J Phys Chem 1990;94:8106-8112.
28. Bose PB, Polavarapu PL, Barron LD, Hecht L. Ab initio and experimental Raman optical activity in (1)-(R)-methyloxirane. J Phys Chem 1990;94:1734-1740.
29. Amos RD. Electric and magnetic properties of CO, HF, HCl, and CH3F. Chem Phys Lett 1982;87:23-26.
30. Polavarapu PL. Ab initio molecular optical rotations and absolute configurations. Mol Phys 1997;91:551-554.
31. Helgaker T, Ruud K, Bak KL, Jørgensen P, Olsen J. Vibrational Raman optical activity calculations using London atomic orbitals. Faraday Discuss 1994;99:165-180.
32. Ruud K, Helgaker T, Bouř P. Gauge-origin independent densityfunctional theory calculations of vibrational Raman optical activity. J Phys Chem A 2002;106:7448-7455.
33. Pecul M, Rizzo A. Raman optical activity spectra: basis set and electron correlation effects. Mol Phys 2003;101:2073-2081.
34. Zuber G, Hug W. Rarefied basis sets for the calculation of optical tensors. I. The importance of gradients on hydrogen atoms for the raman scattering tensor. J Phys Chem A 2004;108:2108- 2118.
35. Reiher M, Liegeois V, Ruud K. Basis set and density functional dependence of vibrational Raman optical activity calculations. J Phys Chem A 2005;109:7567-7574.
36. Stephens PJ, Jalkanen KJ, Devlin FJ, Chabalowski CF. Ab initio calculation of vibrational circular dichroism spectra using accurate post-self-consistent-field force fields: trans-2, 3-dideuteriooxirane. J Phys Chem 1993;97:6107-6110.
37. Hansen AE, Bouman TD. Localized orbital/local origin method for calculation and analysis of NMR shieldings. Applications to 13C shielding tensors. J Chem Phys 1985;82:5035-5047.
38. Bak KL, Jørgensen P, Helgaker T, Ruud K, Jensen HJA. Gauge-origin independent multiconfigurational self-consistent-field theory for vibrational circular dichroism. J Chem Phys 1993;98:8873-8887.
39. Olsen J, Bak KL, Ruud K, Helgaker T, Jørgensen P. Orbital connections for perturbation-dependent basis sets. Theor Chem Acc 1995;90:421-439.
40. Krykunov M, Autschbach J. Calculation of static and dynamic linear magnetic response in approximate time-dependent density functional theory. J Chem Phys 2007;126:024101.
41. Linderberg J, Öhrn Y. Propagators in quantum chemistry, 2nd ed. New Jersey: Wiley; 2004.
42. Olsen J, Jørgensen P. Linear and nonlinear response functions for an exact state and for an MCSCF state. J Chem Phys 1985;82:3235- 3264.
43. Yu GS, Freedman TB, Nafie LA, Deng Z, Polavarapu PL. Experimental measurement and ab initio calculation of Raman optical activity of L-alanine and its deuterated isotopomers. J Phys Chem 1995;99:835-843.
44. Jalkanen KJ, Nieminen RM, Frimand K, Bohr J, Bohr H, Wade RC, Tajkhorshid E, Suhai S. A comparison of aqueous solvent models used in the calculation of the Raman and ROA spectra of L-alanine. Chem Phys 2001;265:125-151.
45. Stephens PJ, Devlin FJ, Cheeseman JR, Frisch MJ. Calculation of optical rotation using density functional theory. J Phys Chem A 2001;105:5356-5371.
46. Pedersen TB, Koch H, Hättig C. Gauge invariant coupled cluster response theory. J Chem Phys 1999;110:8318-8327.
47. Pedersen TB, Fernández B, Koch H. Gauge invariant coupled cluster response theory using optimized nonorthogonal orbitals. J Chem Phys 2001;114:6983-6993.
48. Crawford TD. Ab initio calculation of molecular chiroptical properties. Theor Chem Acc 2006;115:227-245.
49. Helgaker T, Wilson PJ, Amos RD, Handy NC. Nuclear shielding constants by density functional theory with gauge including atomic orbitals. J Chem Phys 2000;113:2983-2989.
50. Sałek P, Vahtras O, Helgaker T, Agren H. Density-functional theory of linear and nonlinear time-dependent molecular properties. J Chem Phys 2002;117:9630-9645.
51. Cheeseman JR, Frisch MJ, Devlin FJ, Stephens PJ. Hartree-Fock and density functional theory ab initio calculation of optical rotation using GIAOs: basis set dependence. J Phys Chem A 2000;104:1039-1046.
52. Ruud K, Helgaker T. Optical rotation studied by density-functional and coupled-cluster methods. Chem Phys Lett 2002;352:533-539.
53. Gross EKU, Kohn W. Time-Dependent Density-Functional Theory. In: Löwdin PO, editor. Density functional theory of Many-Fermion systems, Vol. 21 of Advances in Quantum Chemistry, Academic Press; New York: 1990. p 255-291.
54. Casida ME. Time-dependent density functional response theory for molecules. In: Chong DP, editor. Recent advances in density functional methods. Singapore: World Scientific; 1995. p 155-192.
55. Jalkanen KJ, Gale JD, Jalkanen GJ, McIntosh DF, El-Azhary AA, Jensen GM. trans-1, 2-Dicyano-cyclopropane and other cyano-cyclopropane derivatives: theoretical and experimental VA, VCD, Raman and ROA spectroscopic study. Theor Chem Acc 2008;119: 211-229.
56. Buděšínský M, Šebestík J, Bednárová L, Baumruk V, Šafařík M, Bouř P. Conformational properties of the Pro-Gly motif in the d-Alal- Pro-Gly-d-Ala model peptide explored by a statistical analysis of the NMR, Raman, and Raman optical activity spectra. J Org Chem 2008;73:1481-1489.
57. Buděšínský M, Daněček P, Bednárová L, Kapitán J, Baumruk V, Bouř P. Comparison of quantitative conformer analyses by nuclear magnetic resonance and Raman optical activity spectra for model dipeptides. J Phys Chem A 2008;112:8633-8640.
58. Zuber G, Goldsmith MR, Beratan DN, Wipf P. Towards Raman optical activity calculations of large molecules. ChemPhysChem 2005;6: 595-597.
59. Luber S, Herrmann C, Reiher M. Relevance of the electric-dipoleelectric- quadrupole contribution to Raman optical activity spectra. J Phys Chem B 2008;112:2218-2232.
60. Grimme S, Furche F, Ahlrichs R. An improved method for density functional calculations of the frequency-dependent optical rotation. Chem Phys Lett 2002;361:321-328.
61. Becke AD. Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys 1993;98:5648-5652.
62. Lee C, Yang W, Parr RG. Development of the Colle-Salvetti correlation- energy formula into a functional of the electron density. Phys Rev B 1988;37:785-789.
63. Norman P, Ruud K, Helgaker T. Density-functional theory calculations of optical rotatory dispersion in the nonresonant and resonant frequency regions. J Chem Phys 2004;120:5027-5035.
64. Krykunov M, Kundrat MD, Autschbach J. Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using time-dependent density functional theory. J Chem Phys 2006;125:194110.
65. Jensen L, Autschbach J, Krykunov M, Schatz GC. Resonance vibrational Raman optical activity: a time-dependent density functional theory approach. J Chem Phys 2007;127:134101.
66. Jiemchooroj A, Norman P. Electronic circular dichroism spectra from the complex polarization propagator. J Chem Phys 2007;126: 134102.
67. Bouř P. Calculation of the Raman optical activity via the sum-overstates expansion. Chem Phys Lett 1998;288:363-370.
68. Bouř P. Computations of the Raman optical activity via the sumover- states expansion. J Comp Chem 2001;22:426-435.
69. Liégeois V, Ruud K, Champagne B. An analytical derivative procedure for the calculation of vibrational Raman optical activity spectra. J Chem Phys 2007;127:204105.
70. Quinet O, Champagne B. Time-dependent Hartree-Fock schemes for analytical evaluation of the Raman intensities. J Chem Phys 2001;115:6293-6299.
71. Quinet O, Liégeois V, Champagne B. TDHF evaluation of the dipole-quadrupole polarizability and its geometrical derivatives. J Chem Theory Comput 2005;1:444-452.
72. Coriani S, Høst S, Jansik B, Thøgersen L, Olsen J, Jørgensen P, Reine S, Pawłowski F, Helgaker T, Sałek P. Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory. J Chem Phys 2007;126: 154108.
73. Kussmann J, Ochsenfeld C. A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels. J Chem Phys 2007;127:204103.
74. Niklasson AMN, Challacombe M. Density matrix perturbation theory. Phys Rev Lett 2004;92:193001.
75. Weber V, Niklasson AMN, Challacombe M. Ab initio linear scaling response theory: electric polarizability by perturbed projection. Phys Rev Lett 2004;92:193002.
76. Helgaker T, Jørgensen P. Configuration-interaction energy derivatives in a fully variational formulation. Theor Chim Acc 1989;75:111-127.
77. Kristensen K, Jørgensen P, Thorvaldsen AJ, Helgaker T. Efficient elimination of response parameters in molecular property calculations for variational and nonvariational energies. J Chem Phys 2008;129:214103.
78. Reiher M, Neugebauer J. A mode-selective quantum chemical method for tracking molecular vibrations applied to functionalized carbon nanotubes. J Chem Phys 2003;118:1634-1641.
79. Herrmann C, Ruud K, Reiher M. Can Raman optical activity separate axial from local chirality? A theoretical study of helical deca-alanine. ChemPhysChem 2006;7:2189-2196.
80. Davidson ER. The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. J Comput Phys 1975;17:87-94.
81. Herrmann C, Ruud K, Reiher M. Importance of backbone angles versus amino acid configurations in peptide vibrational Raman optical activity spectra. Chem Phys 2008;343:200-209.
82. Bouř P, Sopková J, Bednárová L, Maloň P, Keiderling TA. Transfer of molecular property tensors in cartesian coordinates: a new algorithm for simulation of vibrational spectra. J Comp Chem 1997;18: 646-659.
83. Fedorovsky M. Raman optical activity: from analyzing to synthesizing vibrational spectra. Universität Fribourg, Switzerland; 2008.
84. Kapitán J, Zhu F, Hecht L, Gardiner J, Seebach D, Barron LD. Solution structures of b-peptides from Raman optical activity. Angew Chem Int Ed 2008;47:6392-6394.
85. Kapitán J, Baumruk V, Bouř P. Demonstration of the ring conformation in polyproline by the Raman optical activity. J Am Chem Soc 2006;128:2438-2443.
86. Andrushchenko V, Wieser H, Bouř P. DNA oligonucleotide-cisplatin binding: ab initio interpretation of the vibrational spectra. J Phys Chem A 2007;111:9714-9723.
87. Bouř P, Baumruk V, Hanzlíková J. Measurement and calculation of the Raman optical activity of a-pinene and trans-pinane. Collect Czech Chem Commun 1997;62:1384-1395.
88. Kapitan J, Baumruk V, Kopecký V Jr, Pohl R, Bouř P. Proline zwitterion dynamics in solution, glass, and crystalline state. J Am Chem Soc 2006;128:13451-13462.
89. Tomasi J, Mennucci B, Cammi R. Quantum mechanical continuum solvation models. Chem Rev 2005;105:2999-3094.
90. Cammi R, Tomasi J. Remarks on the use of the apparent surface charges (ASC) methods in solvation problems: iterative versus matrix- inversion procedures and the renormalization of the apparent charges. J Comp Chem 1995;16:1449-1458.
91. Cancé s E, Mennucci B. New applications of integral equations methods for solvation continuum models: ionic solutions and liquid crystals. J Math Chem 1998;23:309-326.
92. Cammi R, Frediani L, Mennucci B, Tomasi J, Ruud K, Mikkelsen KV. A second-order, quadratically convergent multiconfigurational self-consistent field polarizable continuum model for equilibrium and nonequilibrium solvation. J Chem Phys 2002;117:13-26.
93. Klamt A, Schüürmann G. COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient. J Chem Soc, Perkin Trans 2 1993;5:799-805.
94. Pecul M, Lamparska E, Cappelli C, Frediani L, Ruud K. Solvent effects on Raman optical activity spectra calculated using the polarizable continuum model. J Phys Chem A 2006;110:2807-2815.
95. Kim HJ, Hynes JT. Equilibrium and nonequilibrium solvation and solute electronic structure. I. Formulation. J Chem Phys 1990;93: 5194-5210.
96. Cammi R, Frediani L, Mennucci B, Ruud K. Multiconfigurational self-consistent field linear response for the polarizable continuum model: theory and application to ground and excited-state polarizabilities of para-nitroaniline in solution. J Chem Phys 2003;119: 5818-5827.
97. Cammi R, Mennucci B, Tomasi J. An attempt to bridge the gap between computation and experiment for nonlinear optical properties: macroscopic susceptibilities in solution. J Phys Chem A 2000;104:4690-4698.
98. Ferrighi L, Frediani L, Cappelli C, Sałek P, Agren H, Helgaker T, Ruud K. Density-functional-theory study of the electric-field-induced second harmonic generation (EFISHG) of push-pull phenylpolyenes in solution. Chem Phys Lett 2006;425:267-272.
99. Han WG, Jalkanen KJ, Elstner M, Suhai S. Theoretical study of aqueous N-acetyl-L-alanine N-methylamide: structures and Raman, VCD, and ROA spectra. J Phys Chem B 1998;102:2587-2602.
100. Tajkhorshid E, Jalkanen KJ, Suhai S. Structure and vibrational spectra of the zwitterion L-alanine in the presence of explicit water molecules: a density functional analysis. J Phys Chem B 1998;102:5899-5913.
101. Knapp-Mohammady M, Jalkanen KJ, Nardi F, Wade RC, Suhai S. LAlanyl- L-alanine in the zwitterionic state: structures determined in the presence of explicit water molecules and with continuum models using density functional theory. Chem Phys 1999;240:63-77.
102. Jalkanen KJ, Jürgensen VW, Claussen A, Rahim A, Jensen GM, Wade RC, Nardi F, Jung C, Degtyarenko IM, Nieminen RM, Herrmann F, Knapp-Mohammady M, Niehaus TA, Frimand K, Suhai S. Use of vibrational spectroscopy to study protein and DNA structure, hydration, and binding of biomolecules: a combined theoretical and experimental approach. Int J Quantum Chem 2006;106:1160-1198.
103. Deplazes E, van Bronswijk W, Zhu F, Barron LD, Ma S, Nafie LA, Jalkanen KJ. A combined theoretical and experimental study of the structure and vibrational absorption, vibrational circular dichroism, Raman and Raman optical activity spectra of the L-histidine zwitterion. Theor Chem Acc 2009;119:155-176.
104. Helgaker TU. Hamiltonian expansion in geometrical distortions. In: Jørgensen P, Simons J, editors. Geometrical derivatives of energy surfaces and molecular properties. Dordrecht: Reidel; 1986. p 1-6.
105. Helgaker TU, Almlöf J, Jensen HJA, Jørgensen P. Molecular Hessians for large-scale MCSCF wave functions. J Chem Phys 1986;84:6266-6279.
106. Stanton JF, Gauss J. Analytic second derivatives in high-order many-body perturbation and coupled-cluster theories: computational considerations and applications. Int Rev Phys Chem 2000;19:61-95.
107. Thorvaldsen AJ, Ferrighi L, Ruud K, Agren H, Coriani S, Jørgensen P. Analytic ab initio calculations of coherent anti-Stokes Raman scattering (CARS). Phys Chem Chem Phys 2009;11:2293-2304.
108. Pulay P. Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. Mol Phys 1969;17:197-204.
109. Thorvaldsen AJ, Ruud K, Jaszuński M. Analytic calculations of vibrational hyperpolarizabilities in the atomic orbital basis. J Phys Chem A 2008;112:11942-11950.
110. Reine S, Tellgren E, Helgaker T. A unified scheme for the calculation of differentiated and undifferentiated molecular integrals over solid-harmonic Gaussians. Phys Chem Chem Phys 2007;9:4771- 4779.
111. Larsen H, Jørgensen P, Olsen J, Helgaker T. Hartree-Fock and Kohn-Sham atomic-orbital based time-dependent response theory. J Chem Phys 2000;113:8908-8917.
112. Jørgensen P, Jensen HJA, Olsen J. Linear response calculations for large scale multiconfiguration self-consistent field wave functions. J Chem Phys 1988;89:3654-3661.
113. Zuber G, Hug W. Computational interpretation of vibrational optical activity: The ROA spectra of (4S)-4-methylisochromane and the (4S)- isomers of galaxolide. Helv Chim Acta 2004;87:2208-2234.
114. Pecul M. Theoretical simulation of the ROA spectra of neutral cysteine and serine. Chem Phys Lett 2006;427:166-176.
115. Pecul M, Rizzo A, Leszczynski J. Vibrational Raman and Raman optical activity spectra of D-lactic acid, D-lactate, and D-glyceraldehyde: ab initio calculations. J Phys Chem A 2002;106:11008-11016.
116. Kaminský J, Kapitán J, Baumruk V, Bednárová L, Bouř P. Interpretation of Raman and Raman optical activity spectra of a flexible sugar derivative, the gluconic acid anion. J Phys Chem A 2009; 113:3594-3601.
117. Polavarapu PL, Chakraborty DK, Ruud K. Molecular optical rotation: an evaluation of semiempirical models. Chem Phys Lett 2000; 319:595-600.
118. Coriani S, Baranowska A, Ferrighi L, Forzato C, Marchesan D, Nitti P, Pitacco G, Rizzo A, Ruud K. Solvent effects on the conformational distribution and optical rotation of a-methyl paraconic acids and esters. Chirality 2006;118:357-369.
119. McCann DM, Stephens PJ, Cheeseman JR. Determination of absolute configuration using density functional theory calculation of optical rotation: chiral alkanes. J Org Chem 2004;69:8709-8717.
120. Marchesan D, Coriani S, Forzato C, Nitti P, Pitacco G, Ruud K. Optical rotation calculation of a highly flexible molecule: The case of paraconic acid. J Phys Chem A 2005;109:1449-1453.