New theoretical insight into the interactions and properties of formic acid: development of a quantum-based pair potential for formic acid

We performed ab initio quantum-chemical studies for the development of intra- and intermolecular interaction potentials for formic acid for use in molecular-dynamics simulations of formic acid molecular crystal. The formic acid structures considered in the ab initio studies include both the cis and trans monomers which are the conformers that have been postulated as part of chains constituting liquid and crystal phases under extreme conditions. Although the cis to trans transformation is not energetically favored, the trans isomer was found as a component of stable gas-phase species. Our decomposition scheme for the interaction energy indicates that the hydrogen-bonded complexes are dominated by the Hartree-Fock forces while parallel clusters are stabilized by the electron correlation energy. The calculated three-body and higher interactions are found to be negligible, thus rationalizing the development of an atom-atom pair potential for formic acid based on high-level ab initio calculations of small formic acid clusters. Here we present an atom-atom pair potential that includes both intra- and inter molecular degrees of freedom for formic acid. The newly developed pair potential is used to examine formic acid in the condensed phase via molecular-dynamics simulations. The isothermal compression under hydrostatic pressure obtained from molecular-dynamics simulations is in good agreement with experiment. Further, the calculated equilibrium melting temperature is found to be in good agreement with experiment.     

Free energy perturbation study of water dimer dissociation kinetics

An efficient approach is described for using accurate ab initio calculations to determine the rates of elementary condensation and evaporation processes that lead to nucleation of aqueous aerosols. The feasibility of the method is demonstrated in an application to evaporation rates of water dimer at 230 K. The method, known as ABC-FEP (ab initio/classical free energy perturbation), begins with a calculation of the potential of mean force for the dissociation (evaporation) of small water clusters using a molecular dynamics (MD) simulation with a model potential. The free energy perturbation is used to calculate how changing from the model potential to a potential calculated from ab initio methods would alter the potential of mean force. The difference in free energy is the Boltzmann-weighted average of the difference between the ab initio and classical potential energies, with the average taken over a sample of configurations from the MD simulation. In principle, the method does not require a highly accurate model potential, though more accurate potentials require fewer configurations to achieve a small sampling error in the free energy perturbation step. To test the feasibility of obtaining accurate potentials of mean force from ab initio calculations at a modest number of configurations, the free energy perturbation method has been used to correct the errors when some standard models for bulk water (SPC, TIP4P, and TIP4PFQ) are applied to water dimer. To allow a thorough exploration of sampling issues, a highly accurate fit to results of accurate ab initio calculations, known as SAPT-5s, as been used a proxy for the ab initio calculations. It is shown that accurate values for a point on the potential of mean force can be obtained from any of the water models using ab initio calculations at only 50 configurations. Thus, this method allows accurate simulations of small clusters without the need to develop water models specifically for clusters.     

Ab initio study of the effects of orientation and corrugation for H2 adsorbed on polycyclic aromatic hydrocarbons

This paper reports state-of-the-art ab initio calculations at the second order of Moller-Plesset perturbation theory of molecular hydrogen interaction with polycyclic aromatic hydrocarbons (PAHs) up to coronene (C(24)H(12)). The effects of both H(2) orientation with respect to the PAH plane and of PAH corrugation have been carefully investigated. It was found that the energetic preference for the perpendicular H(2) orientation over the parallel one decreases rapidly as the PAH grows. The detailed study of coronene-H(2) potential energy surface has made it possible to estimate from first principles the graphite-H(2) binding energy. This ab initio estimate is shown to be in fair agreement with experiment. As revealed by the example of benzene-H(2) dimer, the electrostatic energy component plays an important role in PAH-H(2) interactions, that stems largely from the charge penetration effect and, therefore, cannot be reproduced by the simple quadrupole-quadrupole interaction model.     

Compression effect on structure and proton transfer in crystalline benzoic acid

Geometry optimizations for an isolated dimer and a crystal of benzoic acid were performed in order to evaluate the equilibrium geometries and the energy difference between the dimers in isolated and crystalline states using model potentials. The optimization in the crystal field results in a shortening of the O⋯O distance in comparison with that in an isolated dimer. The magnitude of the shortening agrees well with the difference between the observed values of the O⋯O distance in the gaseous (2.703 Å) and crystalline (2.64 Å) states. The energy increase due to this shortening is estimated to be about 0.24–0.40 kcal mol⁻¹ and is found to be one of the causes of the discrepancy between the barrier height of 1–2 kcal mol⁻¹ measured by NMR for crystalline carboxylic acids and that of 7.1–9.1 kcal mol⁻¹ calculated by the ab initio method for the isolated dimer.     

Perturbation calculations of molecular interaction energies: an example,HF....HF

An expression for the interaction energy of two molecules, obtained by expanding the wavefunction for the whole system in terms of antisymmetrized products of free-molecule functions and using a matrix perturbation scheme, is used in ab initio calculations on the HF dimer. The computed interaction energy is fitted with considerable accuracy by a simple analytical formula. The equilibrium geometry and hydrogen-bond energy are in satisfactory agreement with available experimental results.     

Fragmentation Behavior and Ionization Potentials of Lead Clusters Pb_n(n≤30)

The properties of Pbn(n=2―30) clusters including binding energies,second differences in energy,and HOMO-LUMO gaps,especially fragmentation energies and ionization potentials,have been studied by ab initio calculation.The main fragmentation products of Pbn+ are shown to be Pb+Pbn-1+ for n≤14 and two small cluster fragments for larger ones with n14.The Pb13+ appears frequently as the products in the fragmentations of large clusters.Also,the calculated ionization potentials of the clusters are consistent with the experiment data.     

Intermolecular potential calculations for polynuclear aromatic hydrocarbon clusters

Calculations of intermolecular potentials are presented for homo-molecular and hetero-molecular clusters of 24 peri-condensed PAH spanning monomer masses ranging from 78 to 1830 Da. Binding energies of homo-molecular dimers rise rapidly with molecular size and asymptotically approach the experimentally established exfoliation energy for graphite of 5.0 kJ mol(-1) (carbon atom)(-1). Binding energies of hetero-molecular dimers correlate well with the reduced mass of the pair. From calculations of homo-molecular stacks, binding energies were observed to increase with each added molecule and rise asymptotically, approaching a limit which scales linearly with monomer molecular mass. These results are reviewed in the context of molecular growth in flames and in the context of astrophysical observations.     

Critical and phase-equilibrium properties of an ab initio based potential model of methanol and 1-propanol using two-phase molecular dynamics simulations

Two-phase molecular dynamics simulations employing a Monte Carlo volume sampling method were performed using an ab initio based force field model parameterized to reproduce quantum-mechanical dimer energies for methanol and 1-propanol at temperatures approaching the critical temperature. The intermolecular potential models were used to obtain the binodal vapor-liquid phase dome at temperatures to within about 10 K of the critical temperature. The efficacy of two all-atom, site-site pair potential models, developed solely from the energy landscape obtained from high-level ab initio pair interactions, was tested for the first time. The first model was regressed from the ab initio landscape without point charges using a modified Morse potential to model the complete interactions; the second model included point charges to separate Coulombic and dispersion interactions. Both models produced equivalent phase domes and critical loci. The model results for the critical temperature, density, and pressure, in addition to the sub-critical equilibrium vapor and liquid densities and vapor pressures, are compared to experimental data. The model's critical temperature for methanol is 77 K too high while that for 1-propanol is 80 K too low, but the critical densities are in good agreement. These differences are likely attributable to the lack of multi-body interactions in the true pair potential models used here.     

Accurate equilibrium structures obtained from gas-phase electron diffraction data: sodium chloride

A novel method has been developed to allow the accurate determination of equilibrium gas-phase structures from experimental data, thus allowing direct comparison with theory. This new method is illustrated through the example of sodium chloride vapor at 943 K. Using this approach the equilibrium structures of the monomer (NaCl) and the dimer (Na(2)Cl(2)), together with the fraction of vapor existing as dimer, have been determined by gas-phase electron diffraction supplemented with data from microwave spectroscopy and ab initio calculations. Root-mean-square amplitudes of vibration (u) and distance corrections (r(a) - r(e)) have been calculated explicitly from the ab initio potential-energy surfaces corresponding to the vibrational modes of the monomer and dimer. These u and (r(a) - r(e)) values essentially include all of the effects associated with large-amplitude modes of vibration and anharmonicity; using them we have been able to relate the ra distances from a gas-phase electron diffraction experiment directly to the re distances from ab initio calculations. Vibrational amplitudes and distance corrections are compared with those obtained by previous methods using both purely harmonic force fields and those including cubic anharmonic contributions, and the differences are discussed. The gas-phase equilibrium structural parameters are r(e)(Na-Cl)(monomer) = 236.0794(4) pm; r(e)(Na-Cl)(dimer) = 253.4(9) pm; and <(e)ClNaCl = 102.7(11) degrees. These results are found to be in good agreement with high-level ab initio calculations and are substantially more precise than those obtained in previous structural studies.     

On the hydrogen bonding between water and ammonia molecules

The hydrogen bond N·HO between the water and ammonia molecules has been investigated ab initio using the SCF LCAO MO method. The minimal and extended basis sets of Slater type orbitals were used. It was found that the energy of the hydrogen bond is equal to 6.44 kcal/mole and the equilibrium separation of the oxygen and nitrogen atoms in the dimer is 5.72 au. At this intermolecular distance there is only one minimum in the potential energy curve for the motion of proton.     

Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer

We report full-dimensional, ab initio potential energy and dipole moment surfaces, denoted PES and DMS, respectively, for arbitrary numbers of water monomers. The PES is a sum of 1-, 2-, and 3-body potentials which can also be augmented by semiempirical long-range higher-body interactions. The 1-body potential is a spectroscopically accurate monomer potential, and the 2- and 3-body potentials are permutationally invariant fits to tens of thousands of CCSD(T)/aug-cc-pVTZ and MP2/aug-cc-pVTZ electronic energies, respectively. The DMS is a sum of 1- and 2-body DMS, which are covariant fits to tens of thousands MP2/aug-cc-pVTZ dipole moment data. We present the details of these new 2- and 3-body potentials and then extensive applications and tests of this PES are made to the structures, classical binding energies, and harmonic frequencies of water clusters up to the 22-mer. In addition, we report the dipole moment for these clusters at various minima and compare the results against available and new ab initio calculations.     

Polarizable interaction potential for water from coupled cluster calculations. I. Analysis of dimer potential energy surface

A six-dimensional interaction potential for the water dimer has been fitted to ab initio interaction energies computed at 2510 dimer configurations. These energies were obtained by combining the supermolecular second-order energies extrapolated to the complete basis set limit from up to quadruple-zeta quality basis sets with the contribution from the coupled-cluster method including single, double, and noniterative triple excitations computed in a triple-zeta quality basis set. All basis sets were augmented by diffuse functions and supplemented by midbond functions. The energies have been fitted using an analytic form with the induction component represented by a polarizable term, making the potential directly transferable to clusters and the bulk phase. Geometries and energies of stationary points on the potential surface agree well with the results of high-level ab initio geometry optimizations.     

Evolution of the electronic structure of Be clusters

Using a modified symbiotic genetic algorithm approach and many-body interatomic potential derived from first principles, we have calculated equilibrium geometries and binding energies of the ground-state and low-lying isomers of Be clusters containing up to 41 atoms. Molecular-dynamics study was also carried out to study the frequency of occurrence of the various geometrical isomers as these clusters are annealed during the simulation process. For a selected group of these clusters, higher-energy isomers were more often found than their ground-state structures due to large catchment areas. The accuracy of the above ground-state geometries and their corresponding binding energies were verified by carrying out separate ab initio calculations based on molecular-orbital approach and density-functional theory with generalized gradient approximation for exchange and correlation. The atomic orbitals were represented by a Gaussian 6-311G** basis, and the geometry optimization was carried out using the GAUSSIAN 98 code without any symmetry constraint. While the ground-state geometries and their corresponding binding energies obtained from ab initio calculations do not differ much from those obtained using the molecular-dynamics approach, the relative stability of the clusters and the energy gap between the highest occupied and the lowest unoccupied molecular orbitals show significant differences. The energy gaps, calculated using the density-functional theory, show distinct shell closure effects, namely, sharp drops in their values for Be clusters containing 2, 8, 20, 34, and 40 electrons. While these features may suggest that small Be clusters behave free-electron-like and, hence, are metallic, the evolution of the structure, binding energies, coordination numbers, and nearest-neighbor distances do not show any sign of convergence towards the bulk value. We also conclude that molecular-dynamics simulation based on many-body interatomic potentials may not always give the correct picture of the evolution of the structure and energetics of clusters although they may serve as a useful tool for obtaining starting geometries by efficiently searching a large part of the phase space.     

An ab initio study of the fcc and hcp structures of helium

The hexagonal close packed (hcp) and face centered cubic (fcc) structures of helium are studied by using a new ab initio computational model for large complexes comprising small subsystems. The new model is formulated within the framework of the energy incremental scheme. In the calculation of intra- and intersystem energies, model systems are introduced. To each subsystem associated is a set of partner subsystems defined by a vicinity criterion. In the independent calculations of intra- and intersystem energies, the calculations are performed on model subsystems defined by the subsystems considered and their partner subsystems. A small and a large basis set are associated with each subsystem. For partner subsystems in a model system, the small basis set is adopted. By introducing a particular decomposition scheme, the intermolecular potential is written as a sum of effective one-body potentials. The binding energy per atom in an infinite crystal of atoms is the negative value of this one-body potential. The one-body potentials for hcp and fcc structures are calculated for the following nearest neighbor distances (d0): 4.6, 5.1, 5.4, 5.435, 5.5, 5.61, and 6.1 a.u. The equilibrium distance is 5.44 a.u. for both structures. The equilibrium dimer distance is 5.61 a.u. For the larger distances, i.e., d0 > 5.4 a.u., the difference of the effective one-body potentials for the two structures is less than 0.2 microE(h). However, the hcp structure has the lowest effective one-body potential for all the distances considered. For the smallest distance the difference in the effective one-body potential is 3.9 microE(h). Hence, for solid helium, i.e., helium under high pressure, the hcp structure is the preferred one. The error in the calculated effective one-body potential for the distance d0 = 5.61 a.u. is of the order of 1 microE(h) (approximately 0.5%).     

Mapping the interaction energy surfaces of cyclic alkanes: evaluating the transferability of an ab initio based potential model

Detailed interaction energy maps are computed for symmetric cyclopropane and tetrahedrane dimer systems using ab initio methods. Interaction energies of cubane and cyclohexane dimers are also reported. The global minimum energy structures of cyclopropane and tetrahedrane systems are both D(3d) structures with energies of -1.850 and -2.171 kcal mol(-1). The ability of NIPE potential model, based on ab initio nonbonding data of neopentane (N), isobutane (I), propane (P), ethane (E) and all their combinations to predict the pair interaction energies of these strained cyclic hydrocarbons is also investigated. The difference between the energies predicted by NIPE and those obtained from the ab initio calculations increases with ring strain In general, NIPE values are in close agreement with the ab initio results for alkane ring structures having low ring strain.     

Water trimer torsional spectrum from accurate ab initio and semiempirical potentials

The torsional levels of (H2O)3 and (D2O)3 were calculated in a restricted dimensionality (three-dimensional) model with several recently proposed water potentials. Comparison with the experimental data provides a critical test, not only of the pair interactions that have already been probed on the water dimer spectra, but also of the nonadditive three-body contributions to the potential. The purely ab initio CC-pol and HBB potentials that were previously shown to yield very accurate water dimer levels, also reproduce the trimer levels well when supplemented with an appropriate three-body interaction potential. The TTM2.1 potential gives considerably less good agreement with experiment. Also the semiempirical VRT(ASP-W)III potential, fitted to the water dimer vibration-rotation-tunneling levels, gives substantial disagreement with the measured water trimer levels, which shows that the latter probe the potential for geometries other than those probed by the dimer spectrum. Although the three-body nonadditive interactions significantly increase the stability of the water trimer, their effect on the torsional energy barriers and vibration-tunneling frequencies is less significant.     

Simulation of ab initio results for palladium and rhodium clusters by tight‐binding calculations*

The study of metal clusters is nowadays a very active field of research using both experimental and theoretical techniques. Regular trends as well as unexpected behaviors have been observed regarding size‐dependent properties such as ionization potentials and atomization energies. Palladium and rhodium clusters of small size have been extensively studied at various semiempirical and ab initio levels of the theory, but the achievement and the interpretation of these calculations are generally difficult to be performed because of the incomplete shell structure of transition metal clusters. So we have tried to mimic the most important conclusions of the ab initio results available for Pd and Rh clusters by means of tight‐binding calculations, in the original Wolfsberg–Helmholz form, with appropriate parametrized repulsion terms. The occupation numbers of the one‐electron energy levels have been determined by taking into account some predictions of the graph theory. This enables us to study the variation of the atomization energies per atom for these clusters and to derive a bond‐energy systematics for Pd–Pd, Rh–Rh, and Pd–Rh linked atoms. Magic clusters with 13 atoms are considered. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 26–33, 2001     

Magic clusters MAu4 (M=Ti and Zr) and their dimers: how magic are they?

The stability of closed shell bimetallic magic clusters MAu(4) (M=Ti and Zr) is investigated theoretically through ab initio molecular orbital calculations. Both these clusters have tetrahedral structures and are found to be associated with large values of the ionization potential, HOMO-LUMO gap as well as the binding energies, which are characteristic of the magic clusters. However, the cluster-cluster interaction energy corresponding to a dimer formation is found to be unusually high ( approximately 5-7 eV) in contradiction to the usual properties of a magic cluster and is attributed to a 3-center-2-electron M-Au-M type bridge bonding as well as aurophilic attraction. Gross geometrical features of the individual clusters are, however, mostly retained in the dimer, thus satisfying the basic requirements for the cluster-assembled materials. This work would have important implications in the design of novel cluster-based nanomaterials for various nanoscale applications.     

Structural and electronic properties of compound metal clusters

The equilibrium geometries, relative stabilities, and vertical ionization potentials of compound clusters involving Li _n , Na, Mg, and Al atoms have been calculated using ab initio self-consistent field linear combination of atomic orbitals — molecular orbital (SCF-LCAO-MO) method. The exchange energies are calculated exactly using the unrestricted Hartree-Fock (UHF) method whereas the correlation correction is included within the framework of configuration interaction involving pair excitations of valence electrons. While the later correction has no significant effect on the equilibrium geometries of clusters, it is essential for the understanding of relative stabilities. Clusters with even numbers of electrons are found to be more stable than those with odd numbers of electrons regardless of their charge state and atomic composition. The equilibrium geometries of homo-nuclear clusters can be significantly altered by replacing one of its constituent atoms with a hetero-nuclear atom. The role of electronic structure on the geometries and stabilities of compound clusters is discussed.