Anatomy of molecular properties evaluated with explicitly correlated electronic wave functions

Static electric dipole and quadrupole moments were evaluated at the explicitly correlated second-order Møller–Plesset (MP2-F12) level for BH, CO, H₂O, and HF molecules. The electron correlation contributions to the multipole moments were further decomposed into the direct (unrelaxed) and indirect (orbital response) components; we found that both components are equally important for the conventional (MP2) contribution, whereas the F12 correction to these properties originates primarily from the orbital response effects. Finally, the direct contribution dominates in the perturbative Hartree–Fock basis set incompleteness (CABS singles) correction. Two basis set families were employed: the standard aug-cc-pVXZ series and the cc-pVXZ-F12 series designed specifically for the F12 methods. The aug-cc-pVXZ MP2-F12 multipole moments usually have smaller basis set errors than the cc-pVXZ-F12 counterparts, albeit their differences are small at the triple (X = T) and quadruple (X = Q) zeta level. With the MP2-F12 calculations, the basis set errors of dipole and quadrupole moments can be reduced to ～0.001 a.u., or roughly 0.1%, at the aug-cc-pVDZ and aug-cc-pVTZ levels, respectively.     

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.     

Reaction products from a discharge of N2 and H2S: The microwave spectrum of NH2SH

Thiohydroxylamine has been identified as one of the reaction products from the discharge reaction of N₂ + H₂S. Both cis and trans conformers have been observed. The rotational spectra have been studied from 56 to 170 GHz for the normal species and several deuterated isotopic species of each conformer. The electric dipole moments of both conformers have been determined. A number of the transitions of the cis conformer exhibit splittings due to the nuclear quadrupole moment of the ¹⁴N nucleus. A least squares fit of the frequency splittings have led to an analysis of the eQq values. Ab initio calculations using a 4-31G basis set both with and without polarization functions have been carried out to aid in the analysis and to provide a final structural comparison with the microwave results.     

Full relativistic calculations of the quadrupole and electric field gradients for C2, N2, and O2

In the present work we calculate the energies,quadrupole moments,and electric field gradients(EFGs) of molecules C2,N2,and O2 based on the DIRRCI method with basis aug-cc-pVTZ-DK.We prove that the quadratic force constant k2 is the product of charge and EFG at its equilibrium nuclear distance.The dipole charge distributions for these symmetrical molecules are all in equilibrium,however,the quadrupole charge distributions are far from equilibrium;among these,there is the most remarkable deviation from equilibrium for N2,for its many charges concentrate on two sides of the molecule,which is in agreement with the well-known characteristic of the nitrogen molecule.The relativistic effect is remarkable even for the same period.     

Valence shell calculations on polyatomic molecules

Molecular quadrupole moments were calculated for some diatomic, symmetric top and small planar molecules by CNDO/2D and SCC methods. The results resemble those obtained by ab initio minimal basis set calculations and give a fairly good agreement with experimental data. The latter are closely reproduced only by ab initio extended basis set calculations indicating that molecular quadrupoles provide a sensitive test of the quality of the molecular wave functions. Flygare's empirical additivity rules for out-of-plane second moments of electronic charge distribution were rationalized in terms of CNDO/2 MO's over orthogonal AO's. In this model only one-centre terms are important and the sum of one-centre terms was approximately constant for the first-row atoms.     

An ab initio study of vibrational corrections to the electrical properties of the fluoromethanes: CH3F,CH2F2, CHF3 and CF4

Accurate SCF and MP2 quartic property hypersurfaces have been computed for the energy, dipole moments, quadrupole moments and polarizability tensors of the fluorinated methanes CF₄, CHF₃, CH₂F₂ and CH₃F, to establish accurate values of zero-point vibrational corrections to the properties. Using a consistent set of r_e geometries from density functional theory, these ZPVCs are coupled with accurate electrical properties computed using a range of correlated methods, especially BD and BD(T), and a number of purpose-built polarized basis sets, to obtain near definitive estimates of these properties that incorporate the effects of vibrational averaging. Careful attention has been paid to a critical comparison between these theoretical estimates and experimental measurements, and agreement between the two is shown to be exceptionally good. In particular, it is clear that in many instances more precise experimental results would be required in order to discriminate between different correlated results, or between the present results and those which may be obtained with larger basis sets. The work highlights the necessity to allow for the effects of zero-point vibrational averaging when comparing theory with experiment, or even when comparing different theoretical results with one another using experiment as a benchmark. It also points to the need for further precise experimental measurements of some of these properties.     

Relativistic theory of the electric quadrupole moment of a hydrogen-like atom in the <Emphasis Type="Italic">s</Emphasis>1/2 and <Emphasis Type="Italic">p</Emphasis>1/2 states

Relativistic analytical expressions are derived for the electric quadrupole moment induced by the hyperfine interaction of the electron with the nucleus of a hydrogen-like atom in the ns_1/2 and np_1/2 states. The magnetic dipole and electric quadrupole hyperfine interactions are taken into account. The calculations are performed using the generalized virial relationships for the Dirac equation in a central field. The dependences of the electric quadrupole moment on the nuclear charge Z and the principal quantum number n are analyzed. The induced quadrupole moments are compared with the nuclear quadrupole moments.     

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.     

An ab initio analysis of electronic states associated with a silicon vacancy in cubic symmetry

The electronic orbitals localized in the vicinity of a vacancy in a silicon crystal are calculated by an ab initio method based on the density functional theory and analyzed in association with the elastic softening observed by the recent ultrasonic experiments, especially focused on an estimate of the electric quadrupole moments. The localized orbitals due to the existence of a vacancy show largely extended properties and the quadrupole moments calculated from the orbitals indicate the strong dependence on cell sizes up to 511 atoms in the basic cell. Asymptotic values of the quadrupole moments in the limit of large size are obtained by an extrapolating method. It is shown that the quadrupole moments are enhanced due to the extension of the orbitals and the ratio of the quadrupole moments of Γ₅ and Γ₃ symmetries agrees well with the value deduced from the experimental results.     

Site–site potential function and second virial coefficients for linear molecules

The second virial coefficients for several linear molecules were calculated using the 2CLJ potential including the electrostatic and induction effects with modified mixing rules for unlike pairs. Least squares fits of experimental values for B(T) were used to calculate the energy parameters σ and ε in the LJ core potential for N₂, O₂, Cl₂, F₂, CO, CO₂, NO, N₂O, C₂H₆, C₂F₆ and the strongly polar molecules CH₃Cl, CH₃F, CH₃CF₃, CH₃CHF₂, and CF₃CH₂F. The analysis takes into account rotation of the dipole out of the molecular axis. The calculated results for the second virial coefficient agree well with experimental data. In addition, the effect of the induction terms on the potential for calculating the second virial coefficient is shown to be important only for the molecules with strong dipole or quadrupole moments.     

羟基碳纳米管吸附SF6放电分解组分的DFT计算

本文根据密度泛函理论(density functional theory , DFT), 采用MS分子动力学仿真软件对羟基修饰的单壁碳纳米管(SWNT-OH) 吸附SF₆局部放电分解的四种主要组分SOF₂, SO₂F₂, SO₂和CF₄进行了详细的理论计算, 通过分析气体分子和SWNT-OH的前线轨道, 吸附过程中吸附能、电荷转移量和电子态密度的情况, 以及吸附前后SWNT-OH能隙的变化, 评判了SWNT-OH对气体分子的敏感性和选择性, 给出了SWNT-OH是否可以制备气体传感器检测SF₆局部放电分解组分的理论依据.     

Adsorption behaviour of SF6 decomposed species onto Pd4-decorated single-walled CNT: a DFT study

Metal nanocluster decorated single-walled carbon nanotubes (SWCNT) with improved adsorption behaviour towards gaseous molecules compared with intrinsic ones, have been widely accepted as a workable media for gas interaction due to their strong catalysis. In this work, Pd₄ cluster is determined as a catalytic centre to theoretically study the adsorption property of Pd₄-decorated SWCNT upon SF₆ decomposed species. Results indicate that Pd₄-SWCNT possessing good responses and sensitivities towards three composed species of SF₆ could realise selective detection for them according to the different conductivity changes resulting from the varying adsorption ability. The response of Pd₄-SWCNT upon three molecules in order is SOF₂ > H₂S > SO₂, and the conductivity of the proposed material is about to increase in SOF₂ and H₂S systems, while declining in SO₂ system. Such conclusions would be helpful for experimentalists to explore novel SWCNT-based sensors in evaluating the operating state of SF₆ insulation devices.     

Analytical potentials for triatomic molecules from spectroscopic data

A general procedure has been developed for constructing analytical potential functions for triatomic molecules which have more than one minimum, these minima not necessarily being related by symmetry. Explicit potentials have been derived for the ground states of HO₂, SO₂ and ClO₂. For HO₂ a linear hydrogen bonded structure O-H----O is predicted as a metastable species. In the case of SO₂ a second minimum corresponding to the species SOO is predicted and ab initio calculations at the SCF MO double-zeta level have been made to establish the geometry and energy of this. For ClO₂ it has been assumed that the spectroscopically observed states of OClO and ClOO are separate minima on the same surface.     

Spectroscopy and dissociation of sulfuryl halides SO2X2 (X=F,Cl)

The spectroscopy and dissociation of the sulfuryl halides SO₂F₂ and SO₂Cl₂ have been studied in detail using ab initio methods. The possibility of various dissociation channels has been explored taking into account that the fragmented atoms and molecules can stay in their ground state only. An interesting pattern was observed in their dissociation energy spectra for the dissociation channels. The singlet potential energy surfaces for the exit channels of these molecules have been analysed. The release of halogen molecules after dissociation is discussed from an industrial point of view. Finally, the enthalpy of formation of these molecules was computed using the ab initio results. Our results agree very well with the experimental values available.     

The distance dependence and spatial distribution of the molecular quadrupole moments of P2, S2 and Cl2

The quadrupole moments (Θ) of the molecules P₂, S₂ and Cl₂ have been computed at the SCF, CASSCF and CASSCF + 1 + 2 levels of theory, using augmented correlation consistent basis sets. The convergence of Θ as a function of basis set and level of theory is discussed. The variation of Θ from the separated atoms to the equilibrium region is reported. Θ is written as the sum of a sigma and pi contribution, and inaccuracies in the SCF values for P₂ and S₂ are due to the poor representation of the pi system in the SCF theory. A reference state dependent quadrupole moment density, - ½(3cos² θ- 1)r ²δη(r; R), is defined whose integral is the mole2 cular quadrupole moment, and the spatial distributions of the density and its relationship to the density difference δη(r; R) are examined.     

Hyperfine structure and nuclear moments of99Ru and101Ru

The atomic-beam magnetic-resonance method in combination with the triple resonance technique has been used to determine the nuclear magnetic dipole moments of⁹⁹Ru and¹⁰¹Ru. The moments are deduced fromrf transition measurements in the⁵F₅ and⁵F₄ states at magnetic fields between 770 and 2400 Oe. In order to reduce the part of the uncertainty of the moments which arises from the uncertainty of the hyperfine structure constants more precise values of the constants than those available up to now were determined from low field measurements. After making corrections for hyperfine and Zeeman interactions with neighbouring atomic states we obtain the following values for the magnetic dipole moments:μ ₉₉=?0.6381 (51)μ _N andμ ₁₀₁=?0.7152 (60)μ _N (uncorrected for diamagnetic shielding). The results of the present work combined with the results of an earlier hyperfine structure investigation in the⁵F multiplet are analysed with respect to the effective-operator formalism. From this analysis we obtain the following values for the electric quadrupole moments:Q ₉₉=0.076 (7) b andQ ₁₀₁=0.44 (4) b (uncorrected for Sternheimer shielding or antishielding).     

Electric quadrupole and magnetic dipole moments of the first excited 2+ states of186Os and188Os

The spectroscopic quadrupole moments and the magnetic dipole moments of the lowest 2⁺ states in¹⁸⁶Os (137 keV) and¹⁸⁸Os (155 keV) have been determined by Mößbauer transmission experiments. The electric quadrupole momentsQ ₂₊(Os 186)=? (1.80±0.22) b andQ ₂₊(Os 188)=?(1.81±0.24) b as well as their ratioQ ₂₊(Os 188)/Q ₂₊(Os 186)=1.00±0.07 within the limits of error agree withB(E2) data, if a comparison on the basis of the rotational model is made. For the g-factors and their ratio g₂₊(Os 186)=0.281±0.008, g₂₊(Os 188)=0.305±0.015 andg ₂₊(Os 188)/g ₂₊(Os 186)=1.08±0.05 was obtained. All results are compared with recent model calculations.     

Density functional study of the molecular structures,infrared and Raman spectra of carbon suboxide,its sulfur and selenium analogues

Carbon suboxide, and its sulfur and selenium analogues in D _∞h symmetry have been studied in the gas phase by a density functional method using B3LYP as the functional. The basis sets employed are 6-31++G(d,p), 6-311++G(d,p), cc-pVDZ and all calculations have been carried out using Gaussian 03W. Molecular parameters, namely bond lengths, rotational constants, quadrupole moments, and infrared and Raman frequencies are predicted for these molecules. Atomization energies have also been predicted. The calculated molecular parameters and vibrational spectra of the parent molecule, namely carbon suboxide, are in good agreement with literature data. Therefore, data from the present theoretical gas phase study are expected to be valid for the molecular structures and vibrational spectra of carbon subsulfide and carbon subselenide. The results from this study could be used as a reference for these molecules.     

Magnetic dipole,electric quadrupole and magnetic octupole moments of the <Emphasis Type="Italic">Δ</Emphasis> baryons in light cone QCD sum rules

Due to the very short life time of the Δ baryons, a direct measurement on the electromagnetic moments of these systems is almost impossible in the experiment and can only be done indirectly. Although only for the magnetic dipole moments of Δ ⁺⁺ and Δ ⁺ systems there are some experimental data, the theoretical, phenomenological and lattice calculations could play crucial role. In the present work, the magnetic dipole (μ _Δ ), electric quadrupole (Q _Δ ) and magnetic octupole (O _Δ ) moments of these baryons are computed within the light cone QCD sum rules. The results are compared with the predictions of the other phenomenological approaches, lattice QCD and existing experimental data.     

Study of electric quadrupole interactions of111In and111Cd following ion implantation of111In into graphite

The nuclear electric quadrupole interaction of¹¹¹In ion-implanted in hightly oriented pyrolytic graphite has been observed by means of low-temperature nuclear orientation and by means of perturbed angular correlations. From the first kind of experiment, it is concluded that a relatively large number of indium nuclei experience a well-defined macroscopic orientation, which is partly lost after the radioactive decay to cadmium. Indeed, the second kind of experiment revealed a broad distribution of electrid field gradients interacting with the 245 keV Cd excited state, as well as a small faction experiencing a unique electric field gradient. The experimental results are compared with theoretical calculations of the electric field gradient at various lattice positions, in which carbon and indium electronic wavefunctions are allowed to hybridize. Lattice positions of the covalent indium atom between the graphite layers can explain the measured electric field gradient ofV ₂₂=+1.47(11)·10²² V/m², directed parallel to the graphitec-axis.