The computation of the potential energy surface for H2 + OH → H2O + H using ab initio and density functional theory methods

The reaction energy profile for H₂ + OH → H + H₂O was computed using HF, MP2, MP4, QCISD, G1, G2, and G2MP2 ab initio methods. In addition, the B3LYP, B3P86, B3PW91, BLYP, BP291, and SVWN density functional theory (DFT) methods were also used. All the ab initio methods, with the exception of the G series, produced much higher activation barriers and heats of reaction than the experimental values. On the other hand, the DFT methods produced negative forward and reverse barriers which were too low, with the exception of the hybrid DFT methods. The G2 ab initio method generated energies which deviated from the experimental values by ∼ 1 kcal/mol and therefore should be considered a very accurate computational method. The hybrid DFT methods produced positive forward reaction barriers with energies that were 2–4 kcal/mol lower than the experimental values. The geometries of the transition state and energies computed by the ab initio and DFT methods were compared. These results suggest that, in the hybrid exchange functional, the portion of the Slater exchange term should be increased. This may be the reason why the computed energies were too low. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 639–644, 1997     

Water trimer cation

By using density functional theory (DFT) and high-level ab initio theory, we have investigated the structure, interaction energy, electronic property, and IR spectra of the water trimer cation [(H₂O) ₃ ⁺ ]. Two structures of the water trimer cation [the H₃O⁺ containing linear (3Lp) structure versus the ring (3OO) structure] are compared. For the complete basis set (CBS) limit of coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)], the 3Lp structure is 11.9?kcal/mol more stable than the 3OO structure. This indicates that the ionization of water clusters produce the hydronium cation moiety (H₃O⁺) and the hydroxyl radical. It is interesting to note that the calculation results of the water trimer cation vary seriously depending on the calculation level. At the level of M?ller?CPlesset second-order perturbation (MP2) theory, the stability of 3OO is underestimated due to the underestimated O??O hemibonding energy. This stability is also underestimated even for the CCSD(T) single point calculations on the MP2-optimized geometry. For the 3OO structure, the MP2 and CCSD(T) calculations give closed-ring structures with a hemi-bond between two O atoms, while the DFT calculations show open-ring structures due to the overestimated O??O hemibonding energy. Thus, in order to obtain reliable stabilities and frequencies of the water trimer cation, the CCSD(T) geometry optimizations and frequency calculations are necessary. In this regard, the DFT functionals need to be improved to take into account the proper O??O hemibonding energy.     

SCF,MP2, and CEPA-1 calculations on the OH ‥ O hydrogen bonded complexes (H2O)2 and (H2O-H2CO)

Counterpoise corrected ab initio calculations are reported for (H₂O)₂ and H₂O-H₂CO. Geometry searches were done in the moment-optimized basis DZP' at the SCF, MP2, and CEPA-1 levels of theory, followed by more accurate single-point calculations in basis ESPB, which includes bondfunctions to saturate the dispersion energy. The final equilibrium binding energies obtained are ?4.7 ±0.3 kcal/mol for a near-linear (H₂O)₂ structure and ?4.6 ±0.3 kcal/mol for a strongly bent HOH ‥ OCH₂ structure. The energy difference between these systems is much smaller than in all previous ab initio work. Cyclic (C_2h) and bifurcated (C_2v) transition structures for (H₂O)₂ are located at 1.0 ±0.1 kcal/mol and 1.9 ±0.3 kcal/mol above the global minimum, respectively. A new partitioning scheme is presented that rigorously partitions the MP2 correlation interaction energy in intra and intermolecular (dispersion) contributions. These terms are large (up to 2 kcal/mol) but of opposite sign for most geometries studied and hence their overall effect upon the final structures is relatively small. The relative merits of the MP2 and CEPA-1 approaches are discussed are discussed and it is concluded that for economical reasons MP2 is to be preferred, especially for larger systems.     

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 T_d 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 C_2v leads to a minimum on the lowest triplet potential energy surface and the electronic energy difference between the T_d and C_2v 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     

Density functional theory and post-Hartree-Fock studies on molecular structure and harmonic vibrational spectrum of formaldehyde

Density functional theory (DFT) with the Becke's three-parameter exchange correlation functional and the functional of Lee, Yang and Parr, gradient-corrected functionals of Perdew, and Perdew and Wang [the DFT(B3LYP), DFT(B3P86) and DFT(B3PW91) methods, respectively], and several levels of conventional ab initio post-Hartree-Fock theory (second- and fourth-order perturbation theory M?ller-Plesset MP2 and MP4(SDTQ), coupled cluster with the single and double excitations (CCSD), and CCSD with perturbative triple excitation [CCSD(T)], configuration interaction with the single and double excitations [CISD], and quadratic configuration interaction method [QCISD(T)], using several basis sets [ranging from a simple 6-31G(d,p) basis set to a 6-311+ +G(3df, 2pd) one], were applied to study of the molecular structure (geometrical parameters, rotational constants, dipole moment) and harmonized infrared (IR) spectrum of formaldehyde (CH₂O). High-level ab initio methods CCSD(T) and QCISD(T) with the 6-311+ +G(3df, 2pd) predict correctly molecular parameters, vibrational harmonic wavenumbers and the shifts of the harmonic IR spectrum of ¹²CH₂ ¹⁶O upon isotopic substitution. Received: 30 January 1997 / Accepted: 7 May 1997     

Systematic study of the lowest energy states of Pd,Pd2, and Pd3

A systematic study has been carried out for the determination and characterization of the lowest states of Pd, Pd₂, and Pd₃ using some of the best ab initio tools available at present (conventional and DFT). Full electron ab initio calculations using the HF, MP2, MP3, MP4, and QCI methods were compared with DFT methods using several gradient-corrected functionals as well as the hybrid B3LYP functional that performed very well for the energetics studies of these small clusters. A suitable basis set has been found to perform considerably well with palladium atoms, another of double-ζ quality has been found insufficient to reproduce basic characteristics of the smallest palladium clusters. The results indicate that the ground state for Pd is a singlet. The dimer is a triplet; however, it is very difficult to ascertain due to the closeness between singlet and triplet states (0.9 kcal/mol). The trimer ground state was found to be a triplet with a separation from the lowest singlet of 3.2 kcal/mol. The lowest triplet and singlet of Pd₃ were practically equilateral triangles. © 1997 John Wiley & Sons, Inc.     

Electronic structure benchmark calculations of CO2 fixing elementary chemical steps in RuBisCO using the projector-based embedding approach

Ribulose 1,5-bisphosphate carboxylase-oxygenase (RuBisCO) is the main enzyme involved in atmospheric carbon dioxide (CO₂) fixation in the biosphere. This enzyme catalyzes a set of five chemical steps that take place in the same active-site within magnesium (II) coordination sphere. Here, a set of electronic structure benchmark calculations have been carried out on a reaction path proposed by Gready et al. by means of the projector-based embedding approach. Activation and reaction energies for all main steps catalyzed by RuBisCO have been calculated at the MP2, SCS-MP2, CCSD, and CCSD(T)/aug-cc-pVDZ and cc-pVDZ levels of theory. The treatment of the magnesium cation with post-HF methods is explored to determine the nature of its involvement in the mechanism. With the high-level ab initio values as a reference, we tested the performance of a set of density functional theory (DFT) exchange-correlation (xc) functionals in reproducing the reaction energetics of RuBisCO carboxylase activity on a set of model fragments. Different DFT xc-functionals show large variation in activation and reaction energies. Activation and reaction energies computed at the B3LYP level are close to the reference SCS-MP2 results for carboxylation, hydration and protonation reactions. However, for the carbon–carbon bond dissociation reaction, B3LYP and other functionals give results that differ significantly from the ab initio reference values. The results show the applicability of the projector-based embedding approach to metalloenzymes. This technique removes the uncertainty associated with the selection of different DFT xc-functionals and so can overcome some of inherent limitations of DFT calculations, complementing, and potentially adding to modeling of enzyme reaction mechanisms with DFT methods.     

Study of methanetriol decomposition mechanisms

Using ab initio HF/6–31G** and MP2/6–31G** calculations alternative reactions HC(OH)₃ → HCO₂H + H₂O and HC(OH)₃ + H₂O → HCO₂H + 2H₂O are investigated and the results are compared with relevant PM3, HF/3–21G, and HF/6–31G data. Reactant and product complexes as well as transition states are located on corresponding potential energy surfaces. © 1996 John Wiley & Sons, Inc.     

Ab initio study of the unimolecular decomposition of 2‐butenenitrile: Molecular elimination channels

Ab initio molecular orbital calculations have been performed for the unimolecular decomposition of 2‐butenenitrile (CH₃CH?CHCN), especially for HCN and H₂ molecular elimination channels. Structures and energies of the reactants, products, and relevant species in the individual reaction pathways were determined by MP2 gradient optimization and MP4 CCSD(T) single‐point energy calculations. Direct 1,1 and 1,2 molecular eliminations and H or CN migration followed by elimination channels were identified. Dissociation rates for the individual reaction pathways were calculated from vibrational frequencies at the ab initio transition state geometries by employing Rice–Ramsperger–Kassel–Marcus theory, from which channel branching ratios were determined. It was concluded that the most important reaction channel should be the direct 1,1 three‐center molecular elimination of HCN. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Inverse hydrogen bonds between XeH2 and hydride and fluoride derivatives of Li, Be, Na and Mg

A theoretical study of the inverse hydrogen bonds complexes formed by the XeH₂ molecule and hydride and fluoride derivatives of Li, Be, Na and Mg has been carried out by means of DFT (B3LYP/DGDZVP) and ab initio [MP2/DGDZVP and MP2/LJ18/6-311++G(2d,2p)] calculations. The complexes obtained present interaction energies up to ?81 kJ/mol. The analysis of the electron density shows electron transfer from the XeH₂ to the electron acceptor molecules. The calculated absolute chemical shieldings show the high sensitivity of the xenon atom upon complexation.     

Valence bond and molecular orbital studies of the A-F bond lengths in some AFn type molecules and their fluorinated cations

The results of ab initio MP2(full)/cc-pVTZ and DFT MPW1PW91/cc-pVTZ molecular orbital calculations of the bond lengths are reported for non-hypercoordinate and hypercoordinate systems of the general type AF_n^q+, with q≥0 and A = N, P, O, S and Cl. They show that except for OF₄²⁺ the bond lengths decrease as the cationic character increases. Increased-valence structures are used to provide valence bond (VB) rationalizations for the bond length shortenings. In these valence bond structures, the degree of multiple bonding increases as the cationic character increases.     

On the evaluation of molecular electron affinities by approximate density functional theory

The ability of approximate Density Functional Theory to calculate molecular electron affinities has been probed by a series of calculations on the hydrides CH₃, NH₂, OH, and HC₂ as well as the multibonded species CN, BO, N₃, OCN, and NO₂. The simple Hartree–Fock Slater scheme lacks dynamic correlations and underestimates on the average the adiabatic electron affinities (EA_ad) by 0.7 eV. A considerable improvement is obtained by the Local Density Approximation (LDA) in which dynamic correlation is included. Values from LDA calculation underestimate, on the average, the adiabatic electron affinities by 0.4 eV. The best agreement with experiment is obtained by the LDA/NL scheme in which a nonlocal correction recently proposed by Becke is added to the LDA energy expression. The LDA/NL method underestimates EA_ad by 0.2 eV. It is concluded that the LDA/NL method affords EA_ad's in as good agreement with experiment as ab initio techniques in which electron correlation is taken into account by extensive configuration interaction. A full geometry optimization has been carried out on the nine neutral sample molecules as well as the corresponding anions.     

Density functional calculations of difluorodiazete structures with Gaussian-orbital-type approach

The comparison of local nonlocal and hybrid DFT methods with RHF , MP 2, CCSD , and CPF ab initio methods in generating geometries and relative energies of cis- and trans-difluorodiazete, SVWN , BLYP , BP 86, BECKE 3LYP , and BECKE 3P 86 DFT methods with 6-311 + g(2d) and 6-311 + + g(3df) basis sets. The geometries generated with RHF ab initio models are quite different from experimental values and energy evaluation prefers the wrong isomer. The hybrid methods give superior geometries while energies evaluated with nonlocal DFT methods are better than the one obtained with MP 2 or CCDS ab initio methods. The results suggest DFT as the method of choice of studying similar systems. © 1996 John Wiley & Sons, Inc.     

Quantum chemical calculations of stability constants: study of ligand effects on the relative stability of Pd(II)�Cpeptide complexes

Replacement of [Pd(H₂O)₄]²⁺ by cis-[Pd(en)(H₂O)₂]²⁺, [PdCl₄]^2?, and [Pd(NH₃)₄]²⁺ on the hydrolytic cleavage of the Ace-Ala-Lys-Tyr-Gly?CGly-Met-Ala-Ala-Arg-Ala peptide is theoretically investigated by using different quantum chemical methods both in the gas phase an in water solution. First, we carry out a series of validation calculations on small Pd(II) complexes by computing high-level ab initio [MP2 and CCSD(T)] and Density Functional Theory (B3LYP) electronic energies while solvent effects are taken into account by means of a Poisson-Boltzmann continuum model coupled with the B3LYP method. After having assessed the actual performance of the DFT calculations in predicting the stability constants for selected Pd(II)-complexes, we compute the relative free energies in solution of several Pd(II)?Cpeptide model complexes. By assuming that the reaction of the peptide with cis-[Pd(en)(H₂O)₂]²⁺, [Pd(Cl)₄]^2?, and [Pd(NH₃)₄]²⁺ would lead to the initial formation of the respective peptide-bound complexes, which in turn would evolve to afford a hydrolytically active complex [Pd(peptide)(H₂O)₂]²⁺ through the displacement of the en, Cl^?, and NH₃ ligands by water, our calculations of the relative stability of these complexes allow us to rationalize why [Pd(H₂O)₄]²⁺ and [Pd(NH₃)₄]²⁺ are more reactive than cis-[Pd(en)(H₂O)₂]²⁺ and [PdCl₄]^2? as experimentally found.     

Platinum fluorides beyond PtF6?

Quantum-chemical calculations at DFT B3LYP and ab initio MP2, CCSD, and CCSD(T) levels have been performed on various binary fluorides of platinum up to formal oxidation state +VIII, to evaluate the stability of these species. The calculations indicate clearly that elimination of F₂ from PtF₈ is a strongly exothermic reaction, with a moderate activation barrier. An exothermic decay is also observed for the homolytic bond breaking. Furthermore, our investigations suggest that both decomposition channels of PtF₇ are exothermic. The existence of platinum fluorides higher than PtF₆ is therefore highly unlikely.     

Post-Hartree-Fock and DFT level studies on the Cl2CO …︁ Cl2 complex: Accurate molecular parameters,harmonic vibrational frequencies,and interaction energies

The Cl₂CO …︁ Cl₂ complex was studied using ab initio post-Hartree-Fock theory at the MP2 and MP4 levels and, for comparison, the DFT method with 6-311G(2d), 6-311 + G(2d), and Sadlej's medium-size polarized (MSPBS) basis sets. A potential energy search recovered a planar minimum-energy structure characterized by a bent conformation. For this weakly bound complex, the interaction energy corrected for the basis set superposition error amounted to − 0.88, − 1.09, − 1.43, and − 0.38 kcal/mol at the MP4(SDTQ)/6-311G(2d), MP4(SDTQ)/6-311 + G(2d), MP4(SDTQ)/MSPBS, and DFT(Becke3LYP)/6-311 + G(2d) levels of theory, respectively. Two highly symmetrical forms, linear and T-shaped, correspond to transition-state conformers. The analysis of harmonic vibrational frequencies and potential energy distribution was performed at the MP2 and DFT levels with the 6-311 + G(2d) basis set. © 1996 John Wiley & Sons, Inc.     

The [CH2 = CHOH/H2O]+˙ system: A theoretical study of distonic ions,hydrogen-bridged ions and ion–dipole complexes

Several isomeric forms of the vinyl alcohol/water radical cation have been investigated by high-level ab initio molecular orbital theory calculations, including electron correlation effects. Of the ions considered here, the anti form of the ? O ?H ?O? bridged complex is calculated to be the lowest in energy, having a stabilization energy of 100 kJ mol^?1 with respect to the dissociation products [CH₂CHOH]⁺˙ and H₂O. Although the isomeric ions may formally be represented as distonic ions, hydrogen-bridged ions and ion–dipole complexes, the only significant barrier separating the isomers appears to be the anti?syn isomerization barrier. However, in the ? O ?H ?O? bridged complex this barrier is found to be considerably lowered relative to the anti?syn isomerization barrier for the free vinyl alcohol radical cation.     

Sensitivity of the H + CH3 → CH4 recombination rate constant to the shape of the CH stretching potential

Using a potential-energy surface obtained in part from ab initio calculations, the H + CH₃ → CH₄ bimolecular rate constant at T = 300 K is determined from a Monte Carlo classical trajectory study. Representing the CH stretching potential with a standard Morse function instead ofthe ab initio curve increases the calculated rate constant by an order of magnitude. The experimental recombination rate constant is intermediate of the rate constants calculated with the Morse and ab initio stretching potentials.Two properties of the H + CH₃ α CH₄ potential-energy surface which significantly affect the recombination rate constant are the shape of the CH stretching potential and the attenuation of the H₃CH bending frequencies. Ab initio calculations with a hierarchy of basis sets and treatment of electron correlation indicate the latter is properly described [13]. The exact shape of the CH stretching potential is not delineated by the ab initio calculations, since the ab initio calculations are not converged for bond lengths of 2.0–3.0 Å [12]. However, the form of this stretching potential deduced from the highest-level ab initio calculations, and fit analytically by eq. (2), is significantly different from a Morse function. The experimental recombination rate constant is intermediate of the rate constants calculated with the Morse and ab initio CH stretching potentials. This indicates that the actual CH potential energy curve lies between the Morse and ab initio curves. This is consistent with the finding that potential energy curves for diatomics are not well described by a Morse function [12].     

Comparative study of DFT methods applied to small titanium/oxygen compounds

The performance of a number of different local and nonlocal density functional theory (DFT) methods has been investigated for some small titanium—oxygen systems. Equilibrium geometries, ionization potentials, dipole moments, atomization energies, and harmonic vibrational frequencies have been calculated for the TiO, TiO₂, and Ti₂ molecules, and the results are compared with experimental data and ab initio calculations. It is shown that most DFT methods perform much better than the ab initio Hartree—Fock (HF), second-order perturbation theory (MP2), and configuration interaction including single and double excitations (CISD) treatments. For good agreement with experimental data, gradient corrections to the exchange part of the DFT functional are needed, as well as some type of correction for the errors in the calculated energy splittings between different atomic states of titanium. Hybrid methods including a mixture of HF exchange with DFT exchange correlation do not perform as well as “pure” DFT methods for the studied systems. © 1996 John Wiley & Sons, Inc.     

A study of methanetetraol dehydration to carbonic acid

Two alternative dehydration reactions C(OH)₄ → (HO)₂CO + H₂O and C(OH)₄ + H₂O → (HO)₂CO + 2H₂O are studied by ab initio Becke3LYP/6–311 + G^** and MP2/6–31G^** methods. Calculated energy and geometry characteristics of intermediates and transition states predict a catalytic effect of one water molecule and the exothermism of the transformations. Relevant HF/6–311 + G^**, HF/6–31G^**, HF/6–31G, and HF/3–21G calculations were performed for comparison. © 1997 John Wiley & Sons, Inc.