Showing papers in "Molecular Physics in 1971"

Perturbation theory of the non-linear optical polarization of an isolated system

Abstract: The non-linear optical polarization of an isolated atom or molecule is treated, giving careful consideration to secular and resonant terms in the perturbation expansion. The Method of Averages introduced by Bogoliubov and Mitropolsky is used. The case where resonance-induced excited state populations are negligible, which is relevant to a wide range of non-linear optical experiments, is examined in detail for polarizations through third order in the perturbing fields. This yields concise expressions which are valid for any combination of applied field frequencies, including static fields.

Liquid argon: Monte carlo and molecular dynamics calculations

Abstract: Thermodynamic properties of liquid argon are calculated by Monte Carlo and molecular dynamics techniques, using accurate pair-potential functions determined from the properties of solid and gaseous argon, together with the Axilrod-Teller three-body interaction. Satisfactory techniques for evaluating three-body contributions to thermodynamic properties without excessive requirements of computer time are described. Quantum corrections are included. Agreement with experiment is excellent: the best pair and triplet potentials give an excellent description of the properties of solid, gaseous and liquid argon.

Rayleigh and Raman scattering from optically active molecules

Abstract: The intensity of Rayleigh and Raman scattering from optically active molecules is shown to be slightly different in right and left circularly polarized incident light. The circular intensity differential of the Rayleigh line is dependent on components of the optical activity tensor, and that of the Raman lines is a function of the variation of the optical activity with the vibrational coordinates. This circular intensity differential might be of the order of 10-3 times that of the Rayleigh or Raman intensity.

The molecular Zeeman effect in diamagnetic molecules and the determination of molecular magnetic moments (g values), magnetic susceptibilities, and molecular quadrupole moments

Abstract: The experimental and theoretical literature on the molecular Zeeman effect is surveyed. The observation of the linear (H) and quadratic (H 2) Zeeman effect leads to a direct determination of the molecular g values, magnetic susceptibility anisotropies and molecular quadrupole moments. The recent results are discussed and the available molecular g values, magnetic susceptibility anisotropies, and molecular quadrupole moments are tabulated.

Electronic and nuclear relaxation in solutions of transition metal ions with spin S=3/2 and 5/2

Abstract: Electronic relaxation in solutions of solvated Fe3+, Mn2+ (S=5/2) and Cr3+ (S=3/2) is controlled by modulation of the quadratic zero field splitting interaction. The modulation is caused by collisions of the hydrated complex with bulk solvent molecules. Theoretical expressions are derived for the electronic transversal and longitudinal relaxation times T 2e and T 1e and are used to interpret the E.S.R. data of these ions. The analysis yields results for the zero field splitting constants and for the mean lifetime between collisions. The latter are found to be in the range 4–9 × 10-12 s. The nuclear relaxation rate of the solvent nuclei are affected by the dipole-dipole and scalar interaction with the unpaired electrons of the paramagnetic ions. The usual equations for nuclear relaxation due to these interactions are modified to take into account the existence of several T 1e s and T 2e s. These equations are used to analyse proton relaxation data in aqueous solutions of Cr3+, Fe3+ and Mn2+. The E.S.R. and...

A study of the molecular structure and of the barrier to methyl rotation in o-chlorotoluene partially oriented in the nematic phase

Abstract: The N.M.R. spectrum of o-chlorotoluene, dissolved in the nematic phase of 4-methoxybenzylidene-4-amino-α-methylcinnamic acid n-propylester is analysed and the shape of the proton skeleton determined. The position of lowest energy of the potential barrier to methyl rotation is found to be that in which the chlorine atom is staggered to the methyl group, and the height of the barrier is of the order of 5·0 kJ mol-1 (1200 cal/mole).

Orientational correlations in molecular liquids by neutron scattering. Carbon tetrachloride and germanium tetrabromide

Abstract: Neutron diffraction structure factors for liquid carbon tetrachloride and germanium tetrabromide have been measured and are analysed to determine the molecular centre positional correlation function allowing for molecular angular correlation. The analysis shows quite unequivocally that appreciable molecular orientational correlations must exist in these liquids but that it may only extend to nearest neighbours. This is thought to cause the pair distribution function for the molecular liquids to be markedly different from that for atomic liquids such as argon and the difference is discussed.

The dynamics of populating and depopulating the phosphorescent triplet state as studied by microwave induced delayed phosphorescence

Abstract: It is known that at low temperatures relaxation between the spin components of a phosphorescent triplet state of an organic molecule may become very slow as compared to their individual rates of decay. Spectacular changes in the intensity emitted can then be induced by suddenly sweeping a microwave field through one of the zero-field resonances during phosphorescence decay. These microwave induced signals arise because molecules are transferred from a populated non-radiative level to an empty radiative one. In this paper a system of experiments based on this phenomenon is presented which enables one to solve the dynamics of populating and depopulating the individual levels of the phosphorescent state. As a demonstration results of experiments on the aza-naphthalenes quinoline and quinoxaline are given.

Negative ions of polar molecules

Abstract: The influence of a molecule's dipole moment on its ability to capture an electron into a stable bound state is examined. It is proved that, in the fixednuclei approximation, a value greater than 1·625 Debye for the dipole moment suffices to guarantee the existence of a discrete spectrum of negative ion states. Implications for Hartree-Fock calculations of negative ions are discussed. The interaction of electronic, vibrational and rotational motions in negative dipolar ions is studied, and conclusions are drawn for real molecules.

Ab initio molecular orbital calculations of transition metal complexes. I. The electronic structure of nickel tetracarbonyl and chromium hexacarbonyl

Abstract: All electron ab initio SCF-MO calculations in a better-than-minimal basis of the electronic structure of Ni(CO)4 and Cr(CO)6 are reported. The results are compared with the measured ionization potentials, force constants and dissociation energies of these molecules, and with the electronic structures calculated by a number of semi-empirical schemes.

A theoretical interpretation of the bonding, and the photoelectron and ultra-violet spectra of sulphur dioxide

Abstract: Ab initio SCFMO calculations are described for SO2, using Slater-type orbitals expanded in gaussian-type functions. The electronic structures of SO, O3 and O2 are investigated, to facilitate analysis of the nature of sulphur 3d orbital participation in SO2. The theoretical interpretation of the photoelectron and ultra-violet spectra of SO2 is considered.

Thermodynamic properties of solutions based on correlation functions

Abstract: General matrix expressions for solution properties such as the chemical potential, partial molal volume and compressibility are developed in terms of (radial) pair distribution functions and of direct correlation functions.

The intermolecular pair potential of argon

Abstract: The absorption spectrum of diatomic argon in the 780–1080 A region has been re-analysed using the Rydberg-Klein-Rees method. The results of this study together with an analysis of the equilibrium and transport properties of gaseous argon have been used to establish a potential energy function which is consistent with all the available data. The dissociation energy of the argon dimer is estimated at some 7 per cent greater than that indicated in previous analyses of the spectroscopic data.

Ab initio calculation of force constants and equilibrium geometries

Abstract: Force constants of the molecules HF, NH3, CH4 and BH4 - have been calculated ab initio by the force method with a 73/3 + 1 gaussian lobe basis set The results, including a former calculation on H2O, agree well with experiment: the average relative error is 12 per cent for the diagonal force constants and the average absolute error is 0·06 mdyn/A for the off-diagonal ones The trends are also correctly reproduced It is concluded that ab initio calculations of this accuracy can help to solve a number of spectroscopic problems Force constants of BH4 - have been determined from a combination of spectroscopic and ab initio information Geometries have been obtained with little computing work and show good agreement with experiment

Theory of symmetry in nuclear magnetic relaxation including applications to high resolution N.M.R. line shapes

Abstract: It is shown in discussing problems involving magnetic relaxation in liquids that, whilst the usual Hilbert space spanned by all the eigenkets of the spin hamiltonian does not reflect any symmetry inherent in the spin system, the vector space (Liouville space) comprising all operators of the spin system does so. The transformation properties of the Liouville operator, as reflected by those of the high resolution spin hamiltonian and relaxation operators whose effects are introduced by means of Redfield relaxation theory, with respect to arbitrary rotations of the coordinate system are investigated. The use of irreducible tensor operators as a set of basis operators spanning Liouville space is stressed, since it is shown that their super-matrix elements of the Liouville operator are given by the Wigner-Eckart theorem provided that relaxation by anisotropy of the chemical shift or anisotropic random fields is absent. These arguments are independent of the fine details of molecular reorientation in the extrem...

On the Jahn-Teller distortion of CH4 +

Abstract: Ab initio calculations of the vibronic potential surface of the 2 T 2 ground state of CH4 + have been carried out, using a contracted gaussian approximation to a double-zeta basis of Slater orbitals. The minimum energy is found for a tetragonal distortion to the point group D 2d , with two HCH angles of 141° and four of 96°, and all r ch equal. All calculations for distorted CH4 + were carried out with the mean r ch held at 1·147 a, which minimises the energy for Td symmetry. The distortion from Td symmetry lowers the electronic energy by 1·41 ev. Distortions from Td to C 3v lead to a maximum stabilization of 1·22 ev. Vibronic perturbation parameters derived from this surface are employed in discussions of the 2 T 2-1 A 1 photoelectron transition of CH4 and a possible 2 E←2 B 2 absorption transition of CH4 +. A vibrational interval of ∼ 1200 cm-1 observed near the origin of the 2 T 2-1 A 1 photoelectron transition is assigned to one component of v 2 (calculated frequency, 1300 cm-1).

Quantum mechanical computational studies of chemical reactions: I. Close-coupling method for the collinear H + H2 reaction

Abstract: A fully converged, close-coupling calculation, using natural collision coordinates, is presented for the collinear H + H2 system, on a Porter-Karplus potential energy surface in the energy range of 9 to 35 kcal/mole. Eight closed channels were required for convergence in the threshold region. Inclusion of the closed channels alters considerably the numerical results. The effects of the vibrational non-adiabatic coupling terms were demonstrated. Particularly pronounced is the influence of the (energy dependent) inertial centrifugal energy due to the curvature of the reaction path. No evidence for tunnelling was obtained. The considerable difference between the quantal and classical reaction probabilities in the threshold energy region is entirely due to the non-adiabatic coupling terms, which tend to reduce the kinetic energy available along the reaction path, more so in the classical case, thereby leading to a higher dynamic threshold. The Arrhenius plot of the collinear rate constant shows more curvature...

The H2S+ radical ion

Abstract: The emission spectrum between 4000 and 5000 A obtained by Horani, Leach and Rostas by controlled energy electron excitation of H2S is shown to belong to H2S+. The decrease and subsequent increase of the bending vibrational intervals in the A 2 A 1 state of H2S+ and D2S+ indicates a barrier to linearity of approximately 4600 cm-1. A preliminary rotational analysis of the spectrum leads to the following molecular parameters for the ground state: r 0″ = 1·358 A, valence angle 92° 54′. A detailed comparison of the optical and photoelectron spectra has been made and selection rules for the photoelectron spectra are presented. It is shown that in order to understand the vibronic patterns of both types of spectra it is necessary to consider in detail Renner-Teller vibronic interaction. A barrier to linearity in the 2 A 1 state of H2S+ alone is insufficient to account for the interesting change in the spectrum of the 2 A 1-1 A 1 transition at energies corresponding to the potential maximum.

The lowest triplet state of Zn porphin

Abstract: Phosphorescence microwave double resonance experiments are reported on Zn porphin at 1·2 K In glassy solution very broad resonance transitions are observed However, for Zn porphin in a crystalline n-octane matrix—a system known for its sharp optical spectra (Shpolskii effect)—three pairs of microwave transitions with widths of a few MHz are found, all of them corresponding to a decrease in phosphorescence intensity By studying the behaviour of the signals for various methods of preparation of the sample and as a function of the optical bandwidth of excitation and detection, one pair of transitions could be assigned to monomeric solute molecules The corresponding zero-field splittings are |X - Z| = 1355, |Y - Z| = 806 MHz It was further established that by ‘pumping’ either of these transitions a third one can be detected at the difference frequency, so that the order of the levels must be X> Y>Z (or reverse) The results indicate that the molecule no longer possesses a four-fold axis in the excited st

Fast computation of exchange-broadened isotropic E.S.R. spectra

Abstract: A general line shape equation for intramolecular exchange among many sites has been derived by means of the Liouville density matrix theory and adapted to fast computer calculations. Applications of the computer programme ESREXN, which is based on the formalism of the present paper, are shown by examples.

Bandshapes in polymer spectra

Abstract: The shape of the vibrational envelope of an absorption band in the solution spectrum of a helical polymer is related to the shape of the corresponding band in the monomer. The approximation used is expected to be valid in both the strong and weak coupling limits. In the strong coupling limit it is shown that under certain conditions the polymer band consists of an extremely narrow peak shifted from the monomer line, as has been observed in the spectra of some cyanine dyes. The identification of this peak with absorption by a propagating exciton mode is supported by a calculation of the effective distance of excitation transfer as a function of coupling strength.

The photoelectron spectra of the halomethanes

Abstract: The photoelectron bands associated with ionization from the formally non-bonding p orbitals of the halogen atoms in the halomethanes have been interpreted in terms of a pseudo one-electron hamiltonian. Account has been taken of interactions between the halogen atoms, of interactions between the halogen p orbitals and the σ-bonding orbitals, and of spin-orbit coupling. This model leads to a systematic assignment of all the bands of the chloro and bromomethanes, and gives a satisfactory account of the spin-orbit splittings in the bromomethanes.

The dynamic properties of the lowest triplet states of pyrazine and pyrimidine in zero magnetic field

Abstract: The technique of microwave induced delayed phosphorescence has been used to determine the dynamic properties of the lowest triplet states of pyrazine and pyrimidine as guests in benzene host crystals at temperatures at and below 4.2 K. We report values for the total lifetimes of the individual triplet sublevels, their relative radiative decay rates, relative populating rates and relative steady state populations. From these experimental data, we can hope to discover the radiationless and radiative pathways responsible for the population and depopulation of the individual triplet sublevels. To this end, we have analysed the data in terms of simple considerations of the various spin-orbit coupling mechanisms involved in these processes. In most cases there is excellent qualitative agreement between theory and experiment.

Electric dipole moments of open-shell diatomic molecules

Abstract: The electric dipole moments of the diatomic radicals IO, SF, SeF and SeO (1Δ) have been determined by studying the Stark splitting in their gas phase electron resonance spectra. Previous measurements for several other diatomic radicals are repeated and, in particular, earlier results for NS and SO (1Δ) are corrected.

The electronic absorption spectra of phthalocyanine monomers and dimers

Abstract: The electronic spectra of monomeric and dimeric silicon phthalocyanines are described. The spectral differences are interpreted in terms of exciton coupling of neutral-excitation transitions of the two rings of the dimer.

Proton magnetic resonance of non-planar condensed benzenoid hydrocarbons

Abstract: The McWeeny ‘ring current’ theory is tested critically against a set of consistent, accurate experimental chemical shifts for 85 protons in 16 planar unsubstituted condensed benzenoid hydrocarbons, and a regression equation is derived relating quantities calculated from the theory to experimental τ values for the non-hindered protons Systematic deviations of different types of protons from this line are discussed, as also are sigma-bond anisotropy effects and discrepancies observed for overcrowded protons Some of the assumptions about the geometry of planar benzenoid hydrocarbons normally made in these calculations are relaxed The McWeeny theory gives a good account of the chemical shifts of non-hindered protons in planar molecules, and the predictions of the theory are not significantly altered if the calculations are based on experimental x-ray geometry Sigma-bond anisotropy effects are unimportant for non-hindered protons, and, at most, make only a partial contribution to the down-field shifts of h

Near ultra-violet spectra of the s-trans and a second rotamer of acrolein vapour

Abstract: The rotational contour of the 0-0 band of the 1 A″(nπ*)-1 A′ system of s-trans acrolein has been analysed. Interpretation of the excited state rotational constants shows that the changes in angles CCC and CCO, if assumed to be equal, are between +3° and +4° over a large range of Δr C=C, Δr C=O and Δr C-C and, if Δr C=C Δr C=O are assumed equal, then Δr C-C≈ - Δr C=C over a large range. Weaker bands, to low wavenumber of the 1 A″(nπ*)-1 A′ system of s-trans acrolein, are sorted by their temperature dependence and characteristic contours into two systems: the 4120 A system is the 3 A″(nπ*)-1 A′ system of s-trans acrolein while the 4060 A system is shown to be the 1 A″(nπ*)-1 A′ system of s-cis (or possibly ggauche) acrolein. Evidence for this has been obtained from ground state vibration wavenumbers, rotational band contours and temperature effects. Temperature dependence of the intensity of bands has been used to show that the separation of the s-trans and s-cis zero-point levels in the ground electronic s...

Nuclear relaxation and molecular properties

Abstract: The quadrupolar relaxation of the nitrogen nucleus has been studied in organic nitro compounds of the type X-NO2 (with X = C, N, O). Fine structure due to vicinal 14N, 1H coupling has been found in the proton spectra of nitramines and of alkyl nitrates. Complete line shape analysis of the proton resonances leads to the quadrupolar relaxation times T q of the nitrogen nucleus. Quadrupolar coupling constants have been estimated from these T q values. The results indicate that the symmetry of the electron distribution at the NO2 nitrogen site increases in the sense X = C < X = O < X = N. This trend may be rationalized in terms of the effect of the substituent X, within the framework of the Townes and Dailey model for quadrupolar interactions. The major factor leading to low field gradients at the NO2 nitrogen site is found to be inductive electron withdrawal from the nitrogen orbital in the X-NO2 bond by electronegative X substituents. The temperature dependence of T q has also been studied by line shape ana...