Some problems est the calculation of ab initio potential energy curves

The non-adiabatic and adiabatic approaches to the calculation of molecular energy levels are presented. The concept of the potential energy curve, its accuracy and limitations are discussed. Simplified approaches to calculations of the intermolecular potential energy curves are also considered.     

Molecular dynamics simulations of fluid methane properties using ab initio intermolecular interaction potentials

Intermolecular interaction energy data for the methane dimer have been calculated at a spectroscopic accuracy and employed to construct an ab initio potential energy surface (PES) for molecular dynamics (MD) simulations of fluid methane properties. The full potential curves of the methane dimer at 12 symmetric conformations were calculated by the supermolecule counterpoise‐corrected second‐order Møller‐Plesset (MP2) perturbation theory. Single‐point coupled cluster with single and double and perturbative triple excitations [CCSD(T)] calculations were also carried out to calibrate the MP2 potentials. We employed Pople's medium size basis sets [up to 6‐311++G(3df, 3pd)] and Dunning's correlation consistent basis sets (cc‐pVXZ and aug‐cc‐pVXZ, X = D, T, Q). For each conformer, the intermolecular carbon–carbon separation was sampled in a step 0.1 Å for a range of 3–9 Å, resulting in a total of 732 configuration points calculated. The MP2 binding curves display significant anisotropy with respect to the relative orientations of the dimer. The potential curves at the complete basis set (CBS) limit were estimated using well‐established analytical extrapolation schemes. A 4‐site potential model with sites located at the hydrogen atoms was used to fit the ab initio potential data. This model stems from a hydrogen–hydrogen repulsion mechanism to explain the stability of the dimer structure. MD simulations using the ab initio PES show quantitative agreements on both the atom‐wise radial distribution functions and the self‐diffusion coefficients over a wide range of experimental conditions. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

Molecular electrostatic potentials: Comparison of ab initio and CNDO results

The possibilities of utilization of CNDO wave functions for computing molecular electrostatic potentials are studied by comparison with ab initio results for H₂O and H₂CO.

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Zusammenfassung Die Möglichkeiten der Verwendung von CNDO-Wellenfunktionen zur Berechnung molekularer elektrostatischer Potentiale werden durch Vergleich mit ab initio Rechnungen für H₂O und H₂CO untersucht.

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Résumé Les possibilités d'utilisation de fonctions d'onde CNDO pour le calcul des potentiels électrostatiques moléculaires sont étudiées par comparaison avec des résultats ab initio pour H₂O et H₂CO.

     

Potential energy curves for ground and excited states of NaLi from ab initio calculations with effective core polarization potentials

Sixteen low-lying electronic states of NaLi are investigated by SCF/valence Cl calculations including core polarization effects by means of an effective potential. Spectroscopic constants are obtained with estimated uncertainties of ΔR_e ? 0.01 Å, Δω_e ? 0.6 cm^?1 and ΔD_e ? 80 cm^?1. From a comparison of experimental and theoretical G(υ) values, we suggest a ground-state dissociation energy of 7093 ± 5 cm^?1. Using our rovibrational energies and recently measured excitation lines, we are able to improve the T_e values and dissociation energies of five excited states to an accuracv of ±8 cm^?1.     

Relative solvation free energies calculated using an ab initio QM/MM-based free energy perturbation method: dependence of results on simulation length

Molecular dynamics (MD) simulations in conjunction with thermodynamic perturbation approach was used to calculate relative solvation free energies of five pairs of small molecules, namely; (1) methanol to ethane, (2) acetone to acetamide, (3) phenol to benzene, (4) 1,1,1 trichloroethane to ethane, and (5) phenylalanine to isoleucine. Two studies were performed to evaluate the dependence of the convergence of these calculations on MD simulation length and starting configuration. In the first study, each transformation started from the same well-equilibrated configuration and the simulation length was varied from 230 to 2,540 ps. The results indicated that for transformations involving small structural changes, a simulation length of 860 ps is sufficient to obtain satisfactory convergence. In contrast, transformations involving relatively large structural changes, such as phenylalanine to isoleucine, require a significantly longer simulation length (>2,540 ps) to obtain satisfactory convergence. In the second study, the transformation was completed starting from three different configurations and using in each case 860 ps of MD simulation. The results from this study suggest that performing one long simulation may be better than averaging results from three different simulations using a shorter simulation length and three different starting configurations.     

Molecular simulation of the hydration Gibbs energy of barbiturates

In the present work, molecular dynamics calculations of the Gibbs energy of hydration of 10 different substituted barbiturates in SPC/E water were performed using thermodynamic integration. Given that experimental determination of the Gibbs hydration energy for this class of compounds is currently unfeasible, computer simulations appear as the only alternative for the estimation of this important quantity. Several simulation parameters are discussed and optimized based on calculations for barbituric acid. It is concluded that accounting for electrostatic interactions with the Reaction-Field method can be up to two times faster than with Particle-Mesh-Ewald method, without loss of accuracy. Different number of solvent molecules and simulation lengths were also tested. Lennard-Jones and electrostatic contributions were scaled down to zero in an independent way. It is shown that the electrostatic contribution is dominant (representing approximately 90% of the total Gibbs energy of hydration) and that barbiturate intra-molecular interactions cannot be neglected. The importance of the electrostatic contribution is attributed to the formation of hydrogen bonds between the barbiturates and water, which play an important role in the solvation process. The influence of the different substituents and their contribution to the Gibbs energy of hydration was assessed. Finally, the Lennard-Jones contributions and the total hydration Gibbs energy can both be correlated against molecular weight or partition coefficient data for mono- and di-substituted barbiturates.     

An ab initio study of the hydration of alkylammonium groups

Ab initio STO 3G calculations of the electronic structure and interaction energies with water of methyl and ethylammonium ions are reported. It is shown that the calculations predict a preferential attack at the -group (relative to the nitrogen), in agreement with experimental facts, and that successive ethylation reduces the favorable energy of hydration.Further calculations show that due to the large positive charges on the hydrogens, direct C–H... O hydrogen bond formation is possible. Thus a water molecule forms such a hydrogen bond of - 10kcal/mole in NMe ₄ ⁺ ; of –9kcal/mole at an position in the ethylated ions and of –6 kcal/mole at a position. The a preference noted above is thus preserved. It seems unlikely that such interactions significantly change the overall hydration described above. Although twelve sites for H-bonding exist in NMe ₄ ⁺ , they approach each other rather closely and after addition of four water molecules further water molecules introduce such intermolecular repulsions as to reduce rather than increase the total hydration energy which remains always slightly lower than that obtained with water in the axial type of site described above [14].     

Optimized energy landscape exploration using the ab initio based activation-relaxation technique

Unbiased open-ended methods for finding transition states are powerful tools to understand diffusion and relaxation mechanisms associated with defect diffusion, growth processes, and catalysis. They have been little used, however, in conjunction with ab initio packages as these algorithms demanded large computational effort to generate even a single event. Here, we revisit the activation-relaxation technique (ART nouveau) and introduce a two-step convergence to the saddle point, combining the previously used Lanczo?s algorithm with the direct inversion in interactive subspace scheme. This combination makes it possible to generate events (from an initial minimum through a saddle point up to a final minimum) in a systematic fashion with a net 300-700 force evaluations per successful event. ART nouveau is coupled with BigDFT, a Kohn-Sham density functional theory (DFT) electronic structure code using a wavelet basis set with excellent efficiency on parallel computation, and applied to study the potential energy surface of C(20) clusters, vacancy diffusion in bulk silicon, and reconstruction of the 4H-SiC surface.     

Molecular orbital propagation to accelerate self-consistent-field convergence in an ab initio molecular dynamics simulation

Based on the idea of molecular orbital (MO) propagation, we propose a novel effective method for predicting initial guesses for the self-consistent-field calculations in direct ab initio molecular dynamics (AIMD) simulations. This method, called LIMO, adopts the Lagrange interpolation (LI) polynomial technique and predicts initial MO coefficients at the next AIMD step by using several previous results. Taking into account the crossing and/or mixing of MOs leads to orbital invariant formulas for the LIMO method. We also propose a simple method for determining the optimal degree of the LI polynomial, which corresponds to the number of previous steps. Numerical tests confirm that this proposed method is both effective and feasible.     

Structure and dynamics of mesogens using intermolecular potentials derived from ab initio calculations

A method for the calculation of the two-body intermolecular potential which can be applied to large molecules is presented. Each monomer is fragmented in a number of moieties whose interaction energies are used to recover the interaction energy of the whole dimer. For these reasons this strategy has been called fragmentation reconstruction method (FRM). By a judicious choice of the fragmentation scheme it is shown that very accurate interaction energies can be obtained. The sampling of the potential energy surface of a dimer is then used to obtain intermolecular force fields at several levels of complexity, suitable to be employed in bulk phase computer simulations. Applications are presented for benzene and for some mesogenic molecules which constitute the principal interest of the authors. A number of properties ranging from phase stability, thermodynamic quantities, orientational order parameter and collective dynamics properties are computed and discussed.     

Achieving fast convergence of ab initio free energy perturbation calculations with the adaptive force-matching method

This paper studies the possibility of improving the convergence of ab initio free energy perturbation (FEP) calculations by developing customized force fields with the adaptive force-matching (AFM) method. The ab initio FEP method relies on a molecular mechanics (MM) potential to sample configuration space. If the Boltzmann weight of the MM sampling is close to that of the ab initio method, the efficiency of ab initio FEP will be optimal. The difference in the Boltzmann weights can be quantified by the relative energy difference distribution (REDD). The force field developed through AFM significantly improves the REDD when compared with standard MM models, thus improving the convergence of the ab initio FEP calculation. The static dielectric constant ε_s of ice-Ih was studied with PW-91 through ab initio FEP. With a customized force field developed through AFM, we were able to converge ε_s to 80 ± 4 with 3,600 configurations. A similar ab initio FEP calculation with the TIP4P model would require 220 times more configurations to achieve the same accuracy. Our study indicates that the PW-91 functional underestimates ice-Ih ε_s by about 20%.     

Monte Carlo simulation of liquid hydroxylamine using ab initio intermolecular potential functions

A potential model for intermolecular interactions between hydroxylamine (NH₂OH) molecules based on ab initio quantum mechanical calculations is reviewed and critically assessed by analyzing results from a Monte Carlo simulation of liquid hydroxylamine. The liquid structure is studied in detail using radial, energy, and angular distribution functions, coordination numbers, and their distribution. Results indicate a large first solvation shell (5.3 Å), which contains 13 molecules, out of which only 4 are truly bonded by nonlinear, low-energy hydrogen bonds. These are of either the OH…O or the OH…N type, as NH…O and NH…N linear bonds are considerably suppressed, and no cyclic dimers are found. The dependence of the structural and physical properties on the simulation characteristics has also been investigated.     

Application of the multiensemble sampling to the hydration free energy

We demonstrate the feasibility of using multiensemble sampling method (MESM) to determine the free energy difference between two far states for which the configurational distributions do not overlap at all. The MESM is a recently developed non‐Boltzmann sampling technique. The free energy of charging a sodium ion in water is accurately calculated in a single simulation, introducing nine intermediate ionic states. This is due to the ability of the method to explore the relevant parts of configuration space equally for every state, and this ability comes from the universality of weighting function W and the simplicity in adjusting its parameters. Detailed procedures of adjusting the parameters are presented. The comparison with a free energy perturbation method (FEPM) shows that the MESM is more reliable and efficient. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1004–1009, 2001     

Exchange repulsion between effective fragment potentials and ab initio molecules

The exchange repulsion energy and the Fock operator for systems that contain both effective fragment potentials and ab initio molecules have been derived, implemented, and tested on six mixed dimers of common solvent molecules. The implementation requires a balance between accuracy and computational efficiency. The gradient of the exchange repulsion has also been derived. Computational timings and the current challenges facing the implementation of the gradient are discussed.     

Finding minimum energy reaction paths on ab initio potential energy surfaces using the fast marching method

The fast marching method (FMM) for determining minimum-cost paths has been extended to compute the minimum-energy reaction coordinates in chemical reactions. This was accomplished by building an interface between FMM and the Gaussian program. We demonstrate the new method using an S _N 2 reaction, the isomerization of HSCN to HNCS, and a gas-phase rearrangement reaction of relevance in mass spectrometry.     

Density functional and ab initio study of the free radical MgNC

A new “non-terrestrial” molecule present in the envelope of the carbon star IRC + 10216 was described for the first time in 1986. Recently, this molecule was identified as the free radical MgNC, the first Mg-containing molecule in space. We present here the first density functional study performed on this radical, as well as on its isomer MgCN and the transition state connecting these species. It is shown that the optimum geometry obtained at the Becke3LYP/6-311+G(3df) level leads to the most exact rotational constants B_e and B_o calculated up to now. It is also shown that the energy differences between the three species are completely in agreement with the best ab initio calculations available. Furthermore, it is shown that the popular MP2 method fails for this system in the same way that has been demonstrated for other radicals.     

Effects of hydration on scale factors for ab initio force constants

Experimentally measured vibrational frequencies from the polar groups of peptides in aqueous solutions do not agree with frequencies calculated from scaled quantum mechanical force fields (SQMFF) using differential scale factors developed for molecules in the vapor phase. Measured stretching frequencies for carbonyl groups are more than 50 wavenumbers lower than the calculated values. On the other hand, frequencies for non-polar groups calculated using these scale factors are relatively accurate. Our goal is to develop a SQMFF that yields accurate calculated frequencies for peptides in aqueous solutions. To this end, we have calculated scale factors for ab initio force constants for formic acid, acetic acid, and acetone using a least squares fit of calculated and experimental frequencies. We compare these scale factors with changes observed in the ab initio force constants calculated for these molecules at various states of hydration. These force constants are calculated using fully optimized geometries for these hydrated molecules using the 4-31G basis. We present a comparison of the experimental and calculated frequencies, along with their potential energy distributions, for both vapor and aqueous phases. The results indicate that scale factors can simulate the effects of solvation on molecular force constants to yield accurate scaled ab initio force fields.     

Molecular dynamics investigations of the dissociation of SiO2 on an ab initio potential energy surface obtained using neural network methods

The neural network (NN) procedure to interpolate ab initio data for the purpose of molecular dynamics (MD) simulations has been tested on the SiO(2) system. Unlike other similar NN studies, here, we studied the dissociation of SiO(2) without the initial use of any empirical potential. During the dissociation of SiO(2) into Si+O or Si+O(2), the spin multiplicity of the system changes from singlet to triplet in the first reaction and from singlet to pentet in the second. This paper employs four potential surfaces. The first is a NN fit [NN(STP)] to a database comprising the lowest of the singlet, triplet, and pentet energies obtained from density functional calculations in 6673 nuclear configurations. The other three potential surfaces are obtained from NN fits to the singlet, triplet, and pentet-state energies. The dissociation dynamics on the singlet-state and NN(STP) surfaces are reported. The results obtained using the singlet surface correspond to those expected if the reaction were to occur adiabatically. The dynamics on the NN(STP) surface represent those expected if the reaction follows a minimum-energy pathway. This study on a small system demonstrates the application of NNs for MD studies using ab initio data when the spin multiplicity of the system changes during the dissociation process.     

Communication: regularizing binding energy distributions and thermodynamics of hydration: theory and application to water modeled with classical and ab initio simulations

The high-energy tail of the distribution of solute-solvent interaction energies is poorly characterized for condensed systems, but this tail region is of principal interest in determining the excess free energy of the solute. We introduce external fields centered on the solute to modulate the short-range repulsive interaction between the solute and solvent. This regularizes the binding energy distribution and makes it easy to calculate the free energy of the solute with the field. Together with the work done to apply the field in the presence and absence of the solute, we calculate the excess chemical potential of the solute. We present the formal development of this idea and apply it to study liquid water.