Conventional Ab Initio Methods Research Articles

σπ Scheme in Atom‐bond Electronegativity Equalization Method

AbstractAlthough, as we know, the traditional ab initio quantum chemical methods can deal with molecules of medium size, it is still a tremendous task to treat very big organic and biological systems. So even today it is still valuable to develop some meaningful relatively simple methods, such as EEM or ABEEM, to see how well and to what extent those kinds of methods can be employed with a huge savings of time to study very large systems. This kind of effort, including what has been done in this paper, may continue for quite a long period, especially considering dynamic problems in the near future. We will develop an atom‐bond electronegativity equalization method plus σπ (ABEEM σπ) scheme on the basis of DFT, in which the structure of double bond is explicitly treated in the electronegativity equalization method. In this scheme, the effective electronegativity of a region can be expressed as one valence‐state electronegativity (χ*) term, one valence‐state hardness (η*) term, and some other contributing terms coming from other regions' charges in the molecule. By dealing with more than 200 molecules, the parameters χ*, η*, C, and D in the expression of electronegativity are determined through a regression and least‐squares optimization procedure, and their meaning is also discussed. As testing examples, the ABEEM σπ scheme is used to calculate the charge distributions of C18N3O3H27, C15NO2H21, and thyrotropin‐releasing hormone (TRH), and the results show good agreement with those obtained by the ab initio method. However, this scheme is far more time saving and computational‐source saving compared to the conventional ab initio method. All of this indicates that the ABEEM σπ scheme is a reasonable and potential tool for predicting the properties of very large organic and biological systems such as poly‐peptides and proteins, etc.

Comparisons between Density Functional Theory and Conventional ab Initio Methods for 1,2-Elimination of HF from 1,1,1-Trifluoroethane: Test Case Study for HF Elimination from Fluoroalkanes

Density functional theory, DFT, and high-level conventional ab initio calculations, together with RRKM calculations, have been employed to study the nature of the transition state geometry for 1,2 elimination of HF from 1,1,1-trifluoroethane-d0,-d3; these serve as test cases for 1,2-HF elimination from fluorocarbons. Quantities calculated include structural parameters, bond indices, energies, atomic charges, vibrational frequencies, and moments of inertia for the reactant and the transition state geometry. The threshold energies for HF and DF elimination were computed and the vibrational frequencies and moments of inertia data were used with the RRKM theory to calculate the entropies of activation, preexponential factors for thermal activation, and also rate constants and the kinetic isotope effect for both thermally and chemically activated 1,1,1-trifluoroethane-d0,-d3. Of all the methods employed, the hybrid DFT methods incorporating either the three-parameter exchange functional of Becke with the correlation functional of Perdew and Wang or the correlation functional of Lee, Yang, and Parr were found to give results more consistent with the experimental studies. Both the 6-31G(d‘,p‘) and cc-PVDZ basis sets gave comparable agreement with experiment and suggest that basis sets of double-ζ quality in the valence region, which include polarization functions, appear to be adequately flexible to describe the systems studied here. There appears to be little to be gained in going from the computationally efficient DFT calculations to the computationally very expensive methods such as G2 or MP2.

Stepwise hydrogenation of N2 — a large-scale investigation of the performance and basis set convergence of DFT and conventional ab initio methods

The basis set convergence of non-local density functional theory (NL-DFT) using the functionals BLYP, BP86, B3P86, B3PW91 and B3LYP has been investigated. To this end we calculated the heats of hydrogenation of N2, N2H2 and N2H4 at the NL-DFT levels using the Pople basis sets from 6-31G(d) up to 6-311+G(3df,3pd), Dunnings correlation consistent basis sets cc-pVDZ, cc-pVTZ, cc-pVQZ and their augmented versions, as well. We also report additional calculations at the BLYP level using Slater-type basis functions up to TZ2P quality. The results are compared with conventional ab initio calculations at the MP2 and CCSD(T) levels with the Pople and Dunning basis sets as well as with available experimental data. The calculated heat of formation of diazene has been compared with several previously published high-level calculations. The combination of B3LYP with the Pople basis set having at least 6-311+G(d,p) quality gives the best DFT results for the three hydrogenation reactions. The B3LYP/6-311+G(d,p) values are better than the MP2 data with the large Pople basis sets. While B3LYP and the other DFT methods converge smoothly when the Pople basis sets become larger, the behavior of B3LYP with respect to the correlation consistent basis sets is puzzling. The calculated heats of formation at B3LYP level with cc-pVDZ, cc-pVTZ and cc-pVQZ basis oscillate, and the oscillation is enhanced with their augmented versions. MP2 and CCSD(T) converge smoothly within the Dunning's cc-pVxZ series of basis sets and their augmented versions. CCSD(T) gives the overall best results for the calculated heats of hydrogenation, but the values that are obtained with the largest basis set still do not have chemical accuracy (≤1kcalmol−1). Chemical accuracy is achieved with the extrapolation schemes G2 and CBS-Q.

Synthesis and structure of, and bonding in some derivatives of 2,6,9,10-tetraoxatricyclo[3.3.1.1(3,8)]-decane.

Five derivatives of 2,6,9,10-tetraoxatricyclo[3.3.1.1(3,8)]decane were synthesized and their molecular structures in the solid state were determined by means of X-ray diffraction analysis. In addition, the structures of all the molecules were optimized at different levels of computational quantum chemistry (HF/6-31G*, B3LYP/6-31G*). Experimentally determined bond lengths were compared with their calculated counterparts, and striking differences between the Hartree-Fock (HF) results and the experimental data could be traced back to the lack of correlation energy in the geometry optimizations. Two of the compounds under consideration are diastereomers and their relative stability was not only calculated with a conventional ab initio method (ZPE+MP2/6-31G*//HF/6-31G*), but also within the framework of density functional theory (B3LYP/6-31G*). In some of the calculations the influence of the solvent was included in single point calculations by means of an electrostatic model. Moreover, combining experimental as well as computational results, the exclusive axial orientation of a Cl atom in one of the compounds could be explained by an interplay of kinetic and energetic effects.

Ab Initio Studies on the Mechanism of Tyrosine Coupling

Oxidative stress is considered to be a major contributor to dysfunction in a host of disease states. Reactive oxygen species (ROS) mediate distinct oxidative alterations in biopolymers, including DNA, proteins, lipids, and lipoproteins. Currently, the mechanisms of biochemical reactions underlying oxidative stress are poorly understood because of the instability of ROS. One of the consequences of oxidative stress is one-electron oxidation of tyrosine (Tyr) residues in proteins, which represents a hallmark of this insult and is implicated in the pathogenesis of a number of pathological processes leading to atherosclerosis, inflammatory conditions, multiple system atrophy and several neurodegenerative diseases. Major products of oxidation of Tyr include protein-bound dityrosine and isodityrosine. In this report, the mechanism of tyrosine coupling (including structure and stability of a number of proposed reaction intermediates) is studied by high-level density functional and conventional ab initio methods including B3LYP, MP2, CASSCF, and CASPT2. It is demonstrated that dityrosine and isodityrosine are the most stable structures at all theoretical levels applied. In addition to classical structures of the reaction intermediates, evidence is found for a novel transient structure of Tyr dimer, stacked dityrosyl. This dimer is predicted to exist because of strong electron correlation between two tyrosyl moieties. The counterpoise corrected energy of stacked dityrosyl is below the energy of two tyrosyl radicals by about 95 kJ/mol at the PUMP2/6-31G** level. High proton affinity of tyrosyl radical (about 9.4 eV) suggests that positively charged amino acids in the vicinity of a solvent-exposed Tyr residue may increase the probability of tyrosine coupling.

Repulsive Coulomb Barriers in Compact Stable and Metastable Multiply Charged Anions

We demonstrate that a simple Coulomb-energy model can be used to predict the vertical electron detachment energy of an anion of charge (−n) given the detachment energy of the corresponding anion having one less charge (−n + 1). This model was applied earlier by other workers to dianions in which the two charged sites are quite distant. In this paper we show that it can also be applied to more spatially compact species as long as the two orbitals from which the electrons are removed are sufficiently noninteracting. We first demonstrate how to use this model by applying it to a series of electronically stable dianions (MgF42-, BeF42-, TeF82-, SeF82-, and TeCl82-) for which the (−2) to (−1) and (−1) to (neutral) electron detachment energies have been evaluated using conventional ab initio methods. These test calculations allow us to assess the predictive accuracy of the Coulomb model. We then extend the model's use to predict the energies of dianions and trianions that are not electronically stable (SO42-, CO32-, PO43-, and PO42-) and for which application of conventional quantum chemistry methods will not yield reliable predictions. That is, we predict at what energies metastable resonance states of these species will occur. Finally, we use the Coulomb nature of the long-range part of the electron−anion potential to estimate the lifetimes of these resonance states with respect to electron loss.

Diradicaloids: Description by the Spin-Restricted, Ensemble-Referenced Kohn−Sham Density Functional Method

A Kohn−Sham-type computational scheme capable of treating systems with strong nondynamic correlation is presented. The scheme, dubbed the spin-restricted, ensemble-referenced Kohn−Sham (REKS) method, is based on the representation of the density and energy for a strongly correlated system as weighted sums of densities and energies of several Kohn−Sham (KS) determinants. An optimal set of orthonormal KS orbitals and occupation numbers is obtained by minimizing the ground-state energy as a function of the density. Results of REKS calculations are reported and cover the following chemically important situations: (1) avoided crossing of potential energy surfaces, (2) bond-breaking processes, and (3) electronic structure of diradicals. The results of REKS calculations are compared with the available Kohn−Sham solutions for cases in which the exact density is known, as well as with results of conventional multireference ab initio methods and with the currently available density functional approaches.

Experimental and Theoretical Analysis of the Vibrational Spectra and Theoretical Study of the Structures of 3,6-Dichloropyridazine and 3,4,5-Trichloropyridazine

The infrared and Raman spectra of 3,6-dichloropyridazine and 3,4,5-trichloropyridazine were recorded. These spectra were taken in the solid phase and with various solvents (HCCl3, CS2, CCl4), giving wavenumbers and relative intensities of the bands and the qualitative Raman depolarization ratios. Conventional ab initio methods at the Hartree−Fock and MP2 levels using the 3-21G*, 6-31G*, 6-31G**, and 6-311G** basis sets, as well as density functional theory (DFT) using the 6-31G* basis functions and the BLYP and B3LYP functionals, were used to predict the geometries and to calculate the harmonic frequencies and force fields of these molecules. In addition, coupled cluster calculations, i.e., CCSD and CCSD(T), using the 6-311G** basis set were included to evaluate the geometries of pyridazine and 3,6-dichloropyridazine, analyzing in detail the structure of these systems. To fit the calculated wavenumbers to the experimental ones, the B3LYP/6-31G* force field was selected to be scaled. The following two sets of scale factors were tested: (1) a standard set derived from a training set of 30 organic molecules (set A), and (2) a set directly calibrated from the pyridazine molecule (set B). The calculations indicate that pyridazine and its chlorinated derivatives show less aromatic character than expected. The B3LYP exchange-correlation functional with the 6-31G* basis functions gave the most reliable structural parameters for both molecules. The a priori scaled spectra were sufficiently decisive to get a complete assignment of the vibrational spectra. Both series of scale factors led to similar results. However, although the standard set (set A) proved to be an useful tool to carry out the initial assignments, further detailed analysis of the spectra required specific empirical parameters derived from the pyridazine molecule. This was especially true for the most congested spectral areas.

Radial moments of the electron density: Gas phase results and the effects of solvation

The radial moments of the electron density, 〈rn〉, have been calculated for N2 and H2O at the quadratic configuration interaction (with singles and doubles) levels of theory by use of a variety of basis sets. An optimal basis set was chosen from the first set of calculations and then used with several conventional ab initio and density functional methods to compute the moments for a representative set of molecules: N2, CO, CH4, NH3, H2O, HF, SiH4, PH3, H2S, HCl, CH3OH, and CH3SH. The effects of solvation on the radial moments were also studied using the Onsager model and an extension of the Tomasi polarized continuum model.

Ab initio and density functional study of the geometrical, electronic and vibrational properties of 2,2?-bipyridine

The conventional ab initio method at the closed restricted Hartree–Fock level (RHF) and the Density Functional Theory (DFT) approach at the B3-LYP level, using the 6–31G(+*) basis set, are applied to predict the molecular structure and the energetic and vibrational properties (harmonic wavenumbers, force fields and potential energy distributions) of five isotopomers of the neutral molecule 2,2′-bipyridine (22BPY). The theoretical results are compared to the Raman and infrared vibrational data. Using both methods, there is a very good agreement between theory and experiment concerning not only the absolute wavenumbers, but also the isotopic shifts. This accordance allows us to validate the calculated structure of 22BPY. The neutral molecule 22BPY is characterized by an aromatic structure in which two pyridyl rings are linked by a single bond in a trans-planar conformation. From a methodological point of view, the B3-LYP method predicts more accurate structures and harmonic vibrational wavenumbers than the RHF method. Copyright © 2000 John Wiley & Sons, Ltd.

Calculation of dipole moment functions with density functional theory: application to vibrational band intensities

We have calculated fundamental and overtone XH stretching vibrational band intensities for H2O, benzene, cyclohexane, 1,3-butadiene, and HCN. The band intensities were calculated with a simple harmonically coupled anharmonic oscillator local mode model and a series expanded dipole moment function. The dipole moment functions were obtained from local, non-local and hybrid density functional theory calculations with basis sets ranging from 6–31G(d) to 6–311++G(3df,3pd). The calculated band intensities have been compared with intensities calculated with conventional ab initio methods and with experimental results. Compared with conventional correlated ab initio methods, a carefully chosen density functional method and basis set seems to give better fundamental and overtone intensities with far less resources used. We have found that the density functional methods appear to be less sensitive to the choice of basis set, with little difference between the results obtained with a non-local or hybrid density functional method.

Calculation of dipole moment functions with density functional theory: application to vibrational band intensities

We have calculated fundamental and overtone XH stretching vibrational band intensities for H2O, benzene, cyclohexane, 1,3-butadiene, and HCN. The band intensities were calculated with a simple harmonically coupled anharmonic oscillator local mode model and a series expanded dipole moment function. The dipole moment functions were obtained from local, non-local and hybrid density functional theory calculations with basis sets ranging from 6–31G(d) to 6–311++G(3df,3pd). The calculated band intensities have been compared with intensities calculated with conventional ab initio methods and with experimental results. Compared with conventional correlated ab initio methods, a carefully chosen density functional method and basis set seems to give better fundamental and overtone intensities with far less resources used. We have found that the density functional methods appear to be less sensitive to the choice of basis set, with little difference between the results obtained with a non-local or hybrid density functional method.

Favorable performance of the DFT methods in predicting the minimum-energy structure of the lowest triplet state of WF4

The tetrahedral structure of the lowest triplet state of the WF4 complex was examined using different variants of the density functional theory (DFT) and conventional ab initio methods. The low-level, conventional, ab initio methods, such as SCF, MP2, MP3, and CISD, predict the tetrahedral structure to be a minimum, whereas the DFT schemes predict an imaginary frequency for the e vibrational mode. Only after recovering electron correlation effects at the MP4 and higher levels, the conventional electronic structure methods also predict the Td structure to be a second-order stationary point. This is not the correlation but the exchange part of the DFT functionals which is responsible for the discrepancy between the DFT and low-level, conventional, ab initio predictions. The lowering of symmetry to C2v leads to a minimum on the lowest triplet potential energy surface and the electronic energy difference between the Td and C2v stationary points amounts to 0.85 and 0.96 kcal/mol at the B3LYP and CCSD(T) levels, respectively. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 369–375, 1999

Theoretical Study of the Mechanism of the Addition of Diazomethane to Ethylene and Formaldehyde. Comparison of Conventional ab Initio and Density Functional Methods

The 1,3-dipolar cycloaddition reactions of diazomethane with ethylene and formaldehyde as well as the nitrogen elimination reactions from the cycloadducts have been studied using density functional and conventional ab initio methods. The exothermicity of the reactions is underestimated by DFT methods with respect to CCSD(T) due to an overestimation of the C−N dissociation energy of diazomethane. For the cycloaddition reactions all methods lead to similar transition state geometries, and the potential energy barriers computed using DFT methods are similar to the CCSD(T) ones. On the other hand, for the nitrogen elimination reactions transition state geometries and energy barriers are more dependent on the level of calculation. The results obtained show that for the reaction between diazomethane and ethylene the pyrazoline intermediate is more stable than the reactants and that the Gibbs energy barrier for nitrogen elimination is larger than the barrier corresponding to its formation. On the contrary, for formaldehyde the kinetically most favorable cycloadduct, 1,2,3-oxadiazoline, is less stable than the reactants and has a lower barrier for nitrogen elimination.

Comparison of conventional ab initio and density functional methods for the ArHF interaction potential

The geometry and interatomic potential for the ground state of ArHF was determined by HF, MP2, MP4, QCISD and density functional theory (DFT) methods using 6-311G ∗∗ basis set. It was found that there is no agreement between conventional ab initio and DFf methods. Of the two possible conformers investigated in this study, ArHF complex is found to be more stable than the ArFH complex. The present study indicates that the calculated binding energy and geometrical parameters depend on the choice of various density functionals used in the DFT calculation. The results indicate that the 6-311G ∗∗ basis set is not sufficient to reproduce the experimental binding energy and geometry. Addition of diffuse and polarizable functions in the basis set may enhance the quality of prediction.

(Hyper)polarizability of chalcogenophenes C 4H 4X ( X = O, S, Se, Te) Conventional ab initio and density functional theory study

Equilibrium geometries, APT and NPA charge densities, dipole moments, and linear and quadratic polarizabilities of the five-membered chalcogenophenes C 4H 4X ( X = O, S, Se, Te) were calculated by means of the all-electron conventional ab initio and density functional theory methods (S-null, B3-null, S-VWN and B3-LYP) using the specifically optimized Dougherty-Spackman and Sadlej basis sets. Very good agreement is found between theoretical and available experimental data. The results highlight the heteroatom and electron correlation effects on the molecular properties. Both linear and quadratic dipole polarizabilities increase steadily as the atomic number increases, the trend along the series being dominated by the heteroatom property and by the stability of the molecule. Possible correlations between dipole (hyper)polarizability and aromaticity, hardness, and electronic structure were investigated and briefly discussed. The exaltation polarizability parameter τ, a possible new aromaticity index, together with atomization energy evaluations, suggest that, in addition to molecular size effects, thermodynamic stability factors determine the average dipole polarizability values.

Benchmark ab initio potential curves for the light diatomic hydrides. Unusually large nonadiabatic effects in BeH and BH

In order to assess the relative importance of the intrinsic error in high-level conventional ab initio methods and errors inherent in the Born–Oppenheimer approximation, benchmark quality potential curves and spectroscopic constants have been computed for the light diatomic hydrides H 2, LiH, BeH, and BH. The intrinsic error is found to be comparable to or smaller than the nonadiabatic effects. Revised spectroscopic constants are proposed for BeH. BH is predicted to have an unusually large nonadiabatic contribution of about 0.0025 Å to its bond length. Previous arguments favoring the use of atomic rather than nuclear masses are further corroborated.

Coordination of NO2 to Alkaline-Earth Metals. A Theoretical Study

The structure and harmonic vibrational frequencies have been determined for the alkaline-earth metal MNO2 systems (M = Be, Mg, Ca, and Sr) using the B3LYP method. Binding energies have also been calculated using conventional ab initio methods, CCSD(T), and MCPF, with different basis sets. Four different coordination modes of NO2 to the metal have been considered. The C2v η2-O,O coordination mode is the most stable one for all metals. However, for BeNO2 the ground state is a 2B1 state while for the other metals the 2A1 state is the most stable one. Our best estimates for the D0 binding energies are 77 kcal mol-1 for BeNO2, 53 kcal mol-1 for MgNO2, 69 kcal mol-1 for CaNO2, and 71 kcal mol-1 for SrNO2.

A challenge for density functional theory: the XONO and XNO 2 (X=F, Cl, and Br) molecules

The equilibrium geometries, harmonic frequencies, dipole moments, infrared intensities, and relative energies of the cis-XONO, trans-XONO, and XNO2 (X=F, Cl, and Br) have been investigated using four functionals in common use in Kohn-Sham density functional theory (DFT) calculations. Two of the functionals include non-local or gradient correction terms, while the other two also incorporate some exact Hartree-Fock exchange and are labeled hybrid functionals. The quality of the results obtained from the functionals is determined by comparison to previously published high-level coupled-cluster calculations. The hybrid functionals perform better for prediction of the equilibrium geometries, where the two gradient corrected functionals yield qualitatively incorrect molecular structures for cis-FONO and cis-ClONO. None of the functionals perform well in predicting all six harmonic frequencies, showing that the correlation between equilibrium geometries and harmonic frequencies is not as strong for these DFT methods as it is for conventional wavefunction ab initio methods, such as coupled-cluster theory. Results from the various functionals generally come into better agreement with each other and also with the coupled-cluster results moving down the periodic table.

An elongation method to calculate the electronic structure of non-periodical and periodical polymers

To calculate the electronic structure of non-periodical polymers, we developed a novel molecular orbital method, which we call the elongation method. When this new method is incorporated into existing molecular orbital methods, such as ab intio molecular orbital method, the computation time decreases substantially, without sacrificing reliability. This new method has two steps, localization and elongation, and thus simulates the process of polymerization reaction. First, we briefly describe the localization and elongation steps. Then, we describe the results from applying the ab initio elongation molecular orbital method (a combination of the two methods) to three poly-hydrogen bonding systems, (H 2O) n, (HF) n, and (HCONH 2) n. For all three systems, there was excellent agreement in obtained total energy and electron density compared with those calculated using the conventional ab initio molecular orbital method. Finally, this elongation method was incorporated into the PM3 method and used to calculate the electronic structure of the physiologically active oligopeptide, galanine with 30 amino acid residues. Again, the obtained total energy and the electron density agreed with those calculated by the conventional PM3 method. These results confirm that the elongation method is reliable and can be applied to a variety of huge systems such as proteins and nucleic acids by using various types of molecular orbital theory.