Stark effect,polarizabilities and the electric dipole moment of heteronuclear diatomic molecules in 1Σ states

The theory of second-order Stark effect in ¹Σ states of heteronuclear diatomic molecules is thoroughly reviewed. The rigorous treatment given demonstrates that by introducing rotational, vibrational and electronic branch polarizabilities, the intrinsic character of the second-order Stark effect in diatomic molecules can be shown to be related more closely to polarizabilities than to dipole moments. The well-known expression for the Stark shift in ¹Σ levels which is dominated by the square of the dipole moment is only a crude, though sufficient approximation whenever large dipole moments are involved. For small dipole moments, however, this approximation is likely to fail, leading to an erroneous determination of such dipole moments. In the limiting case of negligible influence of the molecular rotation on the vibronic matrix elements, the arithmetic mean of the electronic branch polarizabilities turns out to be equal to the well-known static electronic polarizabilities α_∥ and α_⊥. The results are applied to the interpretation of the Stark splitting in the A¹Σ⁺, υ′ = 5, J′ = 1 level of ⁷LiH, recently determined by Stark quantum-beat spectroscopy.     

Theoretical description of nuclear quadrupole coupling in light diatomic molecules

A practical procedure for calculation of nuclear quadrupole coupling constants for light diatomic molecules is discussed. The procedure is based on a molecular wave function that explicitly describes nuclear motion. The approach is capable of yielding quadrupole coupling constants for excited rovibrational levels of diatomic molecules in their ground and excited electronic states. An application of the procedure to the X¹Σ⁺_g and B¹Σ⁺_u states of HD and D₂ is presented.     

Single-determinantal open- and closed-shell FSGO calculations for some diatomic molecules

Open-shell single-determinantal calculations are reported here for the molecular species H₂, Li₂⁺, N₂, O₂ (triplet), O₂^2?;, O₂^?, O₂²⁺, O₂⁺, and F₂; corresponding closed-shell calculations are reported for the species H₂, N₂, O₂ (singlet), O₂^2?, O₂²⁺, and F₂. The floating spherical Gaussian orbital (FSGO ) method was employed. The calculated trend in bond lengths of isonucleic diatomic molecules is in agreement with experiment. For heteronucleic diatomic molecules, however, the experimental trend in bond lengths is not obtained; in this connection, the effect of lone pairs on bond length is discussed. The dissociation energies of H₂ and Li₂⁺ are evaluated. The energy gap between the triplet and singlet states of the oxygen molecule is calculated to be 8.96 eV compared to the experimental value of 4.54 eV.     

One-electron wavefunctions,dipole polarizabilities

Variational perturbation theory is used to calculate dipole polarizabilities for H⁺₂ as a function of internuclear separation. The variational polarizabilities are used to investigate the accuracy of semi-empirical formulae for computing upper and lower bounds.     

Cationic Complexes of Hydrogen with Helium

High‐resolution mass spectra of helium nanodroplets doped with hydrogen or deuterium reveal that copious amounts of helium can be bound to H⁺, H₂⁺, H₃⁺, and larger hydrogen‐cluster ions. All conceivable He_nH_x⁺ stoichiometries are identified if their mass is below the limit of ≈120 u set by the resolution of the spectrometer. Anomalies in the ion yields of He_nH_x⁺ for x=1, 2, or 3, and n≤30 reveal particularly stable cluster ions. Our results for He_nH₁⁺ are consistent with conclusions drawn from previous experimental and theoretical studies which were limited to smaller cluster ions. The He_nH₃⁺ series exhibits a pronounced anomaly at n=12 which was outside the reliable range of earlier experiments. Contrary to findings reported for other diatomic dopant molecules, the monomer ion (i.e. H₂⁺) retains helium with much greater efficiency than hydrogen‐cluster ions.     

Variational calculation of vibrational energies of triatomic molecules using SCF optimized modes

A self-consistent field optimization of the vibrational coordinates for nonlinear triatomic molecules is presented. The optimal coordinates are obtained by making a three-dimensional rotational transformation of the normal modes and determining the rotation angles as those for which the SCF energy is stationary. The utility of the optimized coordinates in full variational calculations of vibrational energies is studied for the molecules of H₂O, O₃, H₂D⁺, H₂T⁺, and D₂T⁺. For H₂O and O₃, the optimization procedure leads to the local mode representation. It is shown that the use of the optimal coordinates in variational calculations allows a large reduction of the dimension of the Hamiltonian matrix to be diagonalized in order to reach convergence.     

A correlation between polarizabilities and atomic and molecular dimensions

A method of correlating polarizability to the volume of atoms and molecules is proposed. This method can serve to predict atomic and mean molecular polarizabilities. The standard deviation for the group of the hydrogen halides is 0.02 and for the group of the homopolar diatomic molecules 0.05. The interpolated polarizability of the N₃ molecule was found to be 3.017 A³.     

Electron momentum density distribution in homonuclear diatomic molecules

Individual orbital contributions to the electron momentum densities of first-row homonuclear diatomic molecules are discussed. It is shown that the nodal surfaces in the orbital EMDs arise from a diffraction factor with both geometric and electronic components. The positions of the nodal surfaces convey information on the electronic structure. The results are illustrated with a Hartree-Fock-Slater calculation of the F₂(X¹Σ_g⁺) molecule.     

Ab initio calculation of the first order term of the intermolecular energy near the van der Waals minimum

The first order term of the intermolecular energies between two hydrogen molecules and between Li⁺ and H₂ has been computed by three different methods: two of them are based on a perturbative procedure, including or neglecting the overlap between the orbitals of the interacting molecules or atoms in the calculation of the electrostatic and exchange terms. We can then study the effect of the overlap on each of these terms. The third method is the SCF supermolecule treatment which provides results in very good agreement with the perturbative procedure including the overlap. TheT configuration in the case of two hydrogen molecules and theC _2v configuration for Li⁺+H₂ are stable with respect to the first order term.     

Structure and properties of H2CN,H2CC−, H2BO and H2CO+

Ab initio SCF—MO calculations are presented for H₂CN, H₂CC^?, H₂BO and H₂CO⁺, including geometry optimization. One-electron properties are presented and compared with experiment where possible, particularly ESR hyperfine data.     

Comparative analysis of the state of lithium and sodium atoms in water clusters

Structures and energetic characteristics of Li(H₂O) _n and Li⁺(H₂O) _n clusters with n = 1–6, 19, and 27 determined in the second order of the Møller-Plesset perturbation theory with 6–31++G(d,p) basis set are analyzed. The electron density redistribution, which takes place upon the electron addition to a Li⁺(H₂O) _n cluster, is found to be provided by hydrogen-bonded water molecules: initially almost neutral molecules, which are most distant from lithium, become negatively charged. The calculated energies of the electron capture by Li⁺(H₂O) _n clusters are approximated with the appropriate electrostatic model, and estimates of the lithium ionization energy in water clusters of various sizes are found. Similar estimates obtained earlier for sodium are made more accurate.     

Theoretical investigation of the structure and properties of H2B=NH2...Mn+, HB≡NH...Mn+, and Borazine...Mn+ complexes (M = Alkaline and Earth Alkaline Metals)

The nature of H₂B=NH₂...M ⁿ⁺, HB=NH...M ⁿ⁺, and Borazine...M ⁿ⁺ interactions were studied with ab-initio calculations. The interaction energies were calculated at B3LYP/6-31G(d, p) level. The calculations suggest that the size and charge of cation are two influential factors that affect the nature of interaction. The theory of atoms in molecules (AIM) and natural bond orbital (NBO) analysis of complexes indicate that the variation of densities and the extent of charge shifts upon complexation correlate well with the obtained interaction energies.     

The reactions of some interstellar ions with benzene,cyclopropane and cyclohexane

The reactions of the cyclic molecules C₆H₆ (benzene), c-C₃H₆ (cyclopropane) and c-C₆H₁₂ (cyclohexane) with ArH⁺ (ArD⁺), H₃⁺, N₂H⁺, CH₅⁺, HCO⁺, OCSH⁺, C₂H₃⁺, CS₂H⁺ and H₃O⁺ have been studied at 300 K using a SIFT apparatus. All the reactions except those of C₂H₃⁺ proceed via proton transfer and all are fast except the H₃O⁺ and CS₂H⁺ reactions with c-C₆H₁₂ which are endothermic and which establish that the proton affinity of c-C₆H₁₂ is 160 ± 1 kcal mol⁻¹, which is considerably lower than the published value. In the c-C₃H₆ and the c-C₆H₁₂ reactions multiple products are observed and hence “breakdown curves” for the protonated molecules are constructed and the appearance energies of the various ion products are consistent with available thermochemical data. The reactions of C₂H₃⁺ with these cyclic molecules are atypical within this series of reactions in that they appear to proceed largely via hydride ion transfer. The implications of the results of this study to interstellar chemistry are alluded to.     

Investigation of electron correlation on the theoretical prediction of zero-field splittings of 2Π molecular states

First-order ²Π zero-field splittings are computed for the H₂S⁺, BO, NO, CH, CO⁺ and OH ground electronic states by employing ab initio multi-configuration wavefunctions and by including all one-and two-electron spin-orbit interactions in a gaussian AO basis explicitly in the theoretical treatment.     

Quantum mechanical treatment of the collinear H+ + H2 system. The uncoupled system

A fully converged close coupling study is performed of the collinear (H⁺ + H₂) system on the lower potential energy surface. The surface is derived by the DIMZO (diatomic in molecules-zero overlap) method. Transition probabilities for the reactions: H⁺ + H₂ (ν = 0, 1) → H₂ (ν′) + H⁺; ν′ = 0,..., 7 are given for a number of total energies in the range from 1 eV to 3 eV. It is found that for this energy region the transition ν = 0 → ν′ = 0 is the most preferential. This fact leads us to believe that addition of the upper surface will have a minor effect on the calculated probabilities of transitions from ν = 0 in the above-mentioned energy range.     

The Optical Spectrum of Au2+

The electronic structure of the Au₂⁺ cation is essential for understanding its catalytic activity. We present the optical spectrum of mass-selected Au₂⁺ measured via photodissociation spectroscopy. Two vibrationally resolved band systems are observed in the 290–450 nm range (at ca. 440 and ca. 325 nm), which both exhibit rather irregular structure indicative of strong vibronic and spin-orbit coupling. The experimental spectra are compared to high-level quantum-chemical calculations at the CASSCF-MRCI level including spin-orbit coupling. The results demonstrate that the understanding of the electronic structure of this simple, seemingly H₂⁺-like diatomic molecular ion strictly requires multireference and relativistic treatment including spin-orbit effects. The calculations reveal that multiple electronic states contribute to each respective band system. It is shown that popular DFT methods completely fail to describe the complex vibronic pattern of this fundamental diatomic cation.     

A direct interaction between the H+-F1F0-ATPase and the K+ transport within the membrane of anaerobically grown bacteria

An N,N′-dicyclohexylcarbodiimide (DCCD) sensitive 2H⁺-K⁺ exchange with fixed stoichiometry is found in anaerobically grown bacteria and requires the F₁F₀-ATPase and the Trk or similar system. These are assumed to interact with each other directly within the membrane and to form a supercomplex, functioning as an H⁺-K⁺ pump. The findings of reversal of 2H⁺-K⁺ exchange to drive coupled synthesis of ATP as well as of DCCD-sensitive ATPase activity stimulated by K⁺ have confirmed such a “supercomplex model” for the H⁺-K⁺ pump. The phenomenon is absent in bacterial grown anaerobically in the presence of nitrate or aerobically. Under these conditions these transport systems are assumed to operate separately and the Trk or similar system works as an ionophore. Conditions have been studied under which the F₁F₀-ATPase and the Trk or similar system work cooperatively as a supercomplex with local transduction of energy, or separately via energetic mediation by Δμ_H, the transmembranedifference in transport systems within the membrane without mediation by Δμ_H during low effective energetic processes (glycolysis) may be carried out by dithiol-disulphide interchange. A source of reducing equivalents and/or Δμ_H is required. Direct interaction between transport systems with formation of supercomplexes for regulation of cell metabolism could be a general feature among membrane proteins in bacteria.     

In cation interactions with some organics: ab initio molecular orbital and density functional theory

Ab initio molecular orbital and density functional theory studies were undertaken to investigate the structural and energetic characteristics of complexes of In⁺ with several different organic molecules for the first time. HF, MP2, QCISD, and CCD levels of theory in ab initio MO as well as B3LYP, B3PW91 hybrid functionals in density functional theory were used. A valence TZ+P basis set with relativistic effective core potentials was used for the In atom while the 6-311++G(3d, 2p) basis set was utilized for all other atoms. Both closed-shell (H₂O, CH₄, CH₃OH, and C₆H₆) and open-shell (CH₃ and C₂H₃) molecules were considered for complexation with In⁺. In⁺ affinities of 21.5, 24.8, 28.6, 18.4, and 23.0 kcal/mol were obtained with the B3PW91 hybrid functional for H₂O, CH₃OH, C₆H₆, CH₃, and C₂H₃, respectively. The large values for the calculated affinities indicate the validity of our recent experimental detection of In⁺ ion attachment to some organic molecules.     

Correlated polarization propagator calculations of static polarizabilities

We present a systematic comparison of the correlation contribution at the level of the second-order polarization propagator approximation (SOPPA ) and MP 2 to the static dipole polarizability of (1) Be, BeH^?, BH, CH⁺, MgH^?, AIH, SiH⁺, and GeH⁺; (2) BH₃, CH₄, NH₃, H₂O, HF, BF, and F₂; and (3) N₂, CO, CN^?, HCN, C₂H₂, and HCHO . Fairly extended basis sets were used in the calculations. We find that the agreement with experimental values is improved in SOPPA and MP .2 over the results at the SCF level. The signs and magnitudes of the correlation contribution in SOPPA are similar to those obtained in analytical derivative MP 2 calculations. However, it is not possible to say, in general, which method gives the largest correlation contribution or the best agreement with experiment, nor is it possible to make a priori prediction of the sign of the correlation contribution. For the first group of molecules, which have a quasi-degenerate ground state, additional CCDPPA and CCSDPPA calculations were performed and compared with polarizabilities obtained as analytical/numerical derivatives of the CCD and CCSD energies. The CCSDPPA results were found to be in better agreement with other calculations than were the SOPPA results, demonstrating the necessity of using methods based on infinite-order perturbation theory for these systems. © 1994 John Wiley & Sons, Inc.