Conventional Ab Initio Methods Research Articles

The Water Dimer: Post-Hartree-Fock and Density Functional Calculations on the Potential Energy Surface

Conventional ab initio and density functional methods with extended basis sets were employed in the study of a path on the water-dimer potential energy surface. The results show that density functional methods do depend strongly on the type of exchange-correlation potential employed, as well as on the quality of the basis sets – similarly to conventional ab initio methods – and on the density of the grid. Gradient-corrected methods behave, as expected, better than uncorrected ones, the Becke–Lee–Yang–Parr (BLYP) potential being the one that gives the best results. However, too large chemical- and hydrogen-bond lengths and absolute energies, as well as too small relative total and correlation energies demonstrate that even BLYP calculations with a relative large basis set are not good as MP2 calculations of the same size. Adiabatically connected functionals (ACM), represented in this work by B3PW91, provide an improvement on the whole surface.

Density functional theory study on molecular structure and vibrational IR spectra of isocytosine

Density functional theory with the combined Becke3-LYP exchange-correlation energy functional [DFT(B3-LYP) method] using the 6-31G(d, p) basis set is applied to predict molecular parameters (geometries, rotational constants, dipole moments) and vibrational IR spectra (harmonic wavenumbers, absolute intensities) of six tautomers of the isocytosine molecule. The results are compared with the corresponding data calculated at the conventional ab initio Hartree-Fock (HF) level using the same basis set and with available experimental data. Calculations show that (a) three amino tautomers are slightly nonplanar species with, evidently, a distorted amino group, (b) the DFT (B3-LYP)/6-31G(d, p) method predicts better molecular parameters, than do the HF calculations, and (c) the DFT(B3-LYP)-calculated vibrational IR spectra of isocytosine agree well with the available recorded IR spectra, and they show marked improvement over the IR spectra predicted at the HF/6-31G(d, p) level. Tautomeric stabilities of isocytosine are discussed on the basis of computed electronic energies by the DFT(B3-LYP) and ab initio approaches [including the MP2 and MP4(SDQ) calculations of electronic energies] and predicted zero-point vibrational energies by DFT(B3-LYP) and HF methods. This relative energies at 0 K of the tautomeric forms of isocytosine predicted by both conventional ab initio and DFT(B3-LYP) methods correlate well with the experimental data, showing the predominance of the aminohydroxy tautomer of isocytosine for an isolated molecule. © 1997 John Wiley & Sons, Inc.

Infrared spectra of thiouracils: experimental matrix isolation and ab initio Hartree-Fock, post-Hartree-Fock and density functional theory studies

The experimental infrared absorption spectra of 2-thiouracil, 4-thiouracil and 2,4-dithiouracil isolated in low-temperature argon matrices are compared with the spectra of these compounds computed by the density functional theory with the combined Becke3-LYP exchange-correlation energy functional (DFT(B3-LYP)) and conventional ab initio methods (Hartree-Fock (HF), MP2) using the standard 6-31G(d,p) basis set. The vibrational spectra computed at the DFT(B3-LYP)/6-31G(d,p) and HF/6-31G(d,p) levels of theory were found to reproduce well the experimental IR spectra. The results of MP2/6-31G(d,p) calculations predicted the normal modes due to out-of-plane vibrations somewhat less accurately. An assignment of the bands observed in the infrared spectra of the three thiouracils was performed, based on the comparison with the spectra calculated at the DFT(B3-LYP)/6-31G(d,p) level.

Ligand Substitution: An Assessment of the Reliability of ab Initio Calculations

Density functional methods and conventional ab initio molecular orbital methods have been compared in an investigation of the model ligand substitution reaction Pd(N−O)(CH3)(PH3) + CO → Pd(N−O)(CH3)(CO) + PH3 (N−O = NHCHCOO-). Full geometry optimizations were performed for each stationary point using a range of different basis sets, relativistic effective core potentials (RECPs), and levels of theory in order to ascertain a reliable and computationally inexpensive method for probing such reaction mechanisms. For geometries that compare well to experiment, electron correlation and double-ζ valence basis sets with d-type polarization functions on the main group elements are essential. Geometries determined using small-core RECPs and nonlocal density functional theory compared favorably with those produced at the second-order Møller−Plesset (MP2) level, and good agreement with available experimental data was observed. The density functional reaction energetics, however, were poor, apparently due to an unrealistically high Pd−CO binding energy relative to the Pd−PH3 binding energy. This error was reduced by the use of the Becke three-term hybrid exchange functional. The reaction barrier and reaction energy were predicted to be +15.0 kJ/mol and +5.1 kJ/mol, respectively, at the MP2 level with a medium basis set. Approximate large basis set CCSD(T) energetics were determined using an additivity scheme. This method predicted a stabilization of the 5-coordinate transition structure with respect to the 4-coordinate species, reducing the reaction barrier to +4.9 kJ/mol relative to the separated reactants. The associated reaction energy was +8.9 kJ/mol.

Ground State Properties of Hg2. 2. A Quantum Monte Carlo Study

We have carried out variational and pure diffusion quantum Monte Carlo calculations for the Hg atom and the Hg2 molecule. In the case of the Hg atom we have calculated valence correlation energies for relativistic and nonrelativistic 20-valence-electron pseudopotentials. The results are compared with those of conventional ab initio methods. For the Hg2 molecule we have used a 2-valence-electron pseudopotential together with a core-polarization potential. The resulting ground state potential energy curve agrees well with curves derived from configuration interaction calculations. Jastrow factors were found to be an efficient method to describe electron correlation in these systems.

Calculation of molecular geometries, relative conformational energies, dipole moments, and molecular electrostatic potential fitted charges of small organic molecules of biochemical interest by density functional theory

AbstractDensity functional theory is tested on a large ensemble of model compounds containing a wide variety of functional groups to understand better its ability to reproduce experimental molecular geometries, relative conformational energies, and dipole moments. We find that gradient‐corrected density functional methods with triple‐ζ plus polarization basis sets reproduce geometries well. Most bonds tend to be approximately 0.015 Å longer than the experimental results. Bond angles are very well reproduced and most often fall within a degree of experiment. Torsions are, on average, within 4 degrees of the experimental values. For relative conformational energies, comparisons with Hartree‐Fock calculations and correlated conventional ab initio methods indicate that gradient‐corrected density functionals easily surpass the Hartree‐Fock approximation and give results which are nearly as accurate as MP2 calculations. For the 35 comparisons of conformational energies for which experimental data was available, the root mean square (rms) deviation for gradient‐corrected functionals was approximately 0.5 kcal mol−1. Without gradient corrections, the rms deviation is 0.8 kcal mol−1, which is even less accurate than the Hartree‐Fock calculations. Calculations with extended basis sets and with gradient corrections incorporated into the self‐consistent procedure generate dipole moments with an rms deviation of 5%. Dipole moments from local density functional calculations, with more modest basis sets, can be scaled down to achieve roughly the same accuracy. In this study, all density functional geometries were generated by local density functional self‐consistent calculations with gradient corrections added in a perturbative fashion. Such an approach generates results that are almost identical to the self‐consistent gradient‐corrected calculations, which require significantly more computer time. Timings on scalar and vector architectures indicate that, for moderately sized systems, our density functional implementation requires only slightly less computer resources than established Hartree‐Fock programs. However, our density functional calculations scale much better and are significantly faster than their MP2 counterparts, whose results they approach. © 1995 John Wiley & Sons, Inc.

The FO 2 radical: a new success of density functional theory

The structure, heat of reaction and heat of formation of the FO 2 radical in its X 2A″ ground state has been calculated using the three-parameter exchange functional of Becke and the Lee-Yang-Parr functional for correlation energy (B3LYP method). B3LYP geometrical parameters of FO 2 and FO are nearer to experiment than those obtained with conventional ab initio calculations. The calculated ΔH r,0 0 for F + O 2 → FO 2 at this level (−11.1 kcal/mol) is nearer to experiment (−11.68 kcal/mol) than that afforded by any other calculation, including QCISD(T), MP4(SDTQ) or G1 ab initio models. Calculation of the heat of reaction for previously considered isodesmic and isogyric reactions involving the FO 2 radical shows that the agreement is consistent. The root mean square error for the sixteen reactions considered, involving FO, FO 2, FOH and FOOF, with heats of reaction varying from -149 to +56 kcal/mol, is 0.5 kcal/mol at the B3LYP level. The similar rms error for MP4(SDTQ)/6-311+ +G(2d, 2p) calculations is 5.2 kcal/mol. It is concluded that the B3LYP method is faster and more accurate than conventional ab initio methods for the study of reactions involving F-O bonds.

One-electron properties of several small molecules calculated using the local density approximation within density functional theory

Density functional theory (DFT) is a field enjoying a tremendous recent surge in popularity among theoretical and practical chemists alike because of its ability to more easily handle larger molecular systems than conventional ab initio methods. Until recently, however, assessment of the quality of the properties predicted (and therefore the charge density) from DFT had been limited mainly to dipole moments and their nuclear coordinate and electric field derivatives. This paper presents the calculated results for some of the one-electron properties of the eight small molecules (NH3, PH3, H2O, H2S, HF, HCl, CO, and N2). The properties chosen weight different regions of the charge density, from either very close in or at the nucleus (e.g., δ, the electron density at the nucleus) to regions farther out from the nucleus (e.g., the diamagnetic susceptibility 〈r2〉). It is found that properties which depend on an accurate knowledge of the electron density near to the nucleus are predicted poorly by the local density approximation (LDA), while others more dependent on the charge density farther out from the nucleus are predicted much more accurately, possibly due to cancellation of errors. Use of the LDA is therefore not recommended for ‘‘tight’’ properties; use of a functional employing gradient corrections would be more suitable for this purpose.

DFT study of the Diels–Alder reactions between ethylene with buta-1,3-diene and cyclopentadiene

A set of DFT methods (Xa, HFB, S-VWN, B–LYP; B–HandH and Becke3-LYP) has been used for the calculation of the transition states and energy barriers of the Diels–Alder reaction of ethylene with buta-1,3-diene and cyclopentadiene. The pure DFT methods overestimate the bond lengths, while the hybrid methods give values much closer to those obtained by conventional ab initio methods. The ratio of the σ-forming bonds to the π-breaking bonds is in excellent correlation to the predicted electronic energy barriers for these reactions. The local spin density approximation (S–VWN) fails completely giving a negative value for the classical energy barrier height for the addition of ethylene to buta-1,3-diene. On the other hand, the vibrational adiabatic barrier heights predicted by B-LYP/6-31G** and the hybrid Becke3-LYP/6-31G** theoretical models are in excellent agreement with available experimental data for both reactions.

A theoretical reinvestigation of the A 1∏u state of N22+

A new, semi-empirically scaled potential energy surface for the A 1∏u state of N22+ has been developed based on spectroscopic constants and high level ab initio calculations. The scaled surface was used to determine the extent to which conventional ab initio methods underestimate barrier heights and widths of quasibound, diatomic, dication potential energy functions. It was also used to reinvestigate the dissociation dynamics of the A 1Πu state of N22+.

An efficient cluster elongation method in density functional theory and its application to poly-hydrogen-bonding molecules

The elongation method to synthesize the electronic states of polymers is developed at the level of the density functional theory using the linear combination of Gaussian-type orbitals local spin density method. In this treatment, the interactions between the localized molecular orbitals of a cluster and the canonical molecular orbitals of an attacking monomer are successively included, where the Kohn–Sham equation is self-consistently solved instead of the Hartree–Fock equation in the conventional ab initio method. In the process of the cluster extension, an efficient treatment is implemented to calculate the matrix elements of Coulomb integral and exchange-correlation potential. The reliability and the efficiency of this method are examined via applications to hydrogen molecule cluster, linear water cluster (H2O)n and formamide cluster (CHONHH2)n. It was shown that the present method saves significantly the computational time and disk storage in the large cluster calculations, and provides good agreements with the results by the conventional density functional treatment for the whole system.

Semiempirical Fragment Self-Consistent Field Monte Carlo simulations for liquid chlorosilanes

We applied the recently developed Neglect of Diatomic Differential Overlap Fragment Self-Consistent Field Monte Carlo method to the simulation of the liquid state of chlorinated monosilanes. This semiempirical technique divides the periodic simulation cell into subsystem, where the random move of an atom takes place, and environment exerting only secondary effects on the former. Expanding the electronic wave function on the basis of atomic hybrid orbitals, that form strictly localised molecular orbitals corresponding to chemical bonds in classical molecules, the wave function of the environment is determined from coupled 2 × 2 secular equations. For the subsystem the conventional Self-Consistent Field equations, with a perturbation term in the Fockian and a much lower dimensionality than for the whole system, have to be solved. Thus the computational efforts drastically decrease as the dependence on the number of atoms in the environment reduces from quartic or cubic, as in conventional ab initio or semiempirical methods, to quadratic. Our simulation for chlorosilanes predicts that in the liquid state the preferred orientation of two neighbouring molecules is the one with the maximum number of SiH…ClSi hydrogen bonds. We found that gas phase SiCl bond lengths increase by 6 to 16 pm in the liquid state as a result of that association. HSiCl and ClSiCl bond angles change much less, by 2–4 degrees, as compared to the gas phase geometry. Since, to our knowledge, there are no experimental data published for these systems, our results may serve as preliminary information on liquid chlorosilanes.

A Comparative Study of Electron Densities in Carbon Monoxide Calculated from Conventional ab Initio and Density Functional Methods

A Comparative Study of Electron Densities in Carbon Monoxide Calculated from Conventional ab Initio and Density Functional Methods

Novel semiempirical method for quantum Monte Carlo simulation: Application to amorphous silicon

We propose a novel bulk phase Monte Carlo simulation technique, in which the energy is calculated by quantum mechanical methods. The semiempirical fragment self-consistent field technique applied divides the periodic simulation cell into two parts. The first is the subsystem where the important change (the random movement of an atom or molecule) takes place and the second is the environment exerting only secondary effects on the former. Expanding the electronic wave function on the basis of strictly localized molecular orbitals and/or atomic hybrid orbitals the wave function of the environment is obtained from simple coupled 2×2 secular equations. The conventional self-consistent field equations, with a perturbation term in the Fockian, have to be solved only for the subsystem. In this way the computational efforts are decreased drastically, as the dependence on the number of atoms in the environment reduces to quadratic instead of cubic or quartic as in conventional semiempirical or ab initio methods, respectively. We wrote a computer code and applied our method to amorphous silicon. Starting from a distorted tetrahedrally bonded random network model we performed Monte Carlo simulations using the fragment self-consistent field energy calculation. After equilibration we obtained distribution functions almost identical to the ones corresponding to the distortion free tetrahedrally bonded network. This finding confirms the adequacy of our method for this specific case.

Diazasilene (SiNN): a comparative study of electron density distributions derived from Hartree-Fock, second-order Moller-Plesset perturbation theory, and density functional methods

The electron densities of the 3 Σ - ground state of diazasilene (SiNN) derived from density functional methods and conventional ab initio (UHF and UMP2) methods are compared and analyzed. The spin contamination is investigated at the HF, MP2, MP3, MP4, and DFT levels. The optimized geometries and vibrational frequencies obtained by using Becke-Perdew gradient corrections to the LSDA exchange and correlation functionals are also reported. The failure of the Hartree-Fock method, and other methods in which the Hartree-Fock single determinant wave function is used as the reference configuration, to predict a bound structure for SiNN is attributed to the antibonding character of the spin density along the Si-N bond

The performance of a family of density functional methods

The results of a systematic study of molecular properties by density functional theory (DFT) are presented and discussed. Equilibrium geometries, dipole moments, harmonic vibrational frequencies, and atomization energies were calculated for a set of 32 small neutral molecules by six different local and gradient-corrected DFT methods, and also by the ab initio methods Hartree–Fock, second-order Mo/ller–Plesset, and quadratic configuration interaction with single and double substitutions (QCISD). The standard 6-31G* basis set was used for orbital expansion, and self-consistent Kohn–Sham orbitals were obtained by all DFT methods, without employing any auxiliary fitting techniques. Comparison with experimental results shows the density functional geometries and dipole moments to be generally no better than or inferior to those predicted by the conventional ab initio methods with this particular basis set. The density functional vibrational frequencies compare favorably with the ab initio results, while for atomization energies, two of the DFT methods give excellent agreement with experiment and are clearly superior to all other methods considered.

Local density of states of aperiodic polymers using the localized orbitals from an ab initio elongation method

An elongation method, which was already proposed to calculate efficiently the electronic states of aperiodic polymers, is developed to provide the local density of states. Elongation method is carried out by repeating the uniform localization of wave functions with inclusion of the interaction between the cluster and an attacking molecule. At first, we develop this method to the ab initio level. Next, we show that the local density of states (LDOS) is obtained efficiently following the elongation step without treating the whole system directly. The validity of our method is examined via application to a hydrogen molecule cluster by comparing the results with those by the conventional ab initio method for the whole system. This approach makes it possible to investigate the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO), and their density of states on each site of a polymer chain, which will provide a novel approach to examine intra- and intermolecular reactivities within and between aperiodic polymers.

Nitrosyl hypofluorite: another difficult case for conventional ab initio methods

Nitrosyl hypofluorite: another difficult case for conventional ab initio methods