Russian
 Russian
Home » Archive » Vol. 28, 2015 » Issue 05 »

Vol. 28, issue 05, article # 7

Kalugina Yu. N., Cherepanov V. N. Multipole electric moments and higher polarizabilities of molecules: The methodology and some results of ab initio calculations. // Optika Atmosfery i Okeana. 2015. V. 28. No. 05. P. 436-442. DOI: 10.15372/AOO20150507 [in Russian].
Copy the reference to clipboard
Abstract:

A technique for calculation of the electric multipole moments and higher molecular polarizabilities is described. The dipole, quadrupole, octupole, hexadecapole moments and the dipole, dipole-quadrupole, dipole–octupole, quadrupole–quadrupole polarizabilities of H2, O2, N2, CO2, CO, CN, HCl, HCN, NaCl, OH, N2H+, CH4, H2O molecules have been calculated using ab initio methods (R)CCSD(T) and CCSD(T) of high level with different aug-ccVXZ bases (X = Q, 5).

Keywords:

multipole moments, higher polarizabilities, ab initio calculations

References:

  1. Partridge H., Schwenke D.W. The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data // J. Chem. Phys. 1997. V. 106, N 11. P. 4618–4638.
  2. Frisch M.J., Trucks G.W., Schlegel H.B., Scuseria G.E., Robb M.A., Cheeseman J.R., Scalmani G., Barone V., Mennucci B., Petersson G.A., Nakatsuji H., Caricato M., Li X., Hratchian H.P., Izmaylov A.F., Bloino J., Zheng G., Sonnenberg J.L., Hada M., Ehara M., Toyota K., Fu-kuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Vreven T., Montgomery J.A., Jr., Peralta J.E., Ogliaro F., Bearpark M., Heyd J.J., Brothers E., Kudin K.N., Staroverov V.N., Kobayashi R., Normand J., Raghavachari K., Rendell A., Burant J.C., Iyengar S.S., Tomasi J., Cossi M., Rega N., Millam M.J., Klene M., Knox J.E., Cross J.B., Bakken V., Adamo C., Jaramillo J., Gomperts R., Stratmann R.E., Yazyev O., Austin A.J., Cammi R., Pomelli C., Ochterski J.W., Martin R.L., Morokuma K., Zakrzewski V.G., Voth G.A., Salvador P., Dannenberg J.J., Dapprich S., Daniels A.D., Farkas Ö., Foresman J.B., Ortiz J.V., Cioslowski J., Fox D.J. Gaussian 09, Revision D.01. Wallingford: Gaussian, Inc., 2009.
  3. Werner H.-J.,  Knowles P.J., Knizia G., Manby F.R, Schütz M., Celani P.,  Korona T., Lindh R., Mitrushenkov A.,  Rauhut G., Shamasundar K.R., Adler T.B., Amos R.D., Bernhardsson A., Berning A.,  Cooper D.L., Deegan M.J., O’Dobbyn A.J.,  Eckert F. Goll E., Hampel C., Hesselmann A., Hetzer G., Hrenar T., Jansen G., Köppl C., Liu Y., Lloyd A.W., Mata R.A.,  May A.J.,  McNicholas S.J., Meyer W., Mura M.E., Nicklass A., O'Neill D.P., Palmieri P., Peng D., Pflüger K.,  Pitzer R., Reiher M., Shiozaki T.,  Stoll H.,  Stone A.J., Tarroni R.,  Thorsteinsson T., Wang M., Wolf A. Molpro, version 2012.1, a package of ab initio programs.  URL: http://www.molpro.net
  4. CFOUR, a quantum chemical program package written by J.F. Stanton, J. Gauss, M.E. Harding, P.G. Szalay with contributions from A.A. Auer, R.J. Bartlett, U. Benedikt, C. Berger, D.E. Bernholdt, Y.J. Bomble, L. Cheng, O. Christiansen, M. Heckert, O. Heun, C. Huber, T.-C. Jagau, D. Jonsson, J. Jusélius, K. Klein, W.J. Lauderdale, D.A. Matthews, T. Metzroth, L.A. Mück, D.P. O'Neill, D.R. Price, E. Prochnow, C. Puzzarini, K. Ruud, F. Schiffmann, W. Schwalbach, C. Simmons, S. Stopkowicz, A. Tajti, J. Vázquez, F. Wang, J.D. Watts and the integral packages MOLECULE (J. Almlöf and P.R. Taylor), PROPS (P.R. Taylor), ABACUS (T. Helgaker, H.J. Aa. Jensen, P. Jørgensen, J. Olsen), and ECP routines by A.V. Mitin and C. van Wüllen. URL: http://www.cfour.de
  5. Dalton, a molecular electronic structure program, release  Dalton2013.0.  URL: http://daltonprogram.org/
  6. Schmidt M.W., Baldridge K.K., Boatz J.A., Elbert S.T., Gordon M.S., Jensen J.H., Koseki S., Matsunaga N., Nguyen K.A., Su S.J., Windus T.L., Dupuis M., Mont-gomery J.A. General atomic and molecular electronic structure system // J. Comput. Chem. 1993. V. 14, N 11. P. 1347–1363.
  7. TURBOMOLE V6.2 2010, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989–2007, TURBOMOLE GmbH, since 2007. URL: http://www.turbomole.com
  8. Kelih S. Molekuljarnaja nelinejnaja optika: Per. s pol'sk. / Pod red. I.L. Fabelinskogo. M.: Nauka, 1981. 672 p.
  9. Bjekingem Je. Osnovy teorii mezhmolekuljarnyh sil. Primenenie k malym molekulam // Mezhmolekuljarnye vzaimodejstvija: ot dvuhatomnyh molekul do biopolimerov / Pod red. B. Pjul'mana. M.: Mir, 1981. P. 9–98.
  10. Buckingham D. Permanent and induced molecular moments and long-range intermolecular forces // Adv. Chem. Phys. 1967. V. 12. P. 107–142.
  11. Kalugina Yu. Theoretical investigation of the potential energy, dipole moment and polarizability surfaces of the CH4–N2 and C2H4–C2H4 van der Waals complexes: Thesis to obtain the degree of Doctor of Physics. Dijon: ICB, 2010. 206 p.
  12. Salam A. Molecular Quantum Electrodynamics: Long-Range Intermolecular Interactions. New Jersey: John Wiley and Sons, 2010. 399 p.
  13. Atoms, molecules and clusters in electric fields. Theoretical approaches to calculation of electric polarizability. Computational, numerical and mathematical methods in science and engineering. V. 1 / Ed. by G. Maroulis. Singapore: Imperial College Press, 2006. 692 p.
  14. Computational Aspects of Electric Polarizability Calculations: Atoms, Molecules and Clusters / Ed. by G. Maroulis. Amsterdam: IOS Press, 2006. 536 p.
  15. Atomic and Molecular Nonlinear Optics: Theory, Experiment and Computation. A homage to the pioneering work of Stanislaw Kielich (1925–1993) / Ed. by G. Maroulis, T. Bancewicz, B. Champagne, A.D. Buckingham. Amsterdam: IOS Press, 2011. 531 p.
  16. Zvereva-Loëte N., Kalugina Yu.N., Boudon V., Buldakov M.A., Cherepanov V.N. Dipole moment surface of the van der Waals complex CH4–N2 // J. Chem. Phys. 2010. V. 133, N 18. P. 184302.
  17. Buldakov M.A., Cherepanov V.N., Kalugina Yu.N., Zvereva-Loëte N., Boudon V. Static polarizability surfaces of the van der Waals complex CH4–N2 // J. Chem. Phys. 2009. V. 132, N 16. P. 164304.
  18. Kalugina Yu.N., Cherepanov V.N., Buldakov M.A., Zvereva-Loëte N., Boudon V. Theoretical Investigation of the Ethylene Dimer: Interaction Energy and Dipole Moment // J. Comput. Chem. 2012. V. 33, N 3. P. 319–330.
  19. Kalugina Y.N., Buldakov M.A., Cherepanov V.N. Static Hyperpolarizability of the van der Waals Complex CH4–N2 // J. Comput. Chem. 2012. V. 33, iss. 32. P. 2544–2553.
  20. Maroulis G. A systematic study of basis set, electron correlation, and geometry effects on the electric multipole moments, polarizability, and hyperpolarizability of HCl // J. Chem. Phys. 1998. V. 108, N 13. P. 5432–5448.
  21. Stone J. The Theory of Intermolecular Forces. Oxford: Clarendon Press, 2002. 264 p.
  22. Olsen J., Jørgensen P. Linear and nonlinear response functions for an exact state and for an MCSCF state // J. Chem. Phys. 1985. V. 82, N 7. P. 3235–3264.
  23. Buckingham A.D., Cordle J.E. Nuclear motion corrections to some electric and magnetic properties of diatomic molecules // Mol. Phys. 1974. V. 28, N 4. P. 1037–1047.
  24. Wormer P.E.S., Hettema H., Thakkar A.J. Intramolecular bond length dependence of the anisotropic dispersion coefficients for H2-rare gas interactions // J. Chem. Phys. 1993. V. 98, N 9. P. 7140–7144.
  25. Buckingham A.D., Disch R.L., Dummur D.A. The quadrupole moments of some simple molecules // J. Amer. Chem. Soc. 1968. V. 90, N 12. P. 3104–3107.
  26. Bartolomei M., Carmona-Novillo Estela Hernández Marta I., Campos-Martínez José, Hernández-Lamoneda Ramón. Long-Range Interaction for Dimers of Atmospheric Interest: Dispersion, Induction and Electrostatic Contributions for O2–O2, N2–N2 and O2–N2 // J. Comput. Chem. 2011. V. 32, N 2. P. 279–290.
  27. Buckingham A.D., Graham C., Williams J.H. Electric field-gradient-induced birefringence in N2, C2H6, C3H6, Cl2, N2O and CH3F // Mol. Phys. 1983. V. 49, N 3. P. 703–710.
  28. Maroulis G. Accurate electric multipole moment, static polarizability and hyperpolarizability derivatives for N2 // J. Chem. Phys. 2003. V. 118, N 6. P. 2673–2687.
  29. Kling H., Huettner W. The temperature dependence of the Cotton–Mouton effect of N2, CO, N2O, CO2, OCS, and CS2 in the gaseous state // Chem. Phys. 1984. V. 90, N 1–2. P. 207–214.
  30. Maroulis G. Electric (hyper)polarizability derivatives for the symmetric stretching of carbon dioxide // Chem. Phys. 2003. V. 291, N 1. P. 81–95.
  31. Meerts W.L., De Leeuw F.H., Dymanus A. Electric and magnetic properties of carbon monoxide by molecular-beam electric-resonance spectroscopy // Chem. Phys. 1977. V. 22, N 2. P. 319–324.
  32. Roco J.M.M., Calvo Hernandez A., Velasco S. Far-infrared permanent and induced dipole absorption of diatomic molecules in rare-gas fluids. I. Spectral theory // J. Chem. Phys. 1995. V. 103, N 21. P. 9161–9174.
  33. Roco J.M.M., Medina A., Calvo Hernandez A., Velasco S. Far-infrared permanent and induced dipole absorption of diatomic molecules in rare–gas fluids. II. Application to the CO-Ar system // J. Chem. Phys. 1995. V. 103, N 21. P. 9175–9186.
  34. Thomson R., Dalby F.W. Experimental determination of the dipole moments of the X(2Σ+) and B(2Σ+) states of the CN molecule // Can. J. Phys. 1968. V. 46, N 24. P. 2815–2819.
  35. Kaiser E.W. Dipole Moment and Hyperfine Parameters of H35Cl and D35Cl // J. Chem. Phys. 1970. V. 53, N 5. P. 1686–1703.
  36. De Leeuw F.H., Dymanus A. Magnetic properties and molecular quadrupole moment of HF and HCl by molecular-beam electric-resonance spectroscopy // J. Mol. Spectrosc. 1973. V. 48, N 3. P. 427–445.
  37. Maroulis G. A systematic study of basis set, electron correlation, and geometry effects on the electric multipole moments, polarizability, and hyperpolarizability of HCl // J. Chem. Phys. 1998. V. 108, N 13. P. 5432–5445.
  38. Pouchan C., Maroulis G. Accurate electric multipole moments for HCN and HCP from CCSD(T) calculations with large Gaussian basis sets // Theor. Chim. Acta. 1996. V. 93, N 3. P. 131–140.
  39. Hebert A.J., Lovas F.J., Melendres C.A., Hollowell C.D., Story T.L., Jr., Street K., Jr. Dipole Moments of Some Alkali Halide Molecules by the Molecular Beam Electric Resonance Method // J. Chem. Phys. 1968. V. 48, N 6. P. 2824–2825.
  40. Maroulis G. Evaluating the performance of DFT methods in electric property calculations: sodium chloride as a test case // Reports in Theoretical Chemistry. 2013. V. 2, N 1. P. 1–8.
  41. Meerts W.L., Dymanus A. Electric dipole moments of OH and OD by molecular beam electric resonance // Chem. Phys. Lett. 1973. V. 23, N 1. P. 45–47.
  42. Laaksonen L., Muller-Plathe F., Diercksen G.H.F. Fully numerical restricted Hartree–Fock calculations on open-shell hydrides: On the basis-set truncation error // J. Chem. Phys. 1988. V. 89, N 8. P. 4903–4908.
  43. Maroulis G. Electric dipole hyperpolarizability and quadrupole polarizability of methane from finite-field coupled cluster and fourth-order many-body perturbation theory calculations // Chem. Phys. Lett. 1994. V. 226, N 3–4. P. 420–426.
  44. Newell A.C., Baird R.C. Absolute determination of Refractive Indices of Gases at 47.7 Gigahertz // J. Appl. Phys. 1965. V. 36, N 12. P. 3751–3759.
  45. Schmidt J.W., Moldover M.R. Dielectric permittivity of eight gases measured with cross capacitors // Int. J. Thermophys. 2003. V. 24, N 2. P. 375–403.
  46. Parker G.A., Pack R.T. Van der Waals interactions of carbon monoxide // J. Chem. Phys. 1976. V. 64, N 5. P. 2010–2012.
  47. Medved M., Urban M., Kello V., Diercksen G.H.F. Accuracy assessment of the ROHF-CCSD(T) calculations of static dipole polarizabilities of diatomic radicals: O2, CN, and NO // J. Mol. Struct. (Theochem). 2001. V. 547, N 1–3. P. 219–232.
  48. Kumar A., Meath W.J. Integrated dipole oscillator strength and dipole properties for Ne, Ar, Kr, Xe, HF, HCl and HBr // Can. J. Chem. 1985. V. 63, N 7. P. 1616–1630.
  49. Maroulis G., Pouchan C. Molecules in static electric fields: Linear and nonlinear polarizability of HCN and HCP // Phys. Rev. A. 1998. V. 57, N 4. P. 2440–2447.
  50. Maroulis G. Quadrupole polarizability and hyperpolarizability of carbon monoxide // Theor. Chim. Acta. 1992. V. 84, N 3. P. 245–253.
  51. Maroulis G. Dipole–quadrupole and dipole–octopole polarizability for CH4 and CF4 // J. Chem. Phys. 1996. V. 105, N 18. P. 8467–8468.
  52. Dyke T.R., Muenter J.S. Electric dipole moments of low J states of H2O and D2O // J. Chem. Phys. 1973. V. 59, N 6. P. 3125–3127.
  53. Verhoeven J., Dymanus A. Magnetic Properties and Molecular Quadrupole Tensor of the Water Molecule by Beam-Maser Zeeman Spectroscopy // J. Chem. Phys. 1970. V. 52, N 6. P. 3222–3233.
  54. John I.G., Bacskay G.B., Hush N.S. Finite field method calculations. VI. Raman scattering activities, infrared absorption intensities and higher-order moments: SCF and CI calculations for the isotopic derivatives of H2O and SCF calculations for CH4 // Chem. Phys. 1980. V. 51, N 1–2. P. 49–60.
  55. Huiszoon C. Ab initio calculations of multipole moments, polarizabilities and isotropic long range interaction coefficients for dimethylether, methanol, methane, and water // Mol. Phys. 1986. V. 58, N 5. P. 865–885.
  56. Zeiss C.D., Meath W.J. Dispersion energy constants C6(A, B), dipole oscillator strength sums and refractivities for Li, N, O, H2, N2, O2, NH3, H2O, NO and N2O // Mol. Phys. 1977. V. 33, N 4. P. 1155–1176.
  57. Veber A. Vrashhatel'nye spektry KR vysokogo razreshenija v gazah // Spektroskopija kombinacionnogo rassejanija sveta v gazah i zhidkostjah / Pod red. A. Vebera, I.L. Fabelinskogo; per. s angl. I.L. Fabelinskogo. M.: Mir, 1982. P. 93–153.