Structures and vibrational spectra of SO(n)(p-) sulfur oxides, MSO(n)(-) anions, and MSO(n), M2SO(n) salts in the gas phase (n = 1-3; p = 0-2; M = Li, Na, K). A density functional theory study.

This theoretical study focuses on geometries, vibrational spectra, charge distributions, electron affinities, and reaction energies for SO(n)(p-) anions and alkali salts MSO(n)(-), M(1,2)SO(n) in the gas phase (n = 1-3; p = 0-2; M = Li-K). Most of our data for compounds with the S oxidation states 0, 2, and 4 are new in the literature. The bulk of the results are obtained at the B3PW91 level, with CCSD(T)=FC calculations carried out for relative energy calibrations; the 6-311+G(3df) basis set is used throughout. The formation of contact ion pairs is prevalent; they are of type: (i) M(+)(SO(n)(-)) for the π-radicals MSO, MSO(2), MSO(3) of doublet multiplicity; (ii) (M(+))(2)(SO(n)(2-)) for M(2)SO, M(2)SO(2), M(2)SO(3) in their singlet ground states; and (iii) M(ns)(SO(n)(-)) for the radicals MSO(-), MSO(2)(-), MSO(3)(-) in their triplet states. When isolated in matrices, M(2)SO and M(2)SO(2) will facilitate the spectroscopic study of the little known SO(2-) and SO(2)(2-) ions. Divalent M(2)SO(n) salts, due to their large dipole moments, should be highly soluble in polar solvents, first dissociating into MSO(n)(-) + M(+) products. For MSO(3), bidentate coordination OS(O(2)M) is preferred over tridentate S(O(3)M) binding. We confirm that all MSO(2) molecules are planar, at variance with an ESR study assigning to NaSO(2) a nonplanar structure. This study partially support the assignment of an experimental frequency at 918.2 cm(-1) (932 cm(-1), calculated) to the antisymmetric ν(a)(SO) mode of the elusive sulfoxilate ion, SO(2)(2-). A definitive identification, however, would require to record the vibrational spectrum below 800 cm(-1) (apparently not done in the original work) because the missing symmetric ν(s)(SO) mode is here found to lie around 760 cm(-1), exhibiting high intensity in both IR and Raman spectra.

Evidence for [18-Crown-6 Na]2[S2O4] in methanol and dissociation to Na2S2O4 and 18-Crown-6 in the solid state; accounting for the scarcity of simple oxy dianion salts of alkali metal crown ethers in the solid state.

[18-Crown-6 Na](2)S(2)O(4) complex was prepared in methanol solution but dissociates into 18-Crown-6 ((s)) and Na(2)S(2)O(4 (s)) on removal of the solvent. Evidence for complexation in methanol is supported by a quantitative mass analysis and the dissociation in the solid state by vibrational spectroscopy and powder X-ray diffraction. These observations are accounted for by investigating the energetics of complexation in solution and dissociation in the solid state using calculated density functional theory (DFT) gas phase binding enthalpies and free energies combined with conductor-like screening model (COSMO) solvation energies and lattice enthalpy and free energy terms derived from volume based thermodynamics (VBT). Our calculations show that complexation of alkali metal dianion salts to crown ethers are much less favorable than that of the corresponding monoanion salts in the solid state and that the formation of alkali metal crown complexes of stable simple oxy-dianion (e.g., CO(3)(2-), SO(4)(2-)) salts is unlikely. The roles of complexation with 18-Crown-6 and ion pair formation in the process of dissolution of Na(2)S(2)O(4) to methanol are discussed.

Axial asymmetry of the charge- and spin-density distributions in Pi states. Molecular quadrupole moments and hyperfine coupling constants of CH, NH, OH, CF, LiO, NO, and FO.

The axial asymmetry of the charge- and spin-density distributions in Pi states is studied via second-rank traceless tensors P(ii) (ii = xx, yy, zz), namely, quadrupole moments (Theta(ii)), electric field gradients (q(ii)), and magnetic dipolar (T(ii)) hyperfine coupling constants (hfcc's). In linear molecules, it holds that P(xx) does not = P(yy) does not = P(zz) for Pi, but P(xx) = P(yy) does not = P(zz) for Sigma, Delta, Phi,..., states. Thus, traceless P(ii) in Pi states have two independent parameters, P(parallel) = P(zz) is proportional to [r(m)(3 cos2 theta - 1] and deltaP(perpendicular) = |P(xx) - P(yy)| is proportional to [r(m) sin2 theta], with m = 2(Theta(ii)) or -3(q(ii), T(ii)). All linear states have P(parallel) does not = 0, but only Pi states exhibit deltaP(perpendicular) does not = 0, as shown by hfcc's like c = (3/2)T(zz), and d = |T(xx) - T(yy)|, as well as q0 = (-q(zz)) and |q(2)/2| = |q(xx) - q(yy)|. Little is known about Theta(zz) and deltaTheta(perpendicular) = |Theta(xx) - Theta(yy)| in Pi states since most experimental values (gas-phase) are rotational averages, and several theoretical studies have reported Theta(zz) but assumed deltaTheta(perpendicular) = 0. The diatomics studied here have X2Pi(1/2)(pi1) ground states, like CH and NO, or are of type X2Pi(3/2)(pi3), like OH, CF, LiO, and FO. The A3Pi(sigma pi3) state of NH is also included. Our P(parallel) and deltaP(perpendicular) values--calculated at the experimental R(e)'s with the B3LYP/aug-cc-pVQZ method--reproduce well the available literature data. The properties of the CF and FO radicals are not well-known so that our {c, d} and {q0, q2} values should help future experimental studies of their hyperfine spectra. Excluding OH, the complete quadrupole sets {Theta(zz), deltaTheta(perpendicular)} are new for all species discussed here. For comparison purposes, Theta(zz) of a low-lying Sigma state is also calculated for each X2Pi radical.

Quadrupole, octopole, and hexadecapole electric moments of Sigma, Pi, Delta, and Phi electronic states: cylindrically asymmetric charge density distributions in linear molecules with nonzero electronic angular momentum.

The number of independent components, n, of traceless electric 2(l)-multipole moments is determined for C(infinity v) molecules in Sigma(+/-), Pi, Delta, and Phi electronic states (Lambda=0,1,2,3). Each 2(l) pole is defined by a rank-l irreducible tensor with (2l+1) components P(m)((l)) proportional to the solid spherical harmonic r(l)Y(m)(l)(theta,phi). Here we focus our attention on 2(l) poles with l=2,3,4 (quadrupole Theta, octopole Omega, and hexadecapole Phi). An important conclusion of this study is that n can be 1 or 2 depending on both the multipole rank l and state quantum number Lambda. For Sigma(+/-)(Lambda=0) states, all 2(l) poles have one independent parameter (n=1). For spatially degenerate states--Pi, Delta, and Phi (Lambda=1,2,3)--the general rule reads n=1 for l<2/Lambda/ (when the 2(l)-pole rank lies below 2/Lambda/ but n=2 for higher 2(l) poles with l>or=2/Lambda/. The second nonzero term is the off-diagonal matrix element [formula: see text]. Thus, a Pi(Lambda=1) state has one dipole (mu(z)) but two independent 2(l) poles for l>or=2--starting with the quadrupole [Theta(zz),(Theta(xx)-Theta(yy))]. A Delta(Lambda=2) state has n=1 for 2((1,2,3)) poles (mu(z),Theta(zz),Omega(zzz)) but n=2 for higher 2((l>or=4)) poles--from the hexadecapole Phi up. For Phi(Lambda=3) states, it holds that n=1 for 2(1) to 2(5) poles but n=2 for all 2((l>or=6)) poles. In short, what is usually stated in the literature--that n=1 for all possible 2(l) poles of linear molecules--only applies to Sigma(+/-) states. For degenerate states with n=2, all Cartesian 2(l)-pole components (l>or=2/Lambda/) can be expressed as linear combinations of two irreducible multipoles, P(m=0)((l)) and P/m/=2 Lambda)((l)) [parallel (z axis) and anisotropy (xy plane)]. Our predictions are exemplified by the Theta, Omega, and Phi moments calculated for Lambda=0-3 states of selected diatomics (in parentheses): X (2)Sigma(+)(CN), X (2)Pi(NO), a (3)Pi(u)(C(2)), X (2)Delta(NiH), X (3)Delta(TiO), X (3)Phi(CoF), and X (4)Phi(TiF). States of Pi symmetry are most affected by the deviation from axial symmetry.

Theoretical studies on dications and trications of FH, ClH, and BrH. Properties of the bound 1(5)sigma- states. Electron-spin g-factors and fine/hyperfine constants of the metastable X3Sigma- states of ClH2+ and BrH2+.

This theoretical study reports calculations on the fine and hyperfine structure parameters of the metastable X(3)Sigma(-)(sigma(2)pi(2)) state of ClH(2+) and BrH(2+). Data on the repulsive FH(2+) system are also included for comparison purposes. The hyperfine structure (hfs) coupling constants for magnetic (A(iso), A(dip)) and quadrupole (eQq) interactions are evaluated using B3LYP, MP4SDQ, CCSD, and QCISD methods and several basis sets. The fine structure (fs) constants (zero-field splitting lambda and spin-rotation coupling gamma) and electron-spin magnetic moments (g-factor) are evaluated in 2nd-order perturbation theory using multireference CI (MRCI) wave functions. Our calculations find for (35)Cl of ClH(2+) A(iso)/A(dip) = 110/-86 MHz; eQq(0) = -59 MHz; 2lambda = 20.4 cm(-1); g( perpendicular)(v = 0) = 2.02217; and gamma = -0.31 cm(-1) (to be compared with the available experimental A(iso)/A(dip)= 162/-30 MHz). For (79)BrH(2+), the corresponding values are 300/-400 MHz; 368 MHz; 362.6 cm(-1); 2.07302; and -0.98 cm(-1) (experimental 2lambda = 445(+/-80) cm(-1)). We find g( perpendicular)(ClH(2+)) to increase by about 0.0054 between v = 0 and 2, whereas the experimental effective g( perpendicular) changes drastically with vibrational excitation. Nuclear quadrupole coupling constants for halogen atoms X are found to be as large as corresponding A(dip)(X)'s, indicating that both terms may have to be included in the Hamiltonian used to interpret XH(2+) hyperfine spectra. A novel finding relates to the bound character of the 1(5)Sigma(-)(sigmapi(2)sigma) state in FH(2+), as already known for ClH(2+) and BrH(2+), but having a deeper potential well D(e) approximately 4,000 cm(-1) (versus 1,000 cm(-1) in the heavier radicals). Vertical ionization potentials for formation of XH(3+) trications are also discussed.