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.     

An ab initio study on the equilibrium structure and torsional potential energy function of dinitrogen tetroxide

The molecular parameters of dinitrogen tetroxide, N₂O₄, have been determined in large-scale ab initio calculations using the multiconfigurational second-order perturbation method, CASSCF/CASPT2, and basis sets of double- to quadruple-zeta quality. With the largest basis set employed, cc-pVQZ for nitrogen and cc-pVTZ for oxygen, the structural equilibrium parameters are determined to be r(NN) = 1.7940 Å, r(NO) = 1.1906 Å and (NNO) = 112.55°. The potential energy barrier at the staggered conformation of the molecule is found to be 2313 cm⁻¹, and the binding energy of the NN bond is calculated to be 4616 cm⁻¹ (13.2 kcal/mol).     

Equilibrium structure of the carbon dioxide-water complex in the gas phase: an ab initio and density functional study

High-level ab initio (MP2/6-311++G(2d,2p) geometry, Gaussian-2, MP4(SDTQ) and QCISD(T) binding energies) and density-functional (Becke3LYP/6-311++G(2df,2pd)) calculations have been performed on the charge-transfer complex between water and carbon dioxide. The complex appears to have two equivalent non-planar minima of C_s symmetry. Minima are separated by transition states with C₁ symmetry, whereas the totally planar structure with C_2v symmetry is a second-order transition state. All the critical points lie at approximately the same energy (less than 0.05 Kj mol⁻¹ difference). Therefore, the experimentally observable structure should be planar. The best equilibrium intermolecular distance for this complex calculated at the MP2/6-311++G(2d,2p) level is 2.800 Å. Our best estimate of the observable intermolecular distance (corrected for anharmonicity) is 2.84 Å, in agreement with the experimentally derived value of 2.836 Å. Our best estimate of the binding energy at the QCISD(T) level, taking into account the variation of the distance owing to anharmonicity and the use of more sophisticated theoretical treatments, is −12.0 ± 0.2 kJ mol⁻¹. Our best estimate of the barrier to internal rotation, also at the MP2/6-311++G(2d,2p) level, is 4.0 kJ mol⁻¹, outside the error limits of the experimental determination (3.64 ± 0.04 kJ mol⁻¹). Density functional theory at the level employed here gives an equilibrium intermolecular distance that is too large (2.857 Å), a binding energy that is too small (8.1 kJ mol⁻¹), attributable neither to geometry nor to the basis set, and also a barrier to internal rotation that is slightly too small (3.39 kJ mol⁻¹). The overall picture is, however, reasonably good.     

An ab initio and density functional theory study of the structure and bonding of sulfur ylides

Sulfur ylides are useful synthetic intermediates that are formed from the interaction between singlet carbenes and sulfur-containing molecules. Partial double-bond character frequently has been proposed as a key contributor to the stability of sulfur ylides. Calculations at the B3LYP, MP2, and CCSD(T) levels of theory employing various basis sets have been performed on the sulfur ylides H(2)S-CH(2) and (CH(3))(2)S-CH(2) in order to investigate the structure and bonding of these systems. The following general properties of sulfur ylides were observed from the computational studies: C-S bond distances that are close in length to that of a typical C-S double bond, high charge transfer from the sulfide to the carbene, and large torsional rotation barriers. Analysis of the sulfur ylide charge distribution indicates that the unusually short C-S bond distance can be attributed in part to the electrostatic attraction between highly oppositely charged carbon and sulfur atoms. Furthermore, n --> sigma* stabilization arising from donation of electron density from the carbon lone pair orbital into S-H or S-C antibonding orbitals leads to larger than expected torsional barriers. Finally, natural resonance theory analysis indicates that the bond order of the sulfur ylides H(2)S-CH(2) and (CH(3))(2)S-CH(2) is 1.4-1.5, intermediate between a single and double bond.     

Dimers, trimers and oligomers of sulfur oxides: an ab initio and density functional study

Ab initio (HF/3-21G^*), DFT (B3LYP with basis sets 6-31G^*, 6-311+G^* and 6-311+G(2d)) and, in some cases, MP2/6-31G^* calculations, were done on cyclic dimers, trimers, etc. and on acyclic oligomers (with OH and H on the ends) of sulfur monoxide and sulfur dioxide. The four cyclic (SO)_n molecules were (S–O)₂ (1,3,2,4-dioxadithietane, 1a), (S–O)₃ (1,3,5,2,4,6-trioxatrithiane, 2a), (S(=O))₄ (tetrathietane 1,2,3,4-tetraoxide, 1b), and (S(=O))₆ (hexathiane 1,2,3,4,5,6-hexaoxide, 2b). The four cyclic (SO₂)_n molecules were the dioxide of 1a (1,3,2,4-dioxadithietane 2,4-dioxide, 1c), the trioxide of 2a (1,3,5,2,4,6-trioxatrithiane 2,4,6-trioxide, 2c), the tetraoxide of 1b (tetrathietane 1,1,2,2,3,3,4,4-octaoxide, 1d) and the hexaoxide of 2b (hexathiane 1,1,2,2,3,3,4,4,5,5,6,6-dodecaoxide, 2d). The 16 acyclic molecules (oxides of disulfane, trisulfane, etc. and oxides of oxadisulfane, dioxatrisulfane, etc.) were (–S–O–)_n, (–S(=O)–)_n, (–S(=O)O–)_n, and (–S(=O)₂–)_n, with n from 2 to 5 and HO, H at the ends. Most of these species are relative minima on the B3LYP/6-31G^* potential energy surface. In energy content, the SO dimer, etc. lie below, and the SO₂ dimer, etc. above, their SO_x components, at all the electron-correlated levels.     

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.     

The structure of 1-chlorosilatrane: An ab initio molecular orbital and a density functional theory study

The molecular geometries of the 1-chloro-, 1-fluoro-, 1-methyl-, and 1-hydrogenosilatranes were fully optimized by the restricted Hartree-Fock (HF) method supplemented with 3-21G, 3-21G(d), 6-31G(d), and CEP-31G(d) basis sets; by MP2 calculations using 6-31G(d) and CEP-31G(d) basis sets; and by GGA-DFT calculations using 6-31G(d5) basis set with the aim of locating the positions of the local minima on the energy hypersurface. The HF/6-31G(d) calculations predict long (>254 pm) and the MP2/CEP calculations predicted short (∼225 pm) equilibrium Si(SINGLE BOND)N distances. The present GGA-DFT calculations reproduce the available gas phase experimental Si(SINGLE BOND)N distances correctly. The solid phase experimental results predict that the Si(SINGLE BOND)N distance is shorter in 1-chlorosilatrane than in 1-fluorosilatrane. In this respect the HF results show a strong basis set dependence, the MP2/CEP results contradict the experiment, and the GGA-DFT results in electrolytic medium agree with the experiment. The latter calculations predict that 1-chlorosilatrane is more polarizable than 1-fluorosilatrane and also support a general Si(SINGLE BOND)N distance shortening trend for silatranes during the transition from gas phase to polar liquid or solid phase. The calculations predict that the ethoxy links of the silatrane skeleton are flexible. Consequently, it is difficult to measure experimentally the related bond lengths and bond and torsion angles. This is the probable origin of the surprisingly large differences for the experimental structural parameters. On the basis of experimental analogies, ab initio calculations, and density functional theory (DFT) calculations, a gas phase equilibrium (r_e) geometry is predicted for 1-chlorosilatrane. The semiempirical methods predict a so-called exo minimum (at above 310 pm Si(SINGLE BOND)N distance); however, the ab initio and GGA-DFT calculations suggest that this form is nonexistent. The GGA-DFT geometry optima were characterized by frequency analysis. © 1996 by John Wiley & Sons, Inc.     

Molecular structure,conformational mobility,vibrational spectra,and thermochemistry of peroxyacetic acid: an ab initio and density functional study

The structure of the peroxyacetic acid (PAA) molecule and its conformational mobility under rotation about the peroxide bond was studied by ab initio and density functional methods. The free rotation is hindered by the trans-barrier of height 22.3 kJ mol^–1. The equilibrium molecular structure of AcOOH (C _s symmetry) is a result of intramolecular hydrogen bond. The high energy of hydrogen bonding (46 kJ mol^–1 according to natural bonding orbital analysis) hampers formation of intermolecular associates of AcOOH in the gas and liquid phases. The standard enthalpies of formation for AcOOH (–353.2 kJ mol^–1) and products of radical decomposition of the peroxide — AcO^· (–190.2 kJ mol^–1) and AcOO^· (–153.4 kJ mol^–1) — were determined by the G2 and G2(MP2) composite methods. The O—H and O—O bonds in the PAA molecule (bond energies are 417.8 and 202.3 kJ mol^–1, respectively) are much stronger than in alkyl hydroperoxide molecules. This provides an explanation for substantial contribution of non-radical channels of the decomposition of peroxyacetic acid. The electron density distribution and gas-phase acidity of PAA were determined. The transition states of the ethylene and cyclohexene epoxidation reactions were located (E _a = 71.7 and 50.9 kJ mol^–1 respectively).     

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     

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.     

Homopairing possibilities of the DNA base thymine and the RNA base uracil: an ab initio density functional theory study

All planar homopairings of the DNA base thymine and the RNA base uracil are reported for the first time in this study. Using the idea of binding sites discussed in our previous work (Kelly et al. J. Phys. Chem. B 2005, 109, 11933; J. Phys. Chem. B 2005, 109, 22045) and ab initio density functional theory, we predict and relax 10 thymine and 10 uracil homopairs. The stabilization energies of the homopairs vary from just below zero to -0.82 eV. The results on the pair geometry and energetics are compared with those available in the literature. The collected data on all planar thymine and uracil homopairs can be used to construct the thymine and uracil superstructures seen experimentally on various surfaces.     

Structural, energetic and response electric properties of cyclic selenium clusters: an ab initio and density functional theory study

A formal derivation of the nuclear-ensemble method for absorption and emission spectrum simulations is presented. It includes discussions of the main approximations employed in the method and derivations of new features aiming at further developments. Additionally, a method for spectrum decomposition is proposed and implemented. The method is designed to provide absolute contributions of different classes of states (localized, diffuse, charge-transfer, delocalized) to each spectral band. The methods for spectrum simulation and decomposition are applied to the investigation of UV absorption of benzene, furan, and 2-phenylfuran, and of fluorescence of 2-phenylfuran.     

Vibrational spectra and assignments using ab initio and density functional theory analysis on the structure of biotin

Density functional theory (DFT) and Hartree-Fock calculations were performed using the following models: HF/6-311G(d), B3LYP/6-311G(d), B3LYP/6-311+G(d) and B3PW91/6-311G(d) calculations were performed for biotin. It has been characterized by IR and X-ray. The calculated results show that the predicted geometry can well reproduce the structural parameters. Predicted vibrational frequencies have been assigned and compared with experimental IR spectra and they supported each other. On the basis of vibrational analyses, the thermodynamic properties of the title compound at different temperatures have been calculated, revealing the correlations between Cp,m degrees, Sm degrees, Hm degrees and temperatures.     

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.     

Vibrational spectroscopy investigation using ab initio and density functional theory analysis on the structure of 5-amino-o-cresol

The Fourier transform Raman and Fourier transform infrared spectra of 5-amino-o-cresol (5AOC) were recorded in the solid phase. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities were calculated by HF and density functional B3LYP method with the 6-311G(d,p) basis set. The scaled theoretical wavenumbers showed very good agreement with the experimental values. The thermodynamic functions of the title compound were also performed at HF/6-311G(d,p) and B3LYP/6-311G(d,p) levels of theory. A detailed interpretation of the infrared and Raman spectra of 5-amino-o-cresol is reported. The theoretical spectrograms for FT-IR spectra of the title molecule have been constructed.     

Vibrational spectroscopy investigation using ab initio and density functional theory analysis on the structure of 3-aminobenzotrifluoride

In this work, we will report a combined experimental and theoretical study on molecular and vibrational structure of 3-aminobenzotrifluoride. The FT-Raman and Fourier transform infrared spectra of 3-aminobenzotrifluoride (3ABTF) were recorded in the liquid phase. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities, depolarization ratios, reduced masses were calculated by HF and density functional B3LYP method with the 6-31G(d,p) and 6-311G(d,p) basis sets. The scaled theoretical wavenumbers showed very good agreement with the experimental values. The thermodynamic functions of the title compound were also performed at HF/6-31G(d,p)/6-311G(d,p) and B3LYP/6-31G(d,p)/6-311G(d,p) levels of theory. A detailed interpretations of the infrared and Raman spectra of 3ABTF is reported. The theoretical spectrograms for FT-IR spectra of the title molecule have been constructed.     

Vibrational spectroscopy investigation using ab initio and density functional theory analysis on the structure of 3,4-dimethylbenzaldehyde

The FT-IR and FT-Raman spectra of 3,4-dimethylbenzaldehyde (3,4-DMB) has been recorded in the region 4000-400 and 3500-100 cm(-1), respectively. The optimized geometry, frequency and intensity of the vibrational bands of 3,4-DMB were obtained by the ab initio and DFT levels of theory with complete relaxation in the potential energy surface using 6-311G(d,p) basis set. The harmonic vibrational frequencies were calculated and the scaled values have been compared with experimental FT-IR 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.     

Tautomerism and infrared spectra of 2-thiopurine: an experimental matrix isolation and theoretical ab initio and density functional theory study

Infrared spectra of 2-thiopurine (2-mercaptopurine, 2-purinethiol ) isolated in low-temperature Ar and N2 matrixes are reported. These spectra indicate that the compound adopts exclusively the thiol N9H tautomeric form. The theoretical calculations of relative energies of 2-thiopurine tautomers have been carried out at the MP4(SDTQ)//HF level using the 6-31G(d,p) basis set. The thiol N9H tautomer was predicted to be the most stable of all isomers of 2-thiopurine. The infrared spectra of the tautomers of 2-thiopurine have been calculated at the DFT(B3LYP)/6-31G(d,p) level. Good agreement between the experimental spectra and the spectra calculated for thiol N9H tautomer supported the identification of the dominant tautomer. It has also allowed for the reliable assignment of the bands observed in the experimental IR spectrum.     

Torsion potentials and electronic structure of trifluoromethoxy- and trifluoromethylthiobenzene: an ab initio study

Potential functions of internal rotation about the C_sp²X bonds in molecules C₆H₅XCF₃ (X=O, S) were calculated at the second-order Møller-Plesset perturbation level of theory with 6-31G(d) basis set. The profile of the potential function and the rotation barrier (ΔE^#=3.0 kJ/mol) found for C₆H₅OCF₃ suggest that, depending on experimental conditions, there can be either free rotation about the C_sp²O bond or the conformational equilibrium is shifted to the side of the orthogonal form. The rotational barrier for C₆H₅SCF₃ is 14.7 kJ/mol and the molecule exists in the stable orthogonal conformation. The nature of hybridization, energy and population of lone electron pairs (LPs) on the oxygen and sulfur atoms were considered by using the Natural Bond Orbital (NBO) method. The energy of interactions of the LPs with antibonding π^∗-orbitals of the aromatic moiety were estimated for different conformations. The distribution of electron density in the molecules was discussed. The results were compared with analogous calculations on the molecules C₆H₅XCH₃.