The molecular electric quadrupole moment and electric-field-gradient induced birefringence (Buckingham effect) of Cl_2

An ab initio investigation of the molecular properties rationalizing the electric-field-gradient induced birefringence (Buckingham effect) for Cl$_2$ is presented. The quadrupole moment is determined using hierarchies of basis sets and wavefunction models. The electric dipole polarizability, the dipole - dipole - quadrupole and dipole - dipole - magnetic dipole hyperpolarizabilities are determined exploiting a Coupled Cluster Singles and Doubles (CCSD) response approach. The properties are zero-point vibrationally averaged, and the contribution of excited ro-vibrational states accounted for. To this end, the interatomic $^1$Σ$_g^+$ ground state potential has been computed at CCSD plus perturbative triples - CCSD(T) - level employing a large augmented correlation consistent basis set. The effect of relativity is estimated at the Dirac-Hartree-Fock level. Our best value for the quadrupole moment of Cl$_2$ is (2.327 ± 0.010) au and it is in excellent agreement with experiment which, after revision and dependent on the procedure employed for correcting the original estimate of (2.24 ± 0.04) au of Graham et al., [Mol. Phys., 93, 49, (1998)], ranges from (2.31 ± 0.04) au to (2.36 ± 0.04) au.

[1]  Alan Hinchliffe,et al.  Ab initio determination of molecular properties , 1987 .

[2]  Antonio Rizzo,et al.  Ab initio study of the electric-field-gradient-induced birefringence of a polar molecule: CO , 2000 .

[3]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. IX. The atoms gallium through krypton , 1993 .

[4]  D. M. Bishop,et al.  Molecular vibrational and rotational motion in static and dynamic electric fields , 1990 .

[5]  A. D. Buckingham,et al.  The quadrupole moments of dipolar molecules , 1968 .

[6]  N. Bridge,et al.  The polarization of laser light scattered by gases , 1964, Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences.

[7]  Sonia Coriani,et al.  The molecular electric quadrupole moment of N2 , 1998 .

[8]  Geoffrey L. D. Ritchie,et al.  Temperature dependence of electric field-gradient induced birefringence (Buckingham effect) and molecular quadrupole moment of N2. Comparison of experiment and theory , 2003 .

[9]  G. Herzberg,et al.  Molecular Spectra and Molecular Structure , 1992 .

[10]  Sonia Coriani,et al.  On the molecular electric quadrupole moment of C2H2 , 1999 .

[11]  Antonio Rizzo,et al.  Relativistic effects on the electric polarizabilities and their geometric derivatives for hydrogen halides and dihalogens – a Dirac–Hartree–Fock study , 2003 .

[12]  A. D. Buckingham,et al.  The birefringence induced in spherical molecules by an electric field gradient , 1971 .

[13]  B. Taylor,et al.  CODATA recommended values of the fundamental physical constants: 2006 | NIST , 2007, 0801.0028.

[14]  D. M. Bishop,et al.  A perturbation method for calculating vibrational dynamic dipole polarizabilities and hyperpolarizabilities , 1991 .

[15]  A. D. Buckingham,et al.  Molecular quadrupole moments. Quantum correction to the classical formula , 1966 .

[16]  John D. Watts,et al.  Non-iterative fifth-order triple and quadruple excitation energy corrections in correlated methods , 1990 .

[17]  Roger D. Amos,et al.  A theoretical study of hyperpolarizability effects in the measurement of molecular quadrupole moments , 1982 .

[18]  Peter J. Mohr,et al.  CODATA Recommended Values of the Fundamental Constants: 1998 , 2000 .

[19]  A. D. Buckingham,et al.  The quadrupole moment of the carbon dioxide molecule , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[20]  R. E. Raab,et al.  A new molecular theory of field gradient induced birefringence used for measuring electric quadrupole moments , 1991 .

[21]  R. E. Raab,et al.  Measurement of the electric quadrupole moments of CO2, CO, N2, Cl2 and BF3 , 1998 .

[22]  Jens Oddershede,et al.  Dynamic polarizabilities and raman intensities of CO, N2, HCl and Cl2 , 1982 .

[23]  A. D. Buckingham,et al.  Direct Method of Measuring Molecular Quadrupole Moments , 1959 .

[24]  Celestino Angeli,et al.  On a mixed Møller-Plesset Epstein-Nesbet partition of the Hamiltonian to be used in multireference perturbation configuration interaction , 2000 .

[25]  Antonio Rizzo,et al.  The electric-field-gradient-induced birefringence and the determination of molecular quadrupole moments , 2001 .

[26]  Poul Jørgensen,et al.  Response functions from Fourier component variational perturbation theory applied to a time-averaged quasienergy , 1998 .

[27]  Antonio Rizzo,et al.  COUPLED CLUSTER INVESTIGATION OF THE ELECTRIC-FIELD-GRADIENT-INDUCED BIREFRINGENCE OF H2, N2, C2H2, AND CH4 , 1998 .

[28]  M. Head‐Gordon,et al.  A fifth-order perturbation comparison of electron correlation theories , 1989 .

[29]  Trygve Helgaker,et al.  A Lagrangian, integral-density direct formulation and implementation of the analytic CCSD and CCSD(T) gradients , 2003 .

[30]  Mark A. Spackman,et al.  ACCURATE PREDICTION OF STATIC DIPOLE POLARIZABILITIES WITH MODERATELY SIZED BASIS-SETS - MOLECULES CONTAINING P-BLOCK ATOMS FROM BORON TO IODINE , 1994 .

[31]  David E. Woon,et al.  Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties , 1994 .

[32]  Antonio Rizzo,et al.  Linear response coupled cluster calculation of Raman scattering cross sections , 2002 .

[33]  George Maroulis,et al.  Accurate dipole polarizability for Cl2(X1Σ+ g) , 1992 .

[34]  Kirk A. Peterson,et al.  Accurate correlation consistent basis sets for molecular core–valence correlation effects: The second row atoms Al–Ar, and the first row atoms B–Ne revisited , 2002 .

[35]  Sonia Coriani,et al.  The effect of triple excitations in coupled cluster calculations of Raman scattering cross-sections , 2002 .

[36]  Sonia Coriani,et al.  State-of-the-art ab initio calculations of the molecular electric quadrupole moments of hydrogen fluoride , 2001 .

[37]  M. Plesset,et al.  Note on an Approximation Treatment for Many-Electron Systems , 1934 .

[38]  G. Herzberg.  Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules , 1939 .

[39]  A. Weiss,et al.  I. Mills, T. Cvitaš, K. Homann, N. Kallay, and K. Kuchitsu: Quantities, Units and Symbols in Physical Chemistry, Iupac, Physical Chemistry Division, Blackwell Sci. Publication, Oxford 1988. 134 Seiten, Preis: £ 19.95 , 1989 .

[40]  George Maroulis,et al.  Electric properties of chlorine , 1993 .

[41]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited , 2001 .

[42]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .

[43]  Antonio Rizzo,et al.  On the molecular electric quadrupole moment and the electric-field-gradient-induced birefringence of CO2 and CS2 , 2000 .

[44]  Antonio Rizzo,et al.  On the electric field gradient induced birefringence and electric quadrupole moment of CO, N2O, and OCS , 2003 .