An empirical potential for the O-H·O Hydrogen bond: Part I. Comparison with ab initio molecular orbital results

An empirical potential energy function has been devised for the O-H·O hydrogen bond, for use with the MMI force field. The energy of the hydrogen bond is described as the sum of van der Waals, electrostatic and Morse components. The function has been used to calculate the potential energy hypersurface of the water dimer, and the results are compared with published ab initio molecular orbital studies. Satisfactory agreement is obtained except for orientations involving very short H·H contacts. The geometry and hydrogen bond energy of the equilibrium linear form of (H₂O)₂ are calculated to be r(O·O) = 2.84 Å, θ = 36°, ΔE = ?5.35 kcal mol^?1, which are close to the values obtained by experiment, and from molecular orbital calculations. The relative importance of the electrostatic component of the empirical hydrogen bond energy is consistent with molecular orbital energy decomposition studies. The empirical function has also been used to calculate the energy of the water trimer in orientations which serve as models for the crystallographic bifurcated hydrogen bond. The results indicate that, in these orientations, the trimer is typically 0–3 kcal mol^?1 more stable than the dimer, a result which is consistent with ab initio calculations.     

He2分子b3∏g(v=9)态的预解离

The predissociation of the v=9 level in the b³Π_g state by the c³∑_g⁺ state of helium eximer(He₂) was studied based on the newly observed (9, 3) band in the b³Π_g-a³∑_u⁺ system inthe region of 12065～12445 cm^-1 employing optical heterodyne-concentration modulationabsorption spectroscopy. With the help of the previous potential energy curves and molecular constants of He₂, the corresponding predissociation mechanism for the b³Π_g (v=9) state was analyzed. An RKR potential energy curve of b³Π_g and an ab initio potential curve of c³∑_g⁺ were used to calculate the predissociation linewidths that show basic agreement withobservations, which can quantitatively explain the experiments.     

Applicability of multireference many-body perturbation theory to the Ne2+ molecule

The ground state as well as some low-lying excited states of the Ne₂⁺ molecule are calculated by means of the third-order multireference many-body perturbation theory with the “full” eight-orbital valence space using DZP and polarized valence TZ basis sets. The problem encountered with a large number of valence electrons is avoided by a proper definition of the Fermi vacuum. The calculated equilibrium distance of 1.721 Å and chemical dissociation energy D₀ = 1.283 eV are in good agreement with experimental results. A comparison with other ab initio techniques is also provided. © 1997 John Wiley & Sons, Inc.     

An ab initio calculation of the molecular structure and properties of hypofluorous acid

An ab initio LCAO MO SCF calculation has been carried out on hypofluorous acid (HOF) in order to study the electronic structure, geometry and other one-electron properties of this molecule. The minimum energy geometry was found to be R_OF = 1.450 Å, R_OH = 1.080 Å, and θ = 100.8°, which is in good agreement with experiment. In general, the bonds in HOF appear to be similar to the analogous bonds in H₂O and F₂O. The first three ionization potentials 13.97, 14.94, and 17.16 eV compare well with recent photoelectron spectroscopic data.     

Does He2 Exist?

For the electronic ground state X ¹Σ⁺_g, the potential-energy function of He₂ reported by Aziz et al. has been transformed into the form V(z), containing only eight parameters, which is more suitable for the investigation of the existence of states of discrete energy. We found no evidence that a bound vibration-rotational state of the stable diatomic molecule ³He₂ or ⁴He₂, even if rotating, can exist in the electronic ground state.     

A diatomics-in-molecules model for singly-ionized argon clusters

A DIM model using ab initio input for the diatomic interactions predicts a collinear bound Ar₃ ⁺ molecule (in agreement with ab initio calculations) and stable clusters Ar_n ⁺ consisting of an Ar₃ ⁺ ion embedded in (n?3) neutral atoms. These results support existing theories that dynamical size selection may be more relevant in interpreting experimental results than the relative stabilities of clusters in their minimum energy configurations.     

A theoretical study of the hydration of Rb+ by Monte Carlo simulations with refined ab initio-based model potentials

An infinitely diluted aqueous solution of Rb⁺ was studied using ab initio-based model potentials in classical Monte Carlo simulations to describe its structural and thermodynamic features. An existing flexible and polarizable model [Saint-Martin et al. in J Chem Phys 113(24) 10899, 2000] was used for water–water interactions, and the parameters of the Rb⁺–water potential were fitted to reproduce the polarizability of the cation and a sample of ab initio pair interaction energies. It was necessary to calibrate the basis set to be employed as a reference, which resulted in a new determination of the complete basis set (CBS) limit energy of the optimal Rb⁺–OH₂ configuration. Good agreement was found for the values produced by the model with ab initio calculations of three- and four-body nonadditive contributions to the energy, as well as with ab initio and experimental data for the energies, the enthalpies and the geometric parameters of Rb⁺(H₂O) _n clusters, with n = 1,  2,…, 8. Thus validated, the potential was used for simulations of the aqueous solution with three versions of the MCDHO water model; this allowed to assess the relative importance of including flexibility and polarizability in the molecular model. In agreement with experimental data, the Rb⁺–O radial distribution function (RDF) showed three maxima, and hence three hydration shells. The average coordination number was found to be 6.9, with a broad distribution from 4 to 12. The dipole moment of the water molecules in the first hydration shell was tilted to 55° with respect to the ion’s electric field and had a lower value than the average in bulk water; this latter value was recovered at the second shell. The use of the nonpolarizable version of the MCDHO water model resulted in an enhanced alignment to the ion’s electric field, not only in the first, but also in the second hydration shell. The hydration enthalpy was determined from the numerical simulation, taking into account corrections to the interfacial potential and to the spurious effects due to the periodicity imposed by the Ewald sums; the resulting value lied within the range of the various different experimental data. An analysis of the interaction energies between the ion and the water molecules in the different hydration shells and the bulk showed the same partition of the hydration enthalpy as for K⁺. The reason for this similarity is that at distances longer than 3 Å, the ion–water interaction is dominated by the charge-(enhanced) dipole term. Thus, it was concluded that starting at K⁺, the hydration properties of the heavier alkali metal cations should be very similar.     

Ab initio calculations of relativistic and electron correlation effects in polyatomics using the universal Gaussian basis set: XeF2

Ab initio accurate all-electron relativistic molecular orbital Dirac–Fock self-consistent field calculations are reported for the linear symmetric XeF₂ molecule at various internuclear distances with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree–Fock calculations were also performed for XeF₂ at various internuclear distances. The relativistic correction to the electronic energy of XeF₂ was calculated as ～ ?215 hartrees (?5850 eV) by using the Dirac–Fock method. The dominant magnetic part of the Breit interaction correction to the nonrelativistic interelectron Coulomb repulsion was included in our calculations by both the Dirac–Fock–Breit self-consistent field and perturbation methods. The calculated Breit correction is ～6.5 hartrees (177 eV) for XeF₂. The relativistic Dirac–Fock as well as the nonrelativistic HF wave functions predict XeF₂ to be unbound, due to neglect of electron correlation effects. These effects were incorporated for XeF₂ by using various ab initio post Hartree–Fock methods. The calculated dissociation energy obtained using the MP 2(full) method with our extensive basis set of 313 primitive Gaussians that included d and f polarization functions on Xe and F is 2.77 eV, whereas the experimental dissociation energy is 2.78 eV. The calculated correlation energy is ～ ?2 hartrees (?54 eV) at the predicted internuclear distance of 1.986 Å, which is in excellent agreement with the experimental Xe—F distance of 1.979 Å in XeF₂. In summary, electron correlation effects must be included in accurate ab initio calculations since it has been shown here that their inclusion is crucial for obtaining theoretical dissociation energy (D_e) close to experimental value for XeF₂. Furthermore, relativistic effects have been shown to make an extremely significant contribution to the total energy and orbital binding energies of XeF₂. © 1995 John Wiley & Sons, Inc.     

Potential energy curves of several excited states of the Ne2* excimer: Assignment of the transient absorption spectra of the excimer

Most of the excited states of Ne₂, which are correlated with the Rydberg state transitions 2p → 3s, 3p, and 4s of Ne, are studied by ab initio CI calculations. Two transient absorption spectra from the lowest excimer state Σ_u⁺ recently observed by Arai et al., are discussed on the basis of calculated potential energy curves. Possible assignments are presented. The calculated transition energies are in good agreement with the observed ones.     

Highly accurate relativistic universal Gaussian basis set for Dirac–Fock–Breit calculations

Ion mobilities of H₂O⁺ drifting in helium are calculated and compared with experiment. These calculations employ global potential energy surfaces of the H₂O⁺–He complex, which in the present case were calculated ab initio at the unrestricted MP2 level of theory using a basis set of aug‐cc‐pVTZ quality, and treating the ion as a rigid body. Details are presented of the general characteristics of both the ground and first‐excited electronic states of the complex. Although only the ground‐state surface was used for the mobility calculations, the ab initio determination of the ground state necessitated the inclusion of the first‐excited state owing to the presence of a crossing between the two. This crossing is also described. Mobilities calculated from the global surfaces are in good agreement with experiment. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Calculation of the ground‐state energy and studies of other properties of exotic helium atoms with the use of boundary conditions of wave function

The minimum energy and average distance between particles of doubly muonic helium atoms Heμμ (He²⁺ + 2μ ), are calculated with the use of a wave function that satisfies boundary conditions such as the behavior of the wave function when two particles are close to each other or far away from each other. In this wave function, the muon–muon correlation in doubly muonic helium atoms is described to arrive at the correct behavior for r₁₂ tending to zero and infinity. It is shown that the obtained results are very close to the values calculated by others. Finally, to confirm the method and results, calculated values are compared with a similar electronic system, and it is shown that the small differences in the energies of Heμμ and He are due to the reduced masses, as expected. In addition to being very simple, the proposed wave function provides relatively accurate values for the energy and expectation values of r²ⁿ, emphasizing the importance of the local properties of the wave functions. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

CAS SCF/CI calculations of potential energy surfaces of He3+ and He2+

Complete active space MC SCF (CAS SCF) calculations followed by second-order configuration interaction (SOCI) calculations are carried out on the potential energy surfaces (bending surface, linear surfaces) of the ²Σ_g⁺ ground state of He₃⁺. The potential minimum for the ²Σ_g⁺ state occurs at a linear geometry with HeHe bond length of 1.248 Å. The binding energy of He₃⁺ with respect to He + He⁺ + He was calculated to be 2.47 eV at the SOCI level. The energy required to dissociate He₃⁺ (²Σ_g⁺) into He₂⁺ (²Σ_u⁺) and He(¹S) is calculated to be 0.14 eV. The same level of SOCI calculations of He₂⁺ yield a D_e value of 2.36 eV.     

An ab initio potential energy surface and spectroscopic constants for the XΣg state of NO2

A three-dimensional potential energy function has been calculated for the X¹Σ⁺_g state of NO⁺₂ from ab initio MRD-CI data. With this PE function, converged vibrational calculations have also been performed for ten vibrational states, with the aid of a computer program developed in the present work for this purpose. The calculated harmonic frequencies, vibrational term values and rotational constants are in good agreement with experimental data.     

Sensitivity of the H + CH3 → CH4 recombination rate constant to the shape of the CH stretching potential

Using a potential-energy surface obtained in part from ab initio calculations, the H + CH₃ → CH₄ bimolecular rate constant at T = 300 K is determined from a Monte Carlo classical trajectory study. Representing the CH stretching potential with a standard Morse function instead ofthe ab initio curve increases the calculated rate constant by an order of magnitude. The experimental recombination rate constant is intermediate of the rate constants calculated with the Morse and ab initio stretching potentials.Two properties of the H + CH₃ α CH₄ potential-energy surface which significantly affect the recombination rate constant are the shape of the CH stretching potential and the attenuation of the H₃CH bending frequencies. Ab initio calculations with a hierarchy of basis sets and treatment of electron correlation indicate the latter is properly described [13]. The exact shape of the CH stretching potential is not delineated by the ab initio calculations, since the ab initio calculations are not converged for bond lengths of 2.0–3.0 Å [12]. However, the form of this stretching potential deduced from the highest-level ab initio calculations, and fit analytically by eq. (2), is significantly different from a Morse function. The experimental recombination rate constant is intermediate of the rate constants calculated with the Morse and ab initio CH stretching potentials. This indicates that the actual CH potential energy curve lies between the Morse and ab initio curves. This is consistent with the finding that potential energy curves for diatomics are not well described by a Morse function [12].     

The structure of the H3O+ (hydronium) ion

Near Hartree-Fock level ab initio molecular orbital calculations on H₃O⁺ and a minimum energy structure with θ(HOH) = 112.5° and r(OH) = 0.963 Å and an inversion barrier of 1.9 kcal/mole. By comparing these results to calculations on NH₃ and H₂O, where precise experimental geometries are known, we estimate the “true” geometry of isolated H₃O⁺ to have a structure with θ(HOH) = 110-112°, r(OH) = 0.97–0.98 Å and an inversion barrier of 2–3 kcal/mole. Our prediction for the proton affinity of water is ≈ 170 kcal/mole, which is somewhat smaller than the currently accepted value.     

Variational grand-canonical electronic structure of Li+Li at ~10<Superscript>4</Superscript> K with second-order perturbation theory corrections

An ab initio variational grand-canonical electronic structure mean-field method, based on the Gibbs–Peierls–Bogoliubov minimum principle for the Gibbs free energy, is applied to the di-lithium (Li+Li) system at temperatures around T ≈ 10⁴ K and electronic chemical potential of μ ≈ ?0.1E _h . The method is an extension of the Hartree–Fock approach to finite temperatures. We first study the Li₂ molecule at a frozen inter-nuclear distance of R = 3 Å as a function of temperature. The mean-field electronic structure changes smoothly as temperature increases, up to 10⁴ K, where a sharp spontaneous spin-polarization emerges as the variational mean-field solution. Further increase in the temperature extinguishes this polarization. We analyze the mean-field behavior using a correlated single-site Hubbard model and show it arises from an attempt of the mean-field to mimic the polarization of the spin–spin correlation function of the exact solution. Next, we keep constant the temperature at 10⁴ K and examine the electronic structure as a function of inter-nuclear distance R. At R = 3.7 Å, a crossing between two free energy states occurs: One state is “spin-unpolarized” (becomes lower in energy when R > 3.7 Å), while the other is “spin polarized”. This crossing causes near-discontinuous jumps in calculated properties of the system and is associated with using the noninteracting electron character of our mean-field approach. Such problems will likely plague FT-DFT calculations as well. We use second-order perturbation theory (PT2) to study effects of electron correlation on the potential of mean force between the two colliding Li atoms. We find that PT2 correlation free energy at ~10⁴ K is larger than at 0 K and tends to restore the spin-polarized state as the lowest free energy solution.     

Combined ab initio,electron diffraction,molecular mechanics and vibrational investigations of 1,1 -dimethyl-trans-2-decalone

The conformational behavior of 1,1'dimethyl-trans-2-decalone was studied by combined ab initio, electron diffraction, molecular mechanics and vibrational procedures, and the molecule was found to exist in a distorted all-chair ground state with average C-C, C-H and CO bond distances of r_g = 1.543 Å ± 0.002, r_g = 1.122 Å ± 0.007, and r_g = 1.236 Å ± 0.012, respectively. The ab initio calculations were performed on an STO-3G minimal basis and are indicative of the growing usefulness of quantum-mechanical techniques in the study of medium-sized molecular systems.     

Ab initio investigations of structure and stability of the LiBeF3 molecule

Ab initio calculations of the potential energy surface of LiBeF₃ have been performed using the basis set of Roos and Siegbahn. The extremum and saddle points were made more precise with Huzinaga-Dunning basis sets in double-and triple-zeta contractions The “bidentate” structure (symmetry group C_2v) is found to have the lowest energy and is much more advantageous than the others, and the LiBeF₃ molecule turns out to be rigid with respect to migration of the cation around the anion. The calculated internuclear distances and the energy of complex formation are in agreement with experimental values within 0.03 Å and 2 kcal/mole. The results are compared with similar ab initio data for LiBeH₃ and LiNO₃.     

Equilibrium structure and spectroscopic constants of maleic anhydride

The quadratic, cubic, and semi-diagonal quartic force fields of maleic anhydride have been calculated at the MP2 level of theory employing the cc-pVTZ basis set. The spectroscopic constants derived from the force field are in excellent agreement with the corresponding experimental values. The semi-experimental equilibrium structure has been derived from experimental ground state rotational constants and rovibrational corrections calculated from the cubic force field. This semi-experimental equilibrium structure is in excellent agreement with the ab initio structures computed at the CCSD(T) level of theory and it is closer to the ab initio structure than the purely experimental (or empirical) structures r ₀, r _m⁽¹⁾, and r _m⁽²⁾ obtained by microwave spectroscopy as well as the equilibrium structure derived from gas-phase electron diffraction data.     

CEPA calculations on open-shell molecules

Ab initio calculations at SCF and CEPA levels using large Gaussian basis sets have been performed for the two lowest electronic states,X ² Σ⁺ andA ² Π, of HeAr⁺. Spin-orbit coupling (SOC) effects have been added using a semiempirical treatment. The resulting potential curves for the three statesX,A ₁, andA ₂ have been used to evaluate molecular constants such as vibrational intervals ΔG(v + 1/2) and rotational constantsB _v as well as — by means of a Dunham expansion — equilibrium constants such asR _e , ω _e ,B _e etc. Comparison with the experimental data from UV emission spectroscopy shows that the calculated potential curves are slightly too shallow and have too large equilibrium distances:D _e = 242 cm^?1 andR _e = 2.66 Å compared to the experimental values of 262 cm^?1 and 2.585 Å, respectively, for theX ²Σ⁺ ground state. However, the ab initio calculations yield more bound vibrational levels than observed experimentally and allow for a more complete Dunham analysis, in particular for theA ₂ state. The experimental value of 154 cm^?1 for the dissociation energyD _e of this state is certainly too low; our best estimate is 180±5 cm^?1. For theA ₁ state our calculations are predictions since this state has not yet been observed experimentally.