The exchange-correlation potential in ab initio density functional theory

From coupled-cluster theory and many-body perturbation theory we derive the local exchange-correlation potential of density functional theory in an orbital dependent form. We show the relationship between the coupled-cluster approach and density functional theory, and connections and comparisons with our previous second-order correlation potential [OEP-MBPT(2) (OEP-optimized effective potential)] [I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett, J. Chem. Phys. 116, 4415 (2002)]. Starting from a general theoretical framework based on the density condition in Kohn-Sham theory, we define a rigorous exchange-correlation functional, potential and orbitals. Specifying initially to second-order terms, we show that our ab initio correlation potential provides the correct shape compared to those from reference quantum Monte Carlo calculations, and we demonstrate the superiority of using Fock matrix elements or more general infinite-order semicanonical transformations. This enables us to introduce a method that is guaranteed to converge to the right answer in the correlation and basis set limit, just as does ab initio wave function theory. We also demonstrate that the energies obtained from this generalized second-order method [OEP-MBPT2-f] and [OEP-MBPT2-sc] are often of coupled-cluster accuracy and substantially better than ordinary Hartree-Fock based second-order MBPT=MP2.     

Fundamental vibrational frequencies and dominant resonances in methylamine isotopologues by ab initio and density functional theory methods

Ab initio and density functional theory (DFT) calculations were performed for obtaining fundamental vibrational frequencies of methylamine, CH3NH2, and its deuterated variants CH3ND2, CD3NH2, and CD3ND2. The calculations were carried out using the CCSD(T) coupled cluster approximation with cc-pVTZ and cc-pVQZ basis sets, and by the DFT method with the semiempirical hybrid functional B97-1 with polarization consistent pc-2 and pc-3 basis sets. Reasonable performance of the DFT harmonic and ab initio harmonic calculations was found, which improved considerably upon combination of the harmonic fundamental frequencies with anharmonic corrections from the smaller, pc-2, basis. The computed anharmonic fundamental frequencies of methylamine isotopologues agree very well with the experimental values and represent a useful tool for assignment and analysis of the dominant resonances.     

Calculation of bond dissociation energies for oxygen containing molecules by ab initio and density functional theory methods

Two ab initio (ROHF and MP2), one local (SVWN), four hybrid (BHandH, BHandHLYP, Becke3LYP, and Becke3P86), and two nonlocal (BLYP and BP86) density functional theory (DFT) methods are used for calculating the dissociation energies of molecules that contain H(SINGLE BOND)O, O(SINGLE BOND)O and O(SINGLE BOND)C bonds. The sensitivity to the basis set of the prediction of bond dissociation energies with DFT methods was tested with Becke3LYP on the H(SINGLE BOND)O dissociation energy of water. The 6–31 + G(d) methods are chosen as the smallest basis set which produces reasonable results. The calculated values for all other ab initio and DFT methods were performed with these basis sets and then compared with the experimental data. The suitability of DFT methods for computing reliable bond dissociation energies of oxygen containing molecules is discussed. © 1996 John Wiley & Sons, Inc.     

Theoretical studies on nonlinear optical properties of formaldehyde oligomers by ab initio and density functional theory methods

The first and second hyperpolarizability beta and gamma are obtained for formaldehyde oligomers (H2CO)n (n = 1-7) using computational methods. We have used the finite field (FF) approach and hyperpolarizability density analysis (HDA) to predict the microscopic first and second nonlinear hyperpolarizability of the formaldehyde oligomers. The spatial contributions of electrons to the hyperpolarizability by using plots of HDA are presented. It has been found from the numerical stability checking of the hyperpolarizability calculations that the calculated values by FF method are more stable than those by HDA approach. The values of beta are zero when n is even as the molecule possesses centrosymmetry, and when n is odd, the differences among beta values are not clear. The gamma values are increased with increase in n.     

An ab initio and density functional theory study of radical-clock reactions

Density functional theory (DFT) and ab initio (CBS-RAD) calculations have been used to investigate a series of "radical clock" reactions. The calculated activation energies suggest that the barriers for these radical rearrangements are determined almost exclusively by the enthalpy effect with no evidence of significant polar effects. The ring-closure reactions to cyclopentylmethyl radical derivatives and the ring opening of cyclopropylmethyl radicals give different correlations between the calculated heat of reaction and barrier, but the two types of reaction are internally consistent.     

Study of the formamide–methanol dimer with ab initio and density functional theory methods

For the first time, the structures and energies for the hydrogen bonding of a 1:1 complex formed between formamide and methanol molecules have been computed with various pure and hybrid density functional theory (DFT) and ab initio methods at varied basis set levels from 6‐31g to 6‐31+g(d,p). Five reasonable geometries on the potential energy surface of methanol and formamide system are considered and their relative stability is discussed. The infrared (IR) spectrum frequencies, IR intensities, and vibrational frequency shifts are reported. From the systematic studies, it is found that all the DFT methods selected here correctly compute the dimerization energies and geometries, with the B3P86 method predicting the hydrogen bond lengths relatively shorter and BPW91 yielding the interaction energies relatively lower. Finally, the solvent effects on the geometries of the formamide–methanol complexes have also been investigated using self‐consistent reaction field (SCRF) calculations with five different DFT methods at the 6‐31+g(d,p) basis set level. The results indicate that the polarity of the solvent has played an important role on the structures and relative stabilities of different isomers. Moreover, the basis set superposition error correction is critical to the interaction energies in the polar solvents. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Computation of bond dissociation energy for sulfides and disulfides with ab initio and density functional theory methods

The geometries and S-H, S-S, and S-C bond dissociation energies for hydrogen sulfide, hydrogen disulfide, methanethiol, dimethyl disulfide, and dimethyl disulfide were calculated with both ab initio (ROHF and MP2), hybrid (BHandH, BHandHLYP, Becke3LYP and Becke3P86), and nonlocal (BLYP and BP86) density functional theory (DFT) methods. In all studies the 6–31 + G(d) basis set is used. The computed results are compared to the experimentally obtained values, targeting the selection of a suitable ab initio or DFT method for the study of these systems. © 1997 John Wiley & Sons, Inc.     

Carbohydrate-protein recognition probed by density functional theory and ab initio calculations including dispersive interactions

Carbohydrate-protein recognition has been studied by electronic structure calculations of complexes of fucose and glucose with toluene, p-hydroxytoluene and 3-methylindole, the latter aromatic molecules being analogues of phenylalanine, tyrosine and tryptophan, respectively. We use mainly a density functional theory model with empirical corrections for the dispersion interactions (DFT-D), this method being validated by comparison with a limited number of high level ab initio calculations. We have calculated both binding energies of the complexes as well as their harmonic vibrational frequencies and proton NMR chemical shifts. We find a range of minimum energy structures in which the aromatic group can bind to either of the two faces of the carbohydrate, the binding being dominated by a combination of OH-pi and CH-pi dispersive interactions. For the fucose-toluene and alpha-methyl glucose-toluene complexes, the most stable structures involve OH-pi interactions, which are reflected in a red shift of the corresponding O-H stretching frequency, in good quantitative agreement with experimental data. For those structures where CH-pi interactions are found we predict a corresponding blue shift in the C-H frequency, which parallels the predicted proton NMR shift. We find that the interactions involving 3-methylindole are somewhat greater than those for toluene and p-hydroxytoluene.     

Vibrational spectroscopy investigation using ab initio and density functional theory on p-anisaldehyde

The FTIR and FT Raman spectra of p-anisaldehyde has been recorded in the regions 4,000-400 and 3,500-100 cm(-1), respectively. The optimized geometry, frequency and intensity of the vibrational bands of p-anisaldehyde were obtained by ab initio and DFT levels of theory with complete relaxation in the potential energy surface using 6-31G(d,p) basis set. A complete vibrational assignment aided by the theoretical harmonic frequency analysis has been proposed. The harmonic vibrational frequencies calculated have been compared with experimental FTIR and FT Raman spectra. The observed and the calculated frequencies are found to be in good agreement. The experimental spectra also coincide satisfactorily with those of theoretically constructed bar type spectrograms.     

Molecular structure and vibrational spectra of phenobaraitone by density functional theory and ab initio hartree-Fock calculations

Quantum chemistry calculations have been performed using Gaussian03 program to compute optimized geometry, harmonic vibrational frequency along with intensities in IR and Raman spectra at RHF/6-31++G** and B3LYP/6-31++G** levels for phenobarbitone (C₁₂H₁₂N₂O₃) in the ground state. The scaled harmonic vibrational frequencies have been compared with experimental FT-IR and FT-Raman spectra. Theoretical vibrational spectra of the title compound were interpreted by means of potential energy distributions (PEDs) using MOLVIB program. A detailed interpretation of the infrared spectra of the title compound is reported. On the basis of the agreement between the calculated and observed results, the assignments of fundamental vibrational modes of phenobarbitone were examined and some assignments were proposed. The theoretical spectrograms for FT-IR and FT-Raman spectra of the title compound have been constructed.     

Comparison of ab initio and density functional methods for vibrational analysis of TeCl4

Vibrational analysis of tellurium tetrachloride, TeCl₄, was performed with Hartree–Fock (HF), MP2, and generalized gradient approximation density functional theory (DFT) methods supplemented with polarized double-zeta split valence (DZVP) basis sets and relativistic effective core potentials (RECP) of Hay and Wadt. The molecular geometry is best reproduced at the HF and MP2/RECP+DZVP [polarized Hay and Wadt RECP for Te and 6–31G(d) basis set for Cl] levels of theory. The DFT methods gave rise to poorer results, especially those using Becke's 1988 exchange functional. Generally, the vibrational frequencies calculated by the MP2 and B3-type DFT methods with the all electron and RECP+DZVP basis sets as well as at the HF/RECP level were in satisfactory accord with the experimental data. The agreement was good enough to assist the assignment of the measured vibrational spectra. The best agreement with the experimental vibrational frequencies was achieved with the scaled HF/RECP force field. Consistent results were obtained for the unobserved A₂ (ν₄) fundamental, where the results of the best methods were within 4 cm⁻¹. The best force fields were obtained with the following methods: Becke3–Lee–Yang–Parr and Becke3–Perdew/all electron basis, MP2 and Becke3-Perdew/RECP+DZVP, and HF/RECP. The methods using RECPs are advantageous for large-scale computations. The RECP basis set effectively compensates the errors of the HF method for TeCl₄; however, it provides poor results with correlated methods. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 308–318, 1998     

Metahybrid density functional theory and correlated ab initio studies on microhydrated adenine-thymine base pairs

Monohydrated and dihydrated adenine-thymine base pairs are characterized using metahybrid density functional theory and correlated ab initio approaches. The motivation of this work is twofold. First, the high-level geometries and interaction energies computed for different complexes serve as a reference for the testing of recently developed density functional theory (DFT) with respect to its ability to correctly describe the balance between the electrostatic and the dispersion contributions that bind these complexes. Second, these studies of nucleic acid base pairs are important for finding binding sites of water molecules around bases and for a better understanding of the influence of the solvent on the stability of the structure of DNA duplexes.     

Vibrational spectra and assignments of 2-amino-5-iodopyridine by ab initio Hartree-Fock and density functional methods

The Fourier transform Raman and Fourier transform infrared spectra of 2-amino-5-iodopyridine were recorded in the solid phase. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities were calculated by HF and DFT (B3LYP) methods with the 6-31G(d,p) basis set for C, N, H and LANL2DZ pseudopotential for I. The scaled theoretical wavenumbers showed very good agreement with the experimental ones. A detailed interpretation of the infrared and Raman spectra of 2-amino-5-iodopyridine is reported on the basis of the calculated potential energy distribution. The theoretical spectrograms for the IR spectrum of the title molecule have been constructed.     

Differences between ab initio and density functional electron densities

We analyzed the energy contributions and the spatial distribution differences of several electron densities of atoms and small molecules. The results show the insensitivity of local spin density correlation functionals in respect to differences in the electron densities. On the other hand, significant changes in one-electron and two-electron energy contributions are observed, although both compensate each other. The projection of the differences between these electron densities, referred to as the Hartree-Fock density, shows a qualitative resemblance between multideterminantal and Kohn-Sham wavefunctions. Finally, a comparative analysis of the optimized conformational parameters obtained using several methods shows that the inclusion of the correlation energy in SCF or in post-SCF procedures gives similar results and that the exchange potential is more important than is the correlation potential to improve these conformational parameters. © 1997 John Wiley & Sons, Inc.     

Dissociation of sulfur oxoacids by two water molecules studied using ab initio and density functional theory calculations

Using ab initio [SCS‐MP2 and CCSD(T)] and density functional theory (M062X) calculations, we have studied the geometries and energies of sulfur oxoacids H₂S_mO₆ (m = 2–4) and their monohydrated and dihydrated clusters. When including the results from previously reported disulfuric acid (H₂S₂O₇) cases, the gas phase acidity is ordered as H₂S₂O₆ < H₂S₃O₆ < H₂S₂O₇ < H₂S₄O₆. The intramolecular H‐bonding, which may indicate the degree of structural flexibility in this molecular series, is an important factor for the order of the gas phase acidity. All these sulfur oxoacids show dissociated (or deprotonated) geometries with only two water molecules, although the energies of the dissociated conformers are ranked differently. All of the dissociated conformers form a unique H‐bonding network structure in which the protonated first water (H₃O⁺) is triply H‐bonded to each oxygen atom of two SO₃ moieties as well as the second water, which in turn is H‐bonded to a SO₃ moiety. H₂S₃O₆ has the best molecular flexibility for adopting such an H‐bonding network structure, and thereby all the low‐lying conformers of H₂S₃O₆(H₂O)₂ are dissociated. In contrast, the least flexible H₂S₂O₆ forms such a structure with a high strain, and dissociation of H₂S₂O₆(H₂O)₂ is found from the third lowest conformer. Although the gas phase acidity of H₂S₄O₆ is the highest in this series, the lowest dissociated conformer and the lowest undissociated conformer of H₂S₄O₆(H₂O)₂ are very close in energy. This is because forming the H‐bonding network structure is somewhat difficult due to the large distance between the two SO₃ moieties.     

Formation of 2-hexene by cationic dimerization of propene: an ab initio and density functional theory study

The formation of a 2-hexene radical cation from a propene radical cation and a neutral propene molecule is investigated by means of ab initio UHF and spin projected MP2 calculations, as well as the SVWN and B3LYP levels of density functional theory. A stable addition complex, with loose CC bonds, is found. To proceed from the addition complex to the product, a locally planar transition state must be passed, with a migrating hydrogen located half-way between the donating and the accepting carbon atoms. At the highest computational levels considered, PMP2/6-31G(d,p)//MP2/3-21G and B3LYP/6-31G(d,p), this transition state lies approximately 11 and 13 kcal/mol, respectively, above the addition complex. The high barrier is believed to be one reason why radical cation oligomerization of propene has not been detected experimentally, in contrast to the case of ethene, where the corresponding barrier is only a few kcal/mol. Received: 17 December 1996 / Accepted: 12 May 1997     

Halide adsorption on single-crystal silver substrates: dynamic simulations and ab initio density functional theory

We investigate the static and dynamic behaviors of a Br adlayer electrochemically deposited onto single-crystal Ag(100) using an off-lattice model of the adlayer. Unlike previous studies using a lattice-gas model, the off-lattice model allows adparticles to be located at any position within a two-dimensional approximation to the substrate. Interactions with the substrate are approximated by a corrugation potential. Using density functional theory (DFT) to calculate surface binding energies, a sinusoidal approximation to the corrugation potential is constructed. A variety of techniques, including Monte Carlo and Langevin simulations, are used to study the behavior of the adlayer. The lateral root-mean-square (rms) deviation of the adparticles from the binding sites is presented along with equilibrium coverage isotherms, and the thermally activated Arrhenius barrier-hopping model used in previous dynamic Monte Carlo simulations is tested.