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The spectroscopic constants re, ωe, ωexe, αe, De, βe and atomization energy of the barium sulfide molecule, BaS, in its electronic ground state X1Σ+ are calculated using the coupled cluster singles, doubles, triples, and quadruples method CCSDTQ in conjunction with complete basis set (CBS) limit extrapolation and taking spin-orbit coupling into account. Excellent agreement of the calculation results with the available experimental data is observed, e.g., the theoretical values of re and ωe deviate from those obtained from spectroscopic measurements by less than 0.001 A and 1 cm–1, respectively. Correlation of the barium core 5s and 5p electrons is shown to contribute substantially to the values of molecular parameters. Based on an approach combining the coupled cluster theory at the CCSD(T)/CBS level with the multireference configuration interaction (MRCISD+Q) method, a high-accuracy theoretical description of the low-lying excited triplet (a3Π, b3Σ+) and singlet (A′1Π, A1Σ+) electronic states of the BaS molecule is reported for the first time.

Quantum chemical study on TiF3 and VF3 molecules was carried out using the CCSD(T) coupled cluster method using the triple-, quadruple-, and quintuple-zeta basis set and an extrapolation to the complete basis set limit. The methods of multireference configuration interaction MRCISD+Q and perturbation theory MCQDPT2 were used also. The symmetry of the ground electronic state was determined: 2A′1 and 3E″ in TiF3 and VF3, respectively. The adiabatic excitation energies were evaluated: AEE(TiF3, \(\tilde A^2 E'' \leftarrow \tilde X^2 A'_1 \)) = 5000 cm−1, AEE(VF3, \(\tilde A^3 A'_2 \leftarrow \tilde X^3 E''\)) = 1000 cm−1. The Jahn-Teller effect in \(\tilde A^2 E''\) state of TiF3 and \(\tilde X^3 E''\) state of VF3 was investigated. The computed Jahn-Teller stabilization energy D3h → C2v amounts to 555 and 292 cm−1, respectively. The spin-orbit coupling effect on the VF3 molecular structure and spectrum of electronic states is shown to be quite significant. The calculated vibrational frequencies of TiF3 are in excellent agreement with IR spectroscopy data. The atomization enthalpies were evaluated: ΔatH298pO = 430 kcal/mol (TiF3), 393 kcal/mol (VF3).

The coupled-cluster singles and doubles with perturbative triples (CCSD(T)) method in triple-, quadruple-, and quintuple-zeta basis sets with extrapolation to the complete basis set limit is used to analyze the properties of MnF3, FeF3, and CoF3 molecules. The relative energies of low-lying electronic states are determined. The Jahn-Teller effect is investigated in the ground electronic state 5 E′ of the MnF3 molecule and the first excited electronic state 5 E″ of the CoF3 molecule. Geometric parameters, atomization enthalpies, vibrational frequencies, intensities in the infrared and Raman spectra are found with high accuracy. The assignment of the bands observed in the low-frequency region of the IR and Raman spectra of MnF3 and CoF3 molecules are revised.

Equilibrium geometric parameters, normal mode frequencies and intensities in IR spectra, atomization enthalpy, and relative energies of low-lying electronic states of scandium fluoride molecules (ScF, ScF2, and ScF3) are calculated by the coupled-cluster method (CCSD(T)) in triple-, quadruple, and quintuple-zeta basis sets with the subsequent extrapolation of the calculation results to the complete basis set limit. The ScF molecule is also studied by the CCSDT technique. The error in the approximate calculation of triple excitations in the CCSD(T) method does not exceed 0.002 A for the equilibrium internuclear distance Re, 4 cm−1 for the vibrational frequency, and 0.2 kcal/mol for the dissociation energy of the molecule. In the ground electronic state \(\tilde X^2 \)A1(C2ν) of ScF2 molecules, Re(Sc-F) = 1.827 A and αe(F-Sc-F) = 124.2°; the energy barrier to bending (linearization) h = Emin(Dg8h) − Emin(C2ν) = 1652 cm−1. The relative energies of A2Δg and \(\tilde B^2 \)Πg electronic states are 3522 cm−1 and 14633 cm−1 respectively. The bond distance in the ScF3 molecule (\(\tilde X^1 \)A′1, D3h) is refined: Re(Sc-F) = 1.842 A. The atomization enthalpies ΔatH2980 of ScFk molecules are 139.9 kcal/mol, 289.0 kcal/mol, and 444.8 kcal/mol for k = 1, 2, 3 respectively.

This is the first of five connected papers detailing progress on the Gravity Probe B (GP-B) Relativity Mission. GP-B, launched 20 April 2004, is a landmark physics experiment in space to test two fundamental predictions of Einstein’s general relativity theory, the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Data collection began 28 August 2004 and science operations were completed 29 September 2005. The data analysis has proven deeper than expected as a result of two mutually reinforcing complications in gyroscope performance: (1) a changing polhode path affecting the calibration of the gyroscope scale factor C g against the aberration of starlight and (2) two larger than expected manifestations of a Newtonian gyro torque due to patch potentials on the rotor and housing. In earlier papers, we reported two methods, ‘geometric’ and ‘algebraic’, for identifying and removing the first Newtonian effect (‘misalignment torque’), and also a preliminary method of treating the second (‘roll-polhode resonance torque’). Central to the progress in both torque modeling and C g determination has been an extended effort on “Trapped Flux Mapping” commenced in November 2006. A turning point came in August 2008 when it became possible to include a detailed history of the resonance torques into the computation. The East-West (frame-dragging) effect is now plainly visible in the processed data. The current statistical uncertainty from an analysis of 155 days of data is 5.4 marc-s/yr (∼14% of the predicted effect), though it must be emphasized that this is a preliminary result requiring rigorous investigation of systematics by methods discussed in the accompanying paper by Muhlfelder et al. A covariance analysis incorporating models of the patch effect torques indicates that a 3–5% determination of frame-dragging is possible with more complete, computationally intensive data analysis.

A simple pre-flight strategy of the Gravity Probe B (GP-B) data analysis has evolved in the elaborate multi-level structure after the discovery of the complex polhode motion, and of the patch effect torques. We describe a cascade of estimators (filters) that reduce the science data (SQUID and telescope signals) to the estimates of the relativistic drift rates. Those estimators, structured in two “floors”, are based on the polhode-related models for the readout scale factor and patch effect torque. Results of the 1st Floor processing—gyro orientation profiles—manifest clearly the strong geodetic effect but also the presence of classical torque. Modeling of the patch effect torque at the 2nd Floor provides a successful compensation of the torque contributions, and leads to consistent estimates of the relativistic drift rates.

The equilibrium geometrical parameters and frequencies of the normal vibrations of Ln2Cl 7 − ions (Ln = La and Lu) and the enthalpies of the dissociation reactions Ln2Cl 7 − → Ln2Cl6 + Cl− and Ln2Cl 7 − → LnCl3 + LnCl 4 − were calculated at the MP2 and MP4 levels (with regard to single, double, triple, and quadruple perturbations). The basis set superposition errors were eliminated by using the counterpoise approach. The potential energy surface of the Ln2Cl 7 − ions was found to reach a minimum for a configuration with three bridging and four terminal Cl atoms (symmetry C 2). The terminal fragments LnCl2 show almost free inherent rotation. The lanthanide compression of the interatomic Ln-Cl distances differed for the bridging and terminal Ln-Cl bonds. The calculated enthalpies of dissociation of the Ln2Cl 7 − ions were compared with data from high-temperature mass spectrometry.

The potential energy surfaces of the lowest electronic states \( \tilde X \)2A1 and \( \tilde A \)2B1 of the CH2+ molecular ion are calculated in the second order of the perturbation theory with the reference function obtained by the multiconfiguration self-consistent-field method in the complete-active-space approximation. Based on the ab initio calculated potential energy surfaces, the rovibronic energies of CH2+ are calculated by the variational method using the RENNER Hamiltonian. It is found that the accuracy of the perturbation theory method involving many reference configurations is as good as the accuracy of the best ab initio calculations performed by the configuration interaction method with many reference configurations and by the coupled cluster method with a single reference configuration. Empirical refinement of the two parameters of the potential function leads to good agreement between calculation and experiment, except for the wavenumbers of the \( \tilde A \) (0, 3, 0)1 ← \( \tilde X \)(0, 0, 0)0 transitions.

The geometrical parameters of lanthanum and lutetium trihalide dimer molecules Ln2X6 (Ln = La, Lu; X = F, Cl, Br, I) and dissociation energies of Ln2X6 → 2LnX3 were calculated in terms of Mo ller-Plesset fourth order perturbation theory including single, double, triple, and quadruple excitations (SDTQ-MP4). Variation of the properties of molecules in series of compounds Ln2F6 → Ln2Cl6 → Ln2Br6 → Ln2I6 from lanthanum La2X6 to lutetium Lu2X6 compounds and from monomer LnX3 to dimer Ln2X6 molecules has been studied (the parameters of LnX3 molecules were determined in the same SDTQ-MP4 approximation). The lanthanide compression of the metal-halogen internuclear distance Δr(Ln-X) = re(La-X)-re(Lu-X) depends on the nature of the ligand X and coordination number of Ln. The calculated data are compared with previously published experimental and theoretical data on the structure and dissociation energies of Ln2X6 molecules.

Molecular structure and properties of La and Lu tetrahalide ions LnX 4 − ) are studied by the configuration interaction singles-and-doubles method augmented with quadruple excitation correction (CISD+Q) and by the fourth-order Moller-Plesset perturbation theory with account for single, double, triple, and quadruple excitations (SDTQ-MP4). The atomic inner shells are described by Stevens relativistic effective core potentials. Valence basis sets are augmented with diffuse s-, p-, and polarization d-, f-, and g-functions. The equilibrium configuration of nuclei in LnX 4 − ions was found to be tetrahedral. The equilibrium internuclear distances, quadratic force constants, vibrational frequencies, and IR intensities of LnX 4 − ions are compared with the corresponding parameters of La and Lu trihalide molecules (LnX3), calculated within the same approximations. Regularities in the behavior of molecular parameters on going along the LnF 4 − →LnCl 4 − →LnBr 4 − →LnI 4 − series and from La compounds to Lu compounds are revealed. Heights of the energy barriers to the LnX 4 − inversion through the square planar structures (T d → D 4h →T d ) are evaluated: 100–110 and 130–150 kJ/mol for LaX 4 − and LuX 4 − , respectively. Enthalpies of dissociation reactions LnX 4 − →LnX3+X− are calculated and the results obtained are compared with the available experimental data.

For nonrigid MkXYn (k≥1) molecules, a model is constructed that describes the motion of k M nuclei relative to the quasirigid XYn fragment taking into account 3*k degrees of freedom. The parameters of the potential and kinetic terms of the model Hamiltonian are determined from results of ab initio calculations of the properties of a molecule and its fragments. Solutions of the corresponding Schrodinger equations are obtained by a variational method using bases constructed from products of spherical harmonics and harmonic–oscillator eigenfunctions. The form of model Hamiltonians for nonrigid MXY4 and M2XY4 molecules with quasitetrahedral XY4 fragments are discussed in detail. Group–theoretical analysis of the symmetry of the Hamiltonians is performed. It is shown that the molecular symmetry groups of nonrigid MXY4 and M2XY4 molecules are the G24 and G48 groups, which are isomorphic to the Td and Oh point groups, respectively.

The previously developed nonempirical model for M k XY n (k ≥ 1) nonrigid molecules describing the motion of k M nuclei relative to a quasirigid XY n fragment is used to study the dynamics of nuclei in LiReO4 and K2SO4 molecules. The parameters of the kinetic and potential parts of the model Hamiltonian and dipole moment functions are determined from results of ab initio calculations of the molecules and their fragments by the Hartree—Fock and CISD + Q configurational interaction methods. The dynamic problem is solved by the variational method. Energy levels, transition frequencies, transition dipole moments, and mean geometrical parameters of the molecules are calculated. It is shown that the lowest energy levels of LiReO4 and K2SO4 molecules can be described with high accuracy in a harmonic approximation using a quasirigid, single–minimum model, whereas for the energy levels located near and above the barriers of intramolecular rearrangements, these approximations are completely unsuitable.

The equilibrium geometries, isomerization energies, force fields, vibration frequencies, and band intensities in the IR spectra of M2XO4 molecules (M = Li, Na, K; X = S, Se, Te, Cr, Mo, W) were calculated ab initio by the Hartree-Fock method in extended basis sets using relativistic effective core potentials. The relative energies of alternative structures were refined by the configuration interaction method taking into account single- and double-excited configurations, with the Davidson correction for quartic excitations. The results show that the chemical bonds between the metal atom and the acid residue XO4 are highly polar. The majority of M2XO4 molecules have two isomers. In both isomers the XO42- anion coordinates the metal cations M+ in the bisbidentate (bb) fashion. The equilibrium configurations ofthe nuclei in the ground (bb) and excited (bb') isomers have the D2d and Cs symmetry, respectively. In the bb isomer, the cations coordinate at the opposite, and in the bb' isomer, at the adjacent edges of the XO42- anion, having the shape of a distorted tetrahedron. The relative energy of the bb' isomer is 9-28 kJ mol-1. The energy barriers to intramolecular rearrangements bb'(C4s) → bb(D2d) are also low: 15-35 kJ mol-1. These results show that the M2XO4 molecules are structurally nonrigid, with a “polytopic” character of the M-XO4 chemical bonds. The calculation results were compared to the published experimental data on the structure and vibration spectra of the M2XO4 molecules.

The equilibrium geometric parameters, isomerization energies, force fields, vibrational frequencies and intensities in the IR spectra of MReO4 molecules (M = Li, Na, K) are calculated by the configuration interaction method including all singly and doubly excited configurations with Davidson's correction for quartic excitations in expanded basis sets using effective relativistic core potentials. The calculations indicate that the chemical bonds between the metal atoms and the ReO4 anion group are highly polar. It is found that the MReO4 molecule has two isomers. The basic isomer with C2v symmetry has bidentate b coordination of the M+ cation to the ReO4- anion. The excited isomer is of C3v symmetry and corresponds to monodentate m coordination of M+. The low relative energies of the m isomers (17-29 kJ/mole) and the low energy barriers to the intramolecular m→b rearrangements (5-11 kJ/mole) indicate that MReO4 molecules are structurally nonrigid systems where the M–XO4 chemical bonds are “polytopic.” The results of calculations are compared with the available literature data on the structure and vibrational spectra of MReO4 molecules.

The properties of MF4 molecules (M = Cr, Mo, W) are investigated by the restricted Hartree-Fock method using Moller-Plesset second-order perturbation theory and by the second-order configuration interaction method using the multiconfigumtion wave function derived in a complete active space approximation, in wide bases complemented with polarization d and f functions. Relativistic effective potentials are used to describe the core electrons. For CrF4 and MoF4, the tetrahedral configuration of nuclei in the electronic state of3k2 symmetry is energetically most favorable. In the WF4 molecule, the least-energy structure is a D2hstructure in the singlet state 1A1. The D4h,(1 A1g) and Td ( 3A2) configurations in the WF4 molecule are higher on the energy scale than the ground state by 4 and 6305 cm’1 and are saddle points. For all of the analyzed configurations of MF4 molecules, the geometrical parameters, the vibrational spectra, and the energies of vertical electronic transitions are found. The chemical bonding is analyzed and a simple model is proposed to explain the variation of the relative energies of states in the series CrF4→MoF4→WF4.

Molecular structures and vibrational spectra of ScF3, YF3, and LaF3 were studied by the Hartree–Fock– Roothaan method in terms of second-order Moller–Plesset perturbation theory and by the configuration interaction method including all singly and doubly excited configurations and Davidson's correction for quartic excitations (CISD+Q). The atomic core orbitals are defined in terms of the effective relativistic potentials suggested by Stevens et al. The equilibrium nuclear configuration is shown to be planar (D3h symmetry) for ScF3 and YF3 and pyramidal (C3v) for LaF3 with a bond angle \(\alpha _e (F{\kern 1pt} - {\kern 1pt} La{\kern 1pt} - {\kern 1pt} F) = 117.5^ \circ \). The inversion barrier of LaF3 is very low: h = E(D3h)- E(C3v) = 38 cm–1 (CISD+Q). The vibrational spectra were calculated by the variational method using the vibrational Hamiltonian describing the “nonrigidity” of a molecule with respect to out-of-plane deformation. The calculation results are compared with the previously published experimental data. The IR band assignments for matrix-isolated molecular conformations in a vapor over yttrium trifluoride were corrected.

The equilibrium geometrical parameters, force fields, vibration frequencies, and intensities in the IR molecular spectra of M2TeO3 (M-Li, Na, K) are found by the Hartree — Fock ab initio method in the bases complemented with polarization and diffusion functions using relativistic effective core potentials. The relative energies of alternative molecular configurations and the energies of the dissociation M2TeO3→ M2O + TeO2 are refined using Moller — Plessett second-order perturbation theory. It is found that the chemical bond in these molecules can be approximated by the scheme (M+)2[TeO3]2- The equilibrium nuclear configuration has Cs symmetry and corresponds to the bis-bidentate coordination of M+ cations by the pyramidal anion [TeO3]2-. The mono-bidentate structures of Cs symmetry correspond to the saddle points on the potential energy surface of the molecules. The calculated IR molecular spectrum of K2TeO3 agrees with the experimental spectrum obtained by the matrix isolation method by J. Ogden et al. [J. Chem. Soc. Dalton Trans., 1957 (1997)]. Based on the results of the previous ab initio studies of alkali metal sulfites and selenites, the barrier of the intramolecular rearrangement (bb)→(mb)→(bb)’ was found to lower in the series Li2XO3→Na2XO2→K2XO3 (X = S, Se, Te) and M2TeO3→M2SeO3→M2SO3. The degree of deformation of the XO fragment in the M2XO3 molecules decreases when the M atom is replaced by its heavier analog (Li→Na→K).

The equilibrium geometrical parameters, force constants, vibration frequencies, IR intensities, and isomerization and dissociation energies of MAF4 molecules are calculated by Hartree-Fock and second-order Moller — Plessett perturbation theory methods in the Li (9s3pld/4s3pld), Na, Al (12s8pld/6s4pld), K (14s11p3d/9s8p3d), F (9s5pld/4s2pld), and Ga (13s10p5d/6s5p2d) bases of grouped Gaussian functions. The calculations show that the structures corresponding to the bi-(b) and tridentate (t) coordinations of the M+ cation by the AF 4 - anion are isomers. The b configuration is energetically most favorable for LiAF4 molecules. The b and t structures of NaAF4 have close energies, and the t configuration is basic for KAF4 molecules. Simple empirical relations between the molecular constants in the series LiAF4→NaAF4→KAF4 are found and the molecular parameters of RbAF4 and CsAF4 are estimated. A combined analysis of the ab initio and experimental data available in the literature for MAF4 molecules is carried out. A number of bands observed in the IR spectrum of the matrix-isolated MAlF4 molecules are assigned to their tridentate isomer.

Ab initio calculations of the equilibrium geometrical parameters, force constants, and IR vibration frequencies and intensities of Li2F2, Na2F2, K2F2, LiNaF2, LiKF2, and NaKF2 are reported. The calculations use the Hartree-Fock-Roothaan method and second-order Moller-Plesset perturbation theory along with configuration interaction theory including singly and doubly excited configurations and corrections for quartic excitations with basis sets of grouped Gaussian functions: Li — (9s3p1d/4s3p1d), Na — (12s8p1d/6s4p1d), K — (14s11p3d/9s8p3d), F — (9s5p1d/4s2p1d). According to the results of calculations, the equilibrium structures of the molecules are planar cyclic structures of D2h (for M2F2) and C2v (for MM′F2) symmetries. The linear configurations M-F-M′-F (of C∞v symmetry) are 70–190 kJ/mole less stable than the cyclic ones; for all molecules except M-F-K-F, these configurations correspond to local minima on the potential energy surface. The role of correlation effects in ab initio calculations of the geometry, force fields, and IR characteristics of molecules with highly polar chemical bonds is discussed. The theoretical force fields of the molecules are represented in canonical form in a system of redundant natural vibrational coordinates. The force fields of MM′F2 molecules are studied. The results of the ab initio calculations are compared with the experimental structural data and vibrational spectra available in the literature.

The geometrical structure, force fields, and vibrational spectra of the ClO 3 − ion and LiClO3, NaClO3, and KClO3 molecules are studied using the Hartree-Fock (HF) method and second-order Moller-Plesset (MP2) perturbation theory in double-zeta basis sets complemented with polarization and diffuse functions. Routes of intramolecular rearrangements corresponding to migration of the M+ cations around the ClO 3 − anion are investigated. The calculations showed that the molecular structure of alkaline metal chlorates changes in the series LiClO3 → NaClO3 → KClO3. The LiClO3 molecule has an essentially bidentate configuration of Cs symmetry; the KClO3 molecule has tridentate coordination of C3v symmetry. The NaClO3 molecule exists as two isomeric forms having similar energies: tridentate (C3v) and bidentate (Cs) forms separated by a low potential barrier (199 cm−1 − HF, 170 cm−1 − MP2); the energy differences between the isomers are ΔE(Cs − C3v)=−0.5 (HF), 0.4 kJ/mole (MP2). The theoretical vibrational spectra of molecules agree with the available experimental data.

The geometrical structure and the vibrational spectrum of the LiClO3 molecule are studied by the Hartree-Fock-Roothaan (HF) and configurational interaction (CI) methods taking into account single and double excitations and Davidson's correction for quadruple excitations. Double-zeta basis sets of Huzinaga-Dunning and McLean-Chandler complemented with polarization and diffuse functions are used. Potential surface sections corresponding to migration of the Li+ cation around the ClO 3 − fragment are investigated. It was found that the LiClO3 molecule has a single stable configuration of Cs symmetry with the bidentate coordination of the Li+ cation by the ClO 3 − anion. The cyclic fragment Open image in new window is nonplanar (the dihedral angle θ(LiO2Cl)=173°). The tridentate configuration of C3v symmetry lies higher than the equilibrium configuration by 24.5 (HF) or 18.3 (CI) kJ/mole and is not an isomer. The ab initio force field of the molecule was refined by the scaling method. Some assignments of the IR bands of the matrix-isolated molecular forms existing in vapor over lithium chlorate are corrected. The vibration frequencies (cm−1) and IR intensities (km/mole; in parentheses) are calculated with the refined force field: A′ type 1099(236), 856(81), 630(73), 557(119), 481(87), 156(66); A″ type 887(229), 459(35), 367(23).

The Gravity Probe B mission provided two new quantitative tests of Einstein's theory of gravity, general relativity (GR), by cryogenic gyroscopes in Earth's orbit. Data from four gyroscopes gave a geodetic drift-rate of −6601.8 ± 18.3 marc-s yr−1 and a frame-dragging of −37.2 ± 7.2 marc-s yr−1, to be compared with GR predictions of −6606.1 and −39.2 marc-s yr−1 (1 marc-s = 4.848 × 10−9 radians). The present paper introduces the science, engineering, data analysis, and heritage of Gravity Probe B, detailed in the accompanying 20 CQG papers.

The results of the Gravity Probe B relativity science mission published in Everitt et al (2011 Phys. Rev. Lett. 106 221101) required a rather sophisticated analysis of experimental data due to several unexpected complications discovered on-orbit. We give a detailed description of the Gravity Probe B data reduction. In the first paper (Silbergleit et al Class. Quantum Grav. 22 224018) we derived the measurement models, i.e., mathematical expressions for all the signals to analyze. In the third paper (Conklin et al Class. Quantum Grav. 22 224020) we explain the estimation algorithms and their program implementation, and discuss the experiment results obtained through data reduction. This paper deals with the science data preparation for the main analysis yielding the relativistic drift estimates.

Gravity Probe B, launched 20 April 2004, is a space experiment testing two fundamental predictions of Einstein's theory of general relativity (GR), the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Data collection started 28 August 2004 and ended 14 August 2005. Analysis of the data from all four gyroscopes results in a geodetic drift rate of $\ensuremath{-}6601.8\ifmmode\pm\else\textpm\fi{}18.3\text{ }\text{ }\mathrm{mas}/\mathrm{yr}$ and a frame-dragging drift rate of $\ensuremath{-}37.2\ifmmode\pm\else\textpm\fi{}7.2\text{ }\text{ }\mathrm{mas}/\mathrm{yr}$, to be compared with the GR predictions of $\ensuremath{-}6606.1\text{ }\text{ }\mathrm{mas}/\mathrm{yr}$ and $\ensuremath{-}39.2\text{ }\text{ }\mathrm{mas}/\mathrm{yr}$, respectively (``mas'' is milliarcsecond; $1\text{ }\text{ }\mathrm{mas}=4.848\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\text{ }\text{ }\mathrm{rad}$).

The special features of the potential-energy surface (PES) and the paths for the intramolecular rearrangements of the Li2CO2 molecule have been investigated by the SCF method in the double-zeta Huzinaga—Dunning basis supplemented by d-type polarization functions in the carbon and oxygen atoms (DZ + P). It has been shown that there are two minima, which correspond to Cs and C2ν structures, on the PES of the molcule. All the remaining structures of the molecule considered either correspond to saddle points or do not represent special points on the PES at all. The force constants, vibrational frequencies, and intensities of the vibrational transitions in the IR spectra have been calculated for both isomers in the DZ basis. The theoretical values of the vibrational frequencies and the isotope shifts are in good agreement with the experimental data obtained with matrix isolation: the mean deviation of the scaled theoretical frequencies for the Cs isomer amounts to 13 cm−1 or 1.6%. An analysis of the Mulliken populations, as well as a comparison of the geometric parameters and force constants of the isomers of Li2CO2 with the corresponding parameters of the Li2O and CO molecules and of the CO22− ion, have shown that the chemical bonds in both isomers may be represented by the scheme (Li+)2CO22−. The similarity between the PES's of the Li2CO2 and Li2CO3 molecules has been demonstrated and explained in the framework of the Gillespie—Nyholm model.

Gravity Probe B (GP-B) is a landmark physics experiment in space designed to yield precise tests of two fundamental predictions of Einstein's theory of general relativity, the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Launched on 20 April 2004, data collection began on 28 August 2004 and science operations were completed on 29 September 2005 upon liquid helium depletion. During the course of the experiment, two unexpected and mutually-reinforcing complications were discovered: (1) larger than expected 'misalignment' torques on the gyroscopes producing classical drifts larger than the relativity effects under study and (2) a damped polhode oscillation that complicated the calibration of the instrument's scale factor against the aberration of starlight. Steady progress through 2006 and 2007 established the methods for treating both problems; in particular, an extended effort from January 2007 on 'trapped flux mapping' led in August 2007 to a dramatic breakthrough, resulting in a factor of ~20 reduction in data scatter. This paper reports results up to November 2007. Detailed investigation of a central 85-day segment of the data has yielded robust measurements of both relativity effects. Expansion to the complete science data set, along with anticipated improvements in modeling and in the treatment of systematic errors may be expected to yield a 3–6% determination of the frame-dragging effect.

The Hartree-Fock-Roothaan method has been used in a two-exponential basis with and without the inclusion of polarization defunctions on the nitrogen and oxygen atoms to calculate the geometry and the vibrational characteristics of the free NO2 ion and the LiNO2 molecule. The results are compared with published data as regards the nitrite ion and the alkali-metal nitrites. The parameters of the LiO2N rings in LiNO3 and LiNO2 are compared. A study has been made of the effects of the polarization defunctions on the calculated parameters of NO2 and LiNO2. The rigid rotor-harmonic oscillator approximation has been used to calculate the thermodynamic parameters of LiNO2 in the ideal-gas state.

Nonempirical calculations of the equilibrium geometric parameters, force constants, barriers to intramolecular rearrangements, frequencies of normal modes of vibrations, dipole moments, and intensities of vibrations in the IR spectra have been carried out for the Be2O2, Mg2O2, Mg(OH)2, and FMgOH molecules by the MO-LCAO-SCF method with the use of expanded double-zeta basis sets of Gaussian functions supplemented by polarization functions on all the atoms. An analysis of the Mulliken populations has been conducted. It has been found that the equilibrium structures of the Be2O2 and Mg2O2 molecules are planar rings $$\left( {{\text{D}}_{{\text{2}}_{\text{h}} } } \right)$$ , that Mg(OH)2 is characterized by a planar configuration (of C2h symmetry) with a linear O-Mg-O fragment and with OH bonds in trans positions, and that FMgOH has a linear configuration (C∞v). The results of the calculations attest to the occurrence of practically free rotation of the OH groups relative to the O-Mg-O skeleton in magnesium hydroxide. The form of the deformation potential of the Mg-O-H angles in Mg(OH)2 and FMgOH is significantly dependent on the completeness of the basis set used. A comparative analysis of the properties of the molecules under consideration and of isoelectronic compounds of group I and group II metals has been performed.