Calculations of molecular multipole electric moments of a series of exo-insaturated four-membered heterocycles,Y = CCH2CH2X

The influence of ring puckering angle on the multipole moments of sixteen four-membered heterocycles (1-16) was theoretically estimated using MP2 and different DFTs in combination with the 6-31+G(d,p) basis set. To obtain an accurate evaluation, CCSD/cc-pVDZ level and, the MP2 and PBE1PBE methods in combination with the aug-cc-pVDZ and aug-cc-pVTZ basis sets were performed on the planar geometries of 1-16. In general, the DFT and MP2 approaches provided an identical dependence of the electrical properties with the puckering angle for 1-16. Quantitatively, the quality of the level of theory and basis sets affects significant the predictions of the multipole moments, in particular for the heterocycles containing C=O and C=S bonds. Convergence basis sets within the MP2 and PBE1PBE approximations are reached in the dipole moment calculations when the aug-cc-pVTZ basis set is used, while the quadrupole and octupole moment computations require a larger basis set than aug-cc-pVTZ. On the other hand, the multipole moments showed a strong dependence with the molecular geometry and the nature of the carbon-heteroatom bonds. Specifically, the C-X bond determines the behavior of the μ(?), θ(?) and ?(?) functions, while the C=Y bond plays an important role in the magnitude of the studied properties.     

Analytical nuclear gradients of the explicitly correlated Møller–Plesset second-order energy

The analytical computation of nuclear gradients has been derived and implemented for the explicitly correlated second-order Møller–Plesset method (MP2-F12). The implementation has been accomplished in the TURBOMOLE program package for ansatz MP2-F12/2*A. A Slater-type geminal expanded in six Gaussian geminals (STG-6G), a complementary auxiliary basis set (CABS), and robust density fitting approximations are used. In addition, a second-order perturbation theory correction for single excitations into the complementary auxiliary basis set (CABS singles) is included to reduce the Hartree–Fock error. Smooth convergence towards the basis set limit is observed for a selection of molecules. For computations on dimers of weakly interacting molecules in small basis sets, explicitly correlated second-order Møller–Plesset theory outperforms conventional second-order Møller–Plesset theory because basis set superposition errors are largely avoided at the MP2-F12/2*A level.     

Signatures of chiral dynamics in the nucleon to Delta transition⋆

Utilizing the methods of chiral effective field theory we present an analysis of the electromagnetic NΔ-transition current in the framework of the non-relativistic “small scale expansion” (SSE) to leading-one-loop order. We discuss the momentum dependence of the magnetic dipole, electric quadrupole and Coulomb quadrupole transition form factors up to a momentum transfer of Q² < 0.3GeV^2. Particular emphasis is put on the identification of the role of chiral dynamics in this transition. Our analysis indicates that there is indeed non-trivial momentum dependence in the two quadrupole form factors at small Q² < 0.15GeV^2 arising from long-distance pion physics, leading, for example, to negative radii in the (real part of the) quadrupole transition form factors. We compare our results with the EMR(Q²) and CMR(Q²) multipole ratios from pion-electroproduction experiments and find a remarkable agreement up to four-momentum transfer of Q² ≈ 0.3GeV^2. Finally, we discuss the chiral extrapolation of the three transition form factors at Q² = 0, identifying rapid changes in the (real part of the) quark mass dependence of the quadrupole transition moments for pion masses below 200MeV, which arise again from long-distance pion dynamics. Our findings indicate that dipole extrapolation methods currently used in lattice QCD analyses of baryon form factors are not applicable for the chiral extrapolation of NΔ quadrupole transition form factors.     

The calculation of dynamic polarizabilities and of the dipole-dipole and dipole-quadrupole contributions to the dispersion energy

By using a single Slater-type 2p orbital with a frequency-dependent exponent in the basis set for the variation solution of the first-order time-dependent perturbation equation, good results are obtained for the dipole dynamic polarizability of the hydrogen atom. The accuracy attained has been reproduced only by variation calculations with larger basis sets. The same happens with the quadrupole dynamic polarizability: a single 3d Slater-type orbital with a similarly optimized exponent in the basis of states for the variation calculation is enough to yield results which are very close to the exact values for all frequencies. Using the frequency-dependent dipole and quadrupole polarizabilities thus obtained we have calculated the dipole and quadrupole contributions to the dispersion energy of two hydrogen atoms and found results which are within 1 per cent of the exact values.

Considering the simplicity of our wavefunction as compared with the four-term wavefunction used by Chan and Dalgarno [5] to construct the basis for their variation calculation and the excellent agreement we obtain, it is important to emphasize the value of using optimized frequency-dependent exponents in the basis of states used for the variation calculation.     

The multipole polarizabilities and hyperpolarizabilities of the water molecule in liquid state: an ab initio study

A charge perturbation variant of the finite-field method has been used to calculate dipole and quadrupole moments, dipole polarizability, hyper- and principal components of high-order polarizabilities of the water molecule in gas and in liquid phase conditions. Calculations were performed for the ground-state water molecule at the MP2 and MP4 levels of theory. The gas phase values determined allow our methodology for extracting polarizabilities to be tested and a properly balanced, moderate-sized basis set to be selected; the results obtained are in very good agreement with experiment and the most accurate previous theoretical estimates. A local field approach is introduced to mimic the electrostatic environment experienced by a water molecule in the liquid. Within this approach, sets of fixed charges are used to generate the desired electric fields and field gradients. Three different liquid phase models and the corresponding sets of electrical properties are examined. The values obtained from these models and for gas-phase are compared. The magnitudes of the dipole and the quadrupole moments increase moving from gas to liquid phase, where the latter shows greater sensitivity to the choice of liquid model. For a liquid phase water molecule the first hyperpolarizability (β) and first higher polarizability (A) increase markedly, actually changing sign, the second hyperpolarizability (γ) also increases but much less dramatically, and components of the second high-order polarizability tensor (B) demonstrate a rearrangement of contributions. The values reported for the hyper- and high-order polarizability tensors are the first such theoretical estimates for liquid water.     

On the convergence of zero-point vibrational corrections to nuclear shieldings and shielding anisotropies towards the complete basis set limit in water

ABSTRACT

The method and basis set dependence of zero-point vibrational corrections (ZPVCs) to nuclear magnetic resonance shielding constants and anisotropies has been investigated using water as a test system. A systematic comparison has been made using the Hartree–Fock, second-order Møller–Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) and Kohn–Sham density functional theory with the B3LYP exchange-correlation functional methods in combination with the second-order vibrational perturbation theory (VPT2) approach for the vibrational corrections. As basis sets, the correlation consistent basis sets cc-pVXZ, aug-cc-pVXZ, cc-pCVXZ and aug-cc-pCVXZ with X = D, T, Q, 5, 6 and the polarisation consistent basis sets aug-pc-n and aug-pcS-n with n = 1, 2, 3, 4 were employed. Our results show that basis set convergence of the vibrational corrections is not monotonic and that very large basis sets are needed before a reasonable extrapolation to the basis set limit can be performed. Furthermore, our results suggest that coupled cluster methods and a decent basis set are required before the error of the electronic structure approach is lower than the inherent error of the VPT2 approximation.     

Nuclear magnetic moment of161Tb

Nuclear orientation measurements on dilute TbGd are analysed to yield the magnetic dipole and electric quadrupole moments of¹⁶¹Tb g.s. and multipole mixing ratios of transitions in¹⁶¹Dy.     

SCF-CI calculations of the potential energy curve and one-electron property curves of the X 1II ground state of NO

The energy and many important one-electron properties of the nitric oxide molecule in the ground state (X ²II) have been evaluated at various internuclear separations near the equilibrium geometry, using the direct CI method and the Graphical Unitary Group (GUG) method at both single- and multi-reference level. The one-electron properties thus obtained (and vibrationally averaged using Dunham analysis) include the electric field gradients (at both the O and N nuclei) and the multipole moments from dipole to hexadecapole moment (all with respect to the centre of mass).     

Combining rule for interaction energies of the (CO)2, (N2)2 and CO-N2 complexes

The relationship between interaction energies of the most stable structures of the (CO)₂, (N₂)₂ and CO-N₂ complexes is investigated using the supermolecule CCSD(T) and MP4 methods and aug-cc-pVXZ (X = D,T,Q) basis sets extended by a set of midbond functions centred in the middle of the intermolecular bond. A simple combining rule for interaction energies of this triad of clusters is proposed.     

Photoproduction of pairs of neutral fermions with a magnetic moment in the field of a nucleus of arbitrary spin

We have investigated the electromagnetic (Bethe-Heitler) process of the formation of a pair of neutral baryons of spin 1/2 by a photon in the field of a nucleus possessing electric quadrupole and magnetic dipole and octupole moments. The cross section for photoproduction of neutron-antineutron pairs has been found as a function of the electric (Ze, Q) and magnetic (_I, ) multipole moments of the target nucleus. The angular distribution and energy spectrum of the neutron of the pair produced have been studied for⁹Be,¹²C, and⁴⁰Ca nuclei.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 69–75, May, 1982.     

Theoretical study of the transition probabilities among the three lowest electronic states of the SeS molecule

Spin-perturbed CI wavefunctions are reported for the X ³Σ^? electronic states of the SeS molecule. The Breit-Pauli approach is employed using the one- and two-electron spin-orbit operator as the perturbing hamiltonian and a zeroeth-order basis of CI eigenfunctions generated by the standard multireference single- and double-excitation (MRD-CI) formalism. Transition moments are reported between each of the above states for electric and magnetic dipole and electric quadrupole radiative processes, and these results are compared with recent experimental high resolution data obtained by Fink, Kruse, Ramsay and Wang. Generally good agreement is found between computed and observed ratios of such quantities, but the absolute values of the computed transition moments are uniformly found to be only somewhat less than half as large as the corresponding observed results. A simple formula is presented which relates the magnetic moments of the b ¹Σ⁺-X ³Σ1? transitions to twice the square root of the ratio of two observable energy differences and this result promises to be useful in future experimental studies attempting to estimate line strengths for this type of band system. On this basis arguments are also presented supporting the view that the computed absolute intensities may be more accurate than would appear from the original experimental assessment of the SeS spectroscopic data.     

TiO基态 (X 3 Δr) 的势能函数与光谱常数

应用群论及原子分子反应静力学方法推导了TiO分子基态(X³Δ_r)的离解极限.采用不同的计算方法,包括密度泛函B3LYP,B3P86,BP86,B3PW91和MP2,MP4方法,结合不同基组计算了TiO分子基态的平衡核间距、能量和振动频率.研究表明,使用B3LYP方法,对O原子使用6-311+G基组,Ti原子使用6-311+ +G^**基组时计算得到的平衡几何结构、分子离解能和谐振频率与实验值符合得最好.使用优选出的方法和基组对T 关键词： TiO 势能函数 光谱常数 密度泛函理论     

Ab initio dipole polarizabilities and quadrupole moments of the lowest excited states of atomic Yb

The finite-field scalar relativistic coupled cluster and configuration interaction, as well as the spin-orbit configuration interaction, methods are employed to calculate the static dipole polarizabilities for the lowest (6s ²) ¹S, (6s6p) ^1,3^{1,3}P^o and (6s5d) ^1,3^{1,3}D excited states of atomic ytterbium. The results agree very well with existing experimental and best theoretical data and refine the set of ytterbium polarizabilities known so far. Similar techniques are used to calculate the electric quadrupole moments for the ^1,3^{1,3}P^o and ^1,3^{1,3}D states.     

Density functional theory calculations of nuclear quadrupole coupling constants with calibrated 14N quadrupole moments

Density functional calculations of the electric field gradient tensor at the nitrogen nucleus in 13 test molecules, containing 14 nitrogen sites, have been performed using the linear combination of Gaussian-type orbital Kohn-Sham density functional theory (LCGTO-KSDFT) approach. Local and gradient corrected functionals were used for all-electron calculations. All the molecular structures were optimized at their respective levels of theory with extended basis sets. Calibrated ¹⁴N nuclear quadrupole moments were obtained through a fitting procedure between calculated electric field gradients and experimental nuclear quadrupole coupling constants of the test set of molecules for each basis set and functional considered. With these calibrated ¹⁴N nuclear quadrupole moments, the nuclear quadrupole coupling constants of the following selected systems were determined: fluoromethylisonitrile, pyridine, pyrrole, imadazole, pyrazole, 1,8-bis(dimethyl-amino)naphthalene, cyclotetramethylenetetranitramine, cocaine and heroin.     

The X2Π and A2Σ+ states of FH+, ClH+ and BrH+: theoretical study of their g -factors and fine/hyperfine structures

Theoretical calculations on the fine, hyperfine and Zeeman (g-factor) parameters are reported for the X²Π and A²Σ⁺ states of FH⁺, ClH⁺ and BrH⁺. The fine-structure constants [spin–orbit (A), Λ-doubling (p, q) and spin–rotation constants (γ _Π, γ _Σ)] are evaluated up to second order (via SO/L couplings with several excited states) using a multireference configuration interaction (MRCI) method, a Breit–Pauli Hamiltonian and 6-311++(2d,2pd) basis sets. Hyperfine constants of magnetic and electric type [Frosch–Foley (a, b, c, d) and nuclear quadrupole (eQq ₀, eQq ₂)] are studied with density functional methods and various basis sets. Magnetic dipole moments (parameterized via g-factors) are calculated in second order like the fine structure constants. The situation is somewhat complex for X²Π since no less than five different g’s have to be evaluated in second order. In general, our results are in good agreement with those reported in the literature, mostly limited to the ground state. Our calculations confirm that, at equilibrium, all second-order properties are dominated by the couplings between the electronic states X and A.     

Ab initio calculations of multipole moments,polarizabilities and long-range interaction coefficients for the azabenzene molecules

Using LCAO-SCF wave functions on the monomers and a non-empirical Unsöld procedure for the second-order properties we have calculated the (2 ^l ) multipole moments (up to l=6), the (l,l') multipole polarizabilities (up to l + l' = 6) and the related long-range coefficients describing the electrostatic, induction and dispersion interactions for the different azabenzene molecules. The agreement with available experimental data is good, in particular for the dipole polarizabilities. The anisotropy of the long-range interaction potential is dominated by the electrostatic contributions, although the dispersion terms, especially the mixed-pole terms (l≠l') for even n (C₈, C₁₀), also contribute significantly; the induction energy is rather small. The π contributions to the polarizabilities and the dispersion interactions are found to be larger than earlier estimates. Moreover, it is shown by calculating the dipole polarizabilities of some (aza)naphthalenes and (aza)anthracenes, that a bond polarizability model can be applied effectively only if the delocalized π electrons are considered separately from the σ electrons.     

Quantum corrections to thermodynamics of polar hard sphere fluids

The quantum corrections to the thermodynamic properties of polar hard sphere fluids and fluid mixtures are estimated taking into account the influence of dipole and quadrupole moments. Expressions are given for the second virial coefficient, free energy and pressure and results are given for different values ofμ* andϑ*. The first order quantum correction arises due to the translational contribution only. The quantum effect increases with density,μ* andϑ*. Numerical results are also estimated for binary mixtures of (i) hard spheres and dipole hard spheres and (ii) hard spheres and quadrupole hard spheres. The ‘excess’ free energy for dipole hard sphere binary mixture is also reported. It is found that the ‘excess’ quantum effect depends on the concentration and the particle diameter ratio and increases with increase ofμ* andϑ*.     

Core/shell/shell spherical quantum dot with Kratzer confining potential: Impurity states and electrostatic multipoles

An exactly solvable problem of impurity states is considered in core/shell/shell spherical quantum dot. Kratzer molecular potential is taken for confinement potential. The analytical expressions are obtained for the energy spectrum and wave functions of the impurity electron. The dependencies of the total energy and the binding energy of the impurity on the parameters of the confining potential are investigated. The possibility of the impurity electron leakage is shown in the external environment, due to the specific form of the Kratzer potential. The character of the electrostatic field created by the impurity and the electron is observed on the basis of obtained results. The multipole corrections caused by the dipole and quadrupole moments of the electron are calculated. It is shown that the dipole moment is absent, and the problem reduces to the calculation of only z component for the average values of the diagonal elements of the quadrupole moment tensor. The dependencies of the average values of the quadrupole moment on the Kratzer potential parameters are studied.     

The origin of non-planarity in ketyls

A series of one-electron properties, i.e. dipole, quadrupole, octupole moments, diamagnetic susceptibility, second moments and second moment anisotropies of charge distribution, electric field, electric field gradient, diamagnetic shielding, nuclear quadrupole coupling constant, have been obtained by ab initio S.C.F. calculations for the molecules COF₂, SO₂F₂ and SOF₂. The effect of the size of the gaussian basis sets, including d-type polarization functions, as well as the contraction schemes on the latter properties have been studied for the COF₂ molecule. This study enables us to determine the basis giving the best results as compared to experiment. With this basis the calculations have been extended to the properties of the molecules SO₂F₂ and SOF₂. Good overall agreement with experiment is obtained.     

Solvent Effect on Absorption and Fluorescence Spectra of Three Biologically Active Carboxamides (C<Subscript>1</Subscript>, C<Subscript>2</Subscript> and C<Subscript>3</Subscript>). Estimation of Ground and Excited State Dipole Moment from Solvatochromic Method Using Solvent Polarity Parameters

The absorption and fluorescence spectra of three Carboxamides namely (E)-2-(4-Chlorobenzylideneamino)-N-(2-chlorophenyl)-4, 5, 6, 7-tetrahydrobenzo[b]thiophene-3-carboxamide (C₁), (E)-N-(3-Chlorophenyl)-2-(3, 4-dimethoxybenzylideneamino)-4, 5, 6, 7-tetrahydrobenzo[b]thiophene-3-carboxamide (C₂) and (E)-N-(3-Chlorophenyl)-2-(3, 4, 5-trimethoxybenzylideneamino)-4, 5, 6, 7-tetrahydrobenzo[b]thiophene-3-carboxamide (C₃) have been recorded at room temperature in solvents of different polarities using dielectric constant (ε) and refractive index (n). Experimental ground (μ_g) and excited (μ_e) state dipole moments are estimated by means of solvatochromic shift method and also the excited dipole moments are estimated in combination with ground state dipole moments. It was estimated that dipole moments of the excited state were higher than those of the ground state of all three molecules. Further, the changes in dipole moment (Dm \Delta \mu ) were calculated both from solvatochromic shift method and on the basis of microscopic empirical solvent polarity parameter (E_T^N E_T^N ) and the values are compared.