Showing papers in "Molecular Physics in 1978"

Applicability of the multi-reference double-excitation CI (MRD-CI) method to the calculation of electronic wavefunctions and comparison with related techniques

Abstract: Implementation of a multi-reference double-excitation CI (MRD-CI) method is discussed and its results are compared with those of related techniques. This approach employs a configuration selection procedure to order the various generated species according to their energy-lowering capability and then uses an energy extrapolation procedure based on perturbation theory to obtain suitably accurate estimates of the eigenvalues of the entire MRD-CI space. By employing this selection procedure it is possible to test from 2000 to 4000 symmetry-adapted functions (SAF's) per second of CPU time on an IBM 370–168 system, thereby allowing one to apply the energy extrapolation quite conveniently to CI spaces consisting of several hundred thousand species. By systematically increasing the number of reference configurations in the MRD-CI it is clear that the limit of a full CI can be approached and as a result such a computational procedure appears to be generally valid for any type of electronic state and for any nuclea...

Resonance properties of complex-rotated hamiltonians

Abstract: The fundamental work of Balslev, Combes, and Simon has provided a mathematical foundation for the description of atomic and molecular resonances by the complex-rotation method. In the present paper we discuss some formal properties of the complex-rotated hamiltonian operators and the variational criteria for the approximation of their resonance eigenvalues. These criteria are employed in numerical studies of the complex-rotation method, which is illustrated and compared with various stabilization procedures in an application to a simple model potential. We propose a virial-scaling procedure for determining variationally optimal estimates of the resonance position and lifetime and apply the technique to the helium (2s)2 auto-ionizing resonance. Our results lend support to the idea that resonance features in the continuous spectrum can be successfully described by techniques similar to those employed for bound states.

A determination of fundamental Zeeman parameters for the OH radical

Abstract: Measurements of the gas-phase E.P.R. spectra of OH in the J = 9/2 and 11/2 levels of the X2II state at 26 GHz and 35 GHz respectively are reported. Confocal and semi-confocal optical resonators have been used in place of the more conventional microwave cavities for these experiments. The data are analysed, together with previous measurements by Radford on other rotational levels in the determination of six independent g factors: These parameters are interpreted in terms of the electronic structure of the OH radical. In agreement with previous workers, it is found that the major contaminant of the X2II state is the A2Σ+ state and that this pair of states is a good example of Van Vleck's pure precession hypothesis.

A perturbation theory approach to relativistic calculations

Abstract: In this paper a perturbative procedure for the calculation of relativistic effects is proposed, that consistently treats all first-order terms, including relativistic changes of the electronic potential. The results of test calculations on some fifth row elements are compared with full relativistic Dirac-Fock-Slater treatments of the same systems. Both orbital energies and the first order changes in the wave functions are calculated.

Multiple time-step methods in molecular dynamics

Abstract: A new method for molecular dynamics computer simulations, called the multiple time-step (MTS) method, is described, in which two or more time steps of different lengths are used to integrate the equations of motion in systems governed by continuous potential functions. With this method computing speeds have been increased by factors of three to eight over conventional molecular dynamics methods in simulations of monatomic and polyatomic fluids, with only marginal increases in computer storage.

Angular momentum polarization in molecular collisions : Classical and quantum theory for measurements using resonance fluorescence

Abstract: Inelastic or reactive collisions typically produce an anisotropic distribution of rotational angular momentum. An explicit and general treatment is given for the intensity and polarization of resonance fluorescence from molecules produced in such processes. Both classical and quantum results are expressed in terms of bipolar harmonics and state multipoles formed from linear combinations of density matrix elements. The treatment provides an inversion procedure for determining moments of the rotational angular momentum distribution ; twelve independent moments can be obtained. The combinations of angular momentum operators involved are even in eight of these moments and odd in four, with respect to reflection in a plane containing the initial and final relative velocity vectors. Measurements of the even moments require linearly polarized excitation and fluorescence, whereas measurements of the odd moments require circularly polarized excitation. The requisite experimental geometry and other practical aspect...

The description of bimolecular potentials, forces and torques: the S and V function expansions

Abstract: Any scalar function of the orientation of a pair of molecules, of arbitrary shape, can be expanded in terms of a complete orthogonal set of functions called S functions. Any vector function can similarly be expanded in terms of V functions. Although the functions are expressed in terms of Wigner rotation matrices, they can be evaluated efficiently enough for use in molecular dynamics calculations. In particular, trigonometrical function evaluations are not required. The force and torque on a molecule can be derived, as V function expansions, from a potential given in S function form, and the necessary formulae are listed.

The use of multiple quantum transitions for relaxation studies in coupled spin systems

Abstract: The utility of multiple quantum transitions is discussed with regard to the elucidation of relaxation mechanisms in coupled spin systems. The information contained in the decay rates of multiple quantum coherence is analysed in terms of the Redfield formalism, and experimental schemes suitable for their measurement are presented. As an illustration, external paramagnetic relaxation in a two-spin system is investigated, based on measured multiple and single quantum relaxation rates.

Collision-induced rotational Raman scattering by tetrahedral and octahedral molecules

Abstract: The long tails at high Stokes and anti-Stokes frequencies observed in Rayleigh scattering from compressed methane, carbon tetrafluoride and sulphur hexafluoride are attributed to induced rotational transitions. The longest-range contribution to the collision-induced polarizability, the dipoleinduced-dipole term in R -3, where R is the separation of a pair of molecules, does not fluctuate with molecular rotation. However, the dipole-quadrupole polarizability A of the tetrahedron leads to a rotating contribution in R -4. The dipole-octopole polarizability E of an octahedron and a tetrahedron leads to a contribution in R -5 which also rotates with the molecule. The rotational transitions associated with these polarizabilities can explain both the intensity and the shape of the long tails. Approximate values of A for CH4 and CF4 and of E for SF6 are deduced. As in the monatomic case, there is a simple relationship between the total scattered intensity and the second Kerr virial coefficient.

Interfacial and co-existence properties of the Lennard-Jones system at the triple point

Abstract: A molecular dynamics simulation of the three phases of the Lennard-Jones system in co-existence is reported. The triple-point properties are compared with bulk-phase Monte-Carlo results, with experimental data on argon, and with the results of a preliminary simulation of this system. Thermodynamic properties of the crystal-liquid and liquid-vapour interfaces are reported and difficulties in calculating interfacial excess properties are discussed. The crystal-liquid and liquid-vapour interfacial tensions are in accord with previous predictions. It is suggested that the direct simulation of co-existing phases is a potentially practical route to the phase diagram if the thermodynamic equations of state of the individual phases are known.

Electronic structure of the sodium trimer

Abstract: An ab initio configuration-interaction study of the potential energy surface of Na3 is presented. The ground state is predicted to be an obtuse triangle (2 B 2 symmetry), and to be bound by 35·5 kJ/mole relative to Na2(1Σ g +) + Na(2 S). The surface is found to be extremely flat. Two saddle points, an acute triangle (2 A 1 state) and a linear symmetric conformation (2Σ u + state), lie respectively only 2·5 kJ/mole and 12·5 kJ/mole above the minimum. The isotropic hyperfine coupling constant and first ionization potential calculated at the minimum energy geometry are in good agreement with experiment. A simple molecular orbital model involving only the valence s-orbitals provides an adequate qualitative description of the electronic structure. The low-lying empty p and d-orbitals in Na influence the stability of Na3 mainly through contributions to electron correlation and not through orbital hybridization. The dominant features of the surface are discussed in terms of pseudo-rotation and the Jahn-Teller in...

VIBRONIC COUPLING MODEL FOR THE INTENSITIES OF f-f TRANSITIONS IN OCTAHEDRAL LANTHANIDE (III) COMPLEXES

Abstract: A general theory of vibronically induced electric-dipole intensity in the f-f transitions of octahedral (Oh ) six-coordinate trivalent lanthanide ion complexes is developed. The theory is based on a model in which both static (point-charge crystal field) and dynamic (transient ligand dipoles) coupling between the metal ion and the ligands are included. Electric-dipole intensity is introduced into the vibronic components of the parity-forbidden Ln3+ f-f transitions via a vibronic coupling mechanism involving the chromophoric f-electrons and the ν 3(t 1u ), ν 4(t 1u ), and ν 6(t 2u ) skeletal vibrational modes of the octahedral LnL6 system. Calculations based on the theoretical model are carried out for the 7F0→5D1, 7F0→5D2, and 7F1→5D1 transitions of EuCl6 3-, and the results are compared with experimental data reported for Cs2NaEuCl6. Good agreement between the calculated and observed total dipole strengths is achieved, and excellent agreement between theory and experiment is obtained for the distribution...

Equation of state of a hard-core fluid with a Yukawa tail

Abstract: We present Monte Carlo results for the equation of state of a fluid in which the intermolecular potential consists of a hard core of diameter σ and an attractive tail which is of the form of a Yukawa function, - e exp -λ(r - σ)tr with λ=1·8/σ. These results are compared with those obtained from perturbation theory, the mean spherical approximation (MSA), and three related approximation schemes. While perturbation theory works rather well for this system, the MSA is considerably less satisfactory. However, the exponential and linearized exponential modifications of the MSA and the generalized MSA all give good results for this system.

Doublet stability of ab initio SCF solutions for the allyl radical

Abstract: The doublet stability of the SCF solutions for the allyl radical is re-examined for various ab-initio model hamiltonians, based on the minimum, double-zeta and double-zeta plus polarization atomic orbital basis sets in the LCAO scheme. The calculations are carried out for a wide range of the C-C bond lengths (1.3 A to 2·0 A). In all cases the critical bond length, separating regions of stability and instability, is found to be shorter than the corresponding equilibrium C-C bond length (1·36 A versus 1·44 A, respectively, for the minimum basis set). In contrast to the results of McKelvey and Berthier we find that the doublet-stability problem yields at most one negative eigenvalue in the whole range of the C-C bond lengths studied, this implying only one possible (other than spin) symmetry breaking, in complete agreement with the semi-empirical PPP model results for this system. The basis dependence of the doublet instability is also re-examined and the generality of this phenomenon is firmly established f...

The rovibrational Raman spectrum of water vapour v 1 and v 3

Abstract: The OH stretching region in the Raman spectrum of water vapour has been observed and reproduced by computer simulation using rovibrational wave functions derived from the analysis of high-resolution absorption spectra. Relative intensity measurements allow the determination of the depolarization ratio and the ratio of the two non-vanishing second-order irreducible tensor components for v 1. These quantities have been combined with the literature value for the cross section of this band to calculate the principal cartesian components of the v 1 derived polarizability tensor. The cross section for the v 3 vibration was also determined, and these results are considered in terms of the bond polarizability theory.

Molecular pair-correlation function of liquid acetonitrile from X-ray and neutron-diffraction studies

Abstract: X-ray-diffraction studies on liquid acetonitrile at 20°C were carried out at a wavelength of 0·7 A. The data were corrected for polarization, absorption, Compton scattering and multiple scattering. The coherent distinct differential cross section was separated into intramolecular and intermolecular contributions. Whereas from the intramolecular coherent cross section the structure of the molecule in the liquid was determined, the intermolecular coherent cross section, together with intermolecular contributions from neutron-scattering data on CD3C14N and CD3C15N, was employed to determine three expansion coefficients of the molecular pair-correlation function.

Cholesteric states of micellar solutions

Abstract: The effects of optically active compounds on amphiphilic nematics are reported. The following systems have been studied : (1) caesium decylsulphate, decanol, water plus tartaric acid ; (2) ammonium decylsulphate, ammonium sulphate, decanol, water plus brucine sulphate ; and (3) decylammonium chloride, water plus cholesterol. Phase transitions to cholesteric states are induced by the optically active compounds in all systems. Brucine sulphate has the highest twisting power ; tartaric acid the lowest. The results are analysed on the basis of intermolecular interactions and an explanation is proposed for the observed differences in twisting power.

The Coupled Representation Matrix of the Pair Hamiltonian.

Abstract: A complete treatment of the spin hamiltonian for a pair of exchange coupled metal ions is given. The results obtained through the use of the Wigner-Eckart theorem are unrestricted with respect to the relative orientation of the single-ion tensors, and appropriate for both the S 1 = S 2 and S 1 ≠ S 2 cases. The necessary constants are derived so that matrix elements within a given spin multiplet can be treated by ordinary operator algebra with the coupled representation state vectors, |SM>, as a basis set. Explicit algebraic formulae for matrix elements between spin multiplets are presented for the first time. Symmetry restrictions are discussed in general and illustrated for the simple case of two ions related by an inversion centre, pair symmetry Ci .

The depolarized Rayleigh scattering from fluids of spherical molecules

Abstract: A calculation of the depolarized Rayleigh scattering from a liquid of isotropically polarizable molecules is described. The spectrum reflects cooperative, many-particle, structural relaxation which is represented by a generalized Langevin equation for the bilinear number density fluctuations. The theory is applied to the particular case of liquid argon at the triple point and is shown to give a very close quantitative agreement with the experimental lineshape, using data from neutron-scattering experiments on liquid argon and no adjustable parameters. The various features of the observed spectra are related to the behaviour of the correlation functions of different Fourier components of the bilinear number density fluctuations which are interpreted in different limits of the molecular motion, diffusion, gas-like, etc. The sensitivity of the lineshape to modifications of the induced polarizability functional from DID form is investigated. Within the range of physically reasonable modifications little chang...

Transport properties of homonuclear diatomics

Abstract: The molecular dynamics technique has been used to calculate certain time-correlation functions which occur in the transport theory of fluids composed of rigid molecules. These correlation functions are the Green-Kubo integrands of the following hydrodynamic transport coefficients: thermal conductivity, shear, bulk and vortex viscosity, and the corresponding spin viscosities. The calculations were carried out for liquid nitrogen (pressure essentially zero and temperature 78 K) modelled by a diatomic Lennard-Jones potential. For the transport coefficients supported by experimental data, agreement between calculated and experimental values is good. Our calculations predict a highly non-exponential Green-Kubo integrand for vortex viscosity. They also suggest limits at which breakdown can be expected in the conventional Navier-Stokes equation characterizing macroscopic flow of liquid nitrogen.

Collision-induced polarizabilities of inert gas atoms

Abstract: The use of polarizability densities to calculate collision-induced polarizabilities is investigated. One method for computing polarizabilities of inert gas diatoms employs atomic polarizability densities from finite-field Hartree-Fock calculations, together with classical equations for the polarization of dielectrics. It is shown that this model gives inaccurate values for both the local fields and the local response to non-uniform fields. An alternative method incorporating the same physical effects is used to compute the pair polarizabilities to first order in the interatomic interaction. To first order the pair contribution to the trace of the polarizability is negative at short range. The calculated anisotropy does not differ significantly from the DID value, whereas the polarizability density calculation gives a substantial reduction in the anisotropy.

Triple-dipole energies for H, He, Li, N, O, H2, N2, O2, NO, N2O, H2O, NH3 and CH4 evaluated using pseudo-spectral dipole oscillator strength distributions

Abstract: Accurate values for the rotationally averaged triple-dipole dispersion energy coefficients, Cabc , have been determined for all possible triple interactions involving ground state H, He, Li, N, O, H2, N2, O2, NO, N2O, H2O, NH3 and CH4. The calculations have been carried out using pseudo-spectral theory by employing pseudo-dipole oscillator strength distributions for each of the species. This permits the 455 relevant triple-dipole interaction constants to be evaluated economically without sacrificing accuracy. These results are used to make self-consistent tests of the reliability of various combination rules for the Cabc . In particular the combination rule due to Tang, involving like species triple-dipole constants, is found to be very satisfactory. The importance of triple-dipole interaction energies, and some problems in their use, are also discussed briefly.

Analysis of the v 3 and v 1 infra-red bands of SiH4

Abstract: The high-resolution infra-red spectrum of SiH4 in the region 2101 cm-1 to 2265 cm-1 has been analysed. Most of the lines observed have been assigned to transitions of the v 3 and v 1 bands of the abundant isotopic species 28SiH4. The v 1 band is formally forbidden in the infra-red, but a vibration-rotation interaction between v 1 and v 3 lends intensity to the v 1 transitions. The spectrum has been fitted by diagonalizing the v 3 = 1 and v 1 = 1 hamiltonians coupled by the vibration-rotation interaction term. 500 transitions have been fitted with an overall standard deviation of 0·007 cm-1, using only 15 adjustable parameters (ten in the v 3 = 1 hamiltonian, four in the v 1 = 1 hamiltonian, and one interaction coefficient). The calculated intensities are also in good agreement with experiment. Transitions of the other isotopic species 29SiH4 and 30SiH4 have also been observed, but these spectra have not been analysed in detail.

Fermi resonance in dimers : a model study

Abstract: A theoretical model is proposed for symmetric dimers of carboxylic acids which accounts for three effects on an equal footing : (i) coupling between the high and low-frequency modes ; (ii) Davydov-type splitting of the degenerate vibrational states ; and (iii) Fermi resonance between the hydrogen-stretching fundamental and the first overtone of the hydrogen bending. These three mechanisms contribute to the infra-red spectra which have been computed for different values of an anharmonic parameter.

Asymmetric structure and force field of the 1B2(1A′) state of sulphur dioxide

Abstract: The vibrational term values, principal rotational constants and centrifugal distortion constants of the 1 B 2 state of SO2 at 42 573 cm-1 (2350 A)‡ 1 A = 10-10 m. 1 d = 1 dyne = 10-5 N. 1 u = 1 unified atomic mass unit ≈ 1·660 531 × 10-27 kg. are interpreted in a unified treatment using (i) a vibrational hamiltonian based on a double minimum potential in the antisymmetrical stretching coordinate q 3 and strong anharmonic coupling of q 3 with the symmetric stretch q 1; and (ii) a modified treatment of Coriolis coupling and centrifugal distortion, in order to take account of the irregular intervals in the vibrational manifold. This treatment successfully explains a group of observed quantities, including isotopic data, relative intensities and inertial defects, which were not used in determining the constants of the potential function. The analysis indicates that there is a double minimum potential in the antisymmetric mode with a barrier of about 141 cm-1 at the C 2v configuration; the top of the barrier i...

An investigation of self-consistent field perturbation theory applied to the calculation of nuclear spin-spin coupling constants

Abstract: An initio SCF perturbation theory in the formulation of Ditchfield and Snyder has been applied to the calculation of the N.M.R. spin-spin coupling constants in CH4, NH3, H2O and HF using large gaussian basis sets, and including all second-order contributions (Fermi contact, orbital and dipolar). In accordance with most other work, the first-order term in the orbital contribution has been neglected, however. The sensitivity of the coupling constants to variations in the basis set has been studied, and the reliability of the method is discussed in the light of these results. It is shown that the Fermi contact contribution provides the largest component of the calculated coupling constants, with the dipolar term being generally negligible. However, the orbital contribution is found to be non-negligible, particularly in the case of the directly bonded couplings in HF and H2O, and is shown to be the primary reason, at the level of calculation adopted, for variations in the HH geminal couplings in the series CH...

On the anharmonic force field and equilibrium structure of HNC

Abstract: A tentative anharmonic force field, including quadratic, cubic and quartic terms, has been determined for HNC. The force field is based on observed vibration-rotation data for HNC and DNC, a previous ab initio SCF calculation of the quadratic and cubic force constants, and the anharmonic force fields determined earlier for HCN and HCP. Using α constants calculated from the force field, the zero-point rotational constants B 0 for the eight stable isotopic species have been converted to B e, and hence an improved equilibrium structure has been derived. The equilibrium bond lengths are found to be r e(HN) = 0·9940(8) A and r e(NC) = 1·1689(2) A.

A calculation of the helium pair polarizability including correlation effects

Abstract: Direct configuration interaction (CI) calculations, which include all single and double excitation functions, and the finite-field method have been used to calculate the polarizability of a pair of helium atoms at a number of separations in order to assess the importance of correlation effects. A limited basis set of gaussian expansions of Slater orbitals was used. The basis set located on each atom was 5s, 3p, 2d, and was chosen to provide reasonably accurate atomic wavefunctions for both zero and finite electric fields. Agreement is obtained with the long-range results of perturbation theory. For incremental and incremental mean polarizabilities it is apparent that calculation of both self-consistent field (SCF) and CI contributions is required for an accurate determination. The anisotropy, however, seems to be calculable directly from an SCF calculation provided a simple scaling procedure is adopted. Counterpoise corrections have been calculated and found to be appreciable, especially for the increment...

Integral equation approximations for fluids of hard spheres with linear quadrupoles

Abstract: In this paper we solve numerically several integral equation theories for the dense quadrupolar hard-sphere fluid. Closure approximations obtained by expanding the hypernetted-chain equation are shown to give pair-correlation functions and internal energies in good agreement with Monte Carlo calculations. The mean spherical approximation, however, is found to be extremely poor.

M.C.D./M.C.P.L. saturation theory with application to molecules in D ∞h and its subgroups

Abstract: The M.C.D. of a system with a paramagnetic ground state will deviate from simple H/T dependence at sufficiently high field and/or low temperature, and this deviation is referred to as a saturation effect. A detailed theoretical discussion of this phenomenon is presented, and specific application is made to molecules in point group D ∞h and in its subgroups down through C 3. A single general formula is found to apply in all cases to an allowed electronic transition between two ‘isolated’ electronic states. The properties and applications of this formula are described in some detail. The formula is then generalized to apply to saturation behaviour for the corresponding emission phenomenon, magnetic circularly polarized luminescence (M.C.P.L.), where the additional effect of photoselection must be considered. A saturation analysis in M.C.D. is also presented for one special case of accidental degeneracy, that for a 2P3/2 ‘atomic’ ground state in a linear molecule. Various experimental considerations in satur...