High level ab initio and density functional theory study of bond selective dissociation of CH3SH and CH3CH2SH radical cations

Selective bond dissociation energies for CH₃SH and CH₃CH₂SH radical cations were evaluated with G1, G2, G2MP2, B3LYP, BLYP, and SVWN computational methods. It was determined that both G2 and CBSQ evaluate very accurate bond dissociation energies for thiol radical cations, while gradient-corrected BLYP computes the best energies of three employed DFT methods. For the CH₃CH₂SH radical cation, new, higher than previously estimated selective bond dissociation energies were suggested. Received: 10 September 1997 / Accepted: 9 September 1998 / Published online: 11 November 1998     

Harmonic frequency scaling factors for Hartree-Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2 with the Sadlej pVTZ electric property basis set

Scaling factors for obtaining fundamental vibrational frequencies from harmonic frequencies calculated at six of the most commonly used levels of theory have been determined from regression analysis for the polarized-valence triple-zeta (pVTZ) Sadlej electric property basis set. The Sadlej harmonic frequency scaling factors for first- and second-row molecules were derived from a comparison of a total of 900 individual vibrations for 111 molecules with available experimental frequencies. Overall, the best performers were the hybrid density functional theory (DFT) methods, Becke's three-parameter exchange functional with the Lee–Yang–Parr fit for the correlation functional (B3-LYP) and Becke's three-parameter exchange functional with Perdew and Wang's gradient-corrected correlation functional (B3-PW91). The uniform scaling factors for use with the Sadlej pVTZ basis set are 0.9066, 0.9946, 1.0047, 0.9726, 0.9674 and 0.9649 for Hartree–Fock, the Slater–Dirac exchange functional with the Vosko–Wilk–Nusair fit for the correlation functional (S-VWN), Becke's gradient-corrected exchange functional with the Lee–Yang–Parr fit for the correlation functional (B-LYP), B3-LYP, B3-PW91 and second-order M?ller–Plesset theory with frozen core (MP2(fc)), respectively. In addition to uniform frequency scaling factors, dual scaling factors were determined to improve the agreement between computed and observed frequencies. The scaling factors for the wavenumber regions below 1800 cm⁻¹ and above 1800 cm⁻¹ are 0.8981 and 0.9097, 1.0216 and 0.9857, 1.0352 and 0.9948, 0.9927 and 0.9659, 0.9873 and 0.9607, 0.9844 and 0.9584 for Hartree–Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2(fc), respectively. Hybrid DFT methods along with the Sadlej pVTZ basis set provides reliable theoretical vibrational spectra in a cost-effective manner. Received: 22 May 2000 / Accepted: 30 August 2000 / Published online: 28 February 2001     

Density functional calculations of the pseudorotational flexibility of tetrahydrofuran

The flexibility of the five-membered ring in tetrahydrofuran was investigated using quantum mechanical methods involving density functional, Hartree-Fock, and many-body perturbation theory (MP2, MP4) calculations. We found that motion along the pseudorotational path of tetrahydrofuran is nearly free. The 0.1 kcal/mol energy barrier for pseudorotation, calculated at the highest MP4(SDQ)/6-311++G(2d,p)//MP2/6-311++G(2d,p) level of theory, agrees well with the experimental value of 0.16±0.03 kcal/mol. Similar results were obtained with the S-VWN, B3-LYP and B-LYP density functional calculations using the 6-31G(d) set of atomic orbitals. Also the density functional dipole moments and geometries were in good agreement with both the MP2 and experimental benchmarks. However, all density functional methods that utilized the default integration grid in the Gaussian 94 program were found to provide false stationary points of the C ₁ symmetry near the pseudorotational angle of 100°. These stationary points disappeared when a denser spherical-product grid was used. Overall, the hybrid B3-LYP functional was found to be the most promising quantum mechanical method for the modeling of biomolecules containing the furanose ring. Received: 17 June 1997 / Accepted: 20 November 1997     

Evaluation of density functional theory in the bond rupture of octane

Density functional methods at the 6-31G* level are applied to the rupture of n-octane into methyl–heptyl, ethyl–hexyl, propyl–pentyl, and butyl–butyl radical fragments. The energetics of the radicals at UMP3, UMP2/6-31G*//UHF/6-31G* (hereafter referred to as UMP), are compared to UB3LYP/6-31G* results (referred to as UB). Although the UMP approach matches additivity energies to within 5 kcal/mol, it fails to mimic the overall energetic trend. The UB energies agree with additivity estimates and trends to within 1–2 kcal/mol and radical entropies deviate by only 2 e.u. from available experimental data. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 154–167, 1998     

Spin-projected coupled-cluster theory with single and double excitations

Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an analysis of the expectation value of the spin operator, Ŝ ². Contamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, P^, represented by the product of the spin annihilation operators ? _{s+ 1} and ?_s+2. The computational cost of such a projection scales with O(M ⁶) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from the corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contaminant in an approximate way. In the case of single-bond cleavage, APCSSD leads to a significant improvement of the energy in the region where the bonding electrons recouple from a closed shell to an open shell singlet electron pair. Received: 13 April 2000 / Accepted: 12 July 2000 / Published online: 24 October 2000     

Ab initio quantum chemical study of the formation, decomposition and isomerization of the formaldiminoxy radical (CH2NO): comparison of the Gaussian-2 and CASPT2 techniques in the calculation of potential energy surfaces

The reaction between triplet methylene and nitric oxide, producing the formaldiminoxy (CH₂NO) radical, and the subsequent decomposition and isomerization reactions of CH₂NO have been studied using ab␣initio quantum chemical techniques that include the Gaussian-2 (G2), CASSCF and CASPT2 methods. Stationary points on the potential energy surfaces were located at MP2/6-31G(d) and CASSCF/cc-pVDZ levels of theory, while the electronic energies were determined using G2, G2(MP2), QCISD(T)/cc-pVTZ, RCCSD(T)/cc-pVTZ and CASPT2/cc-pVTZ approaches. G2 is believed to be reliable at equilibrium geometries, but the determination of certain transition state geometries and energies requires a MCSCF-based approach. The calculations suggest that CH₂NO (²A^′) forms in a barrierless reaction and could readily decompose to H+HCNO. A subsequent abstraction reaction then results in H₂+CNO. No molecular elimination channel was found. An alternative pathway is the formation of CH₂ON, which readily isomerizes to CH₂NO. Received: 8 May 1998 / Accepted: 11 August / Published online: 9 October 1998     

Generalization of coupled-cluster response theory to multireference expansion spaces: application of the coupled-cluster singles and doubles effective Hamiltonian

Employing separate cluster ansatz in time-independent and time-dependent wave-operators, coupled-cluster (CC) response theory is generalized to multireference (MR) expansion spaces. For state energies, this corresponds to the MR secular problem with an arbitrary similarity-transformed effective Hamiltonian, H˜=Ω⁻¹ HΩ. The effective Hamiltonian can be generated via size-extensive CC methods. Thus the states in MR linear response theory (MRLRT) maintain the usual CC core-extensive properties. We have used the Gelfand unitary group basis of the spin-adapted configurations to construct the matrix of H˜ in the MR excitation space. As a preliminary application, the CC singles and doubles effective Hamiltonian is applied to excitation and photoionization energies of the CH⁺ and N₂ molecules, and is compared with experimental results and results from other numerical procedures including conventional CC linear response theory (CC-LRT), MR and full configuration interaction (MRCI and FCI) methods. The numerical results indicate that MRLRT reproduces valence and external excited states quantitatively, combining the best features of CC-LRT and MRCI. Received: 2 July 1998 / Accepted: 28 August 1998 / Published online: 11 November 1998     

Degenerate symmetry-adapted perturbation theory of weak interactions between closed- and open-shell monomers: application to Rydberg states of helium hydride

Symmetry-adapted perturbation theory is extended to the (quasi) degenerate, open-shell case. The new formalism is tested in calculations of the interaction energies for a helium atom in the ground state interacting with an excited hydrogen atom. It is shown that the method gives satisfactory results if the coupling with higher Rydberg states of the dimer is small, as is the case for the A²Σ⁺,B²Π,E²Π,3²Π, and 1²Δ states of HeH. For the C²Σ⁺ state convergence of the method is very slow, but it can be improved by including the n=3 states in the model space. Received: 3 June 1998 / Accepted: 9 September 1998 / Published online: 7 December 1998     

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.     

Theoretical study of reaction of trifluoromethyl radical with hydroxyl and hydrogen radicals

Ab initio molecular orbital theory and density functional theory calculations have been carried out on the reactions of the trifluoromethyl radical with the hydroxyl and the hydrogen radicals. These reactions are key reactions that underlie a new fire extinguishing mechanism of non-bromine-containing halon replacements. The activation energies calculated by the MP2 and QCISD methods are in good agreement with the experimental values. The B3LYP, as well as MP2 and QCISD, give good results for the calculations of the heats of reactions. The GAUSSIAN-1 and GAUSSIAN-2 theory calculations present the most acxcurate results on both the activation energies and the heats of reactions. The effects of the scaling factors on the activation energies and the heats of reactions are also evaluated. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 277–289, 1998     

Analytic UHF-CCSD(T) second derivatives: implementation and application to the calculation of the vibration-rotation interaction constants of NCO and NCS

An implementation of analytic open-shell UHF-CCSD(T) second derivatives is presented. To demonstrate applicability and test the accuracy of the UHF-CCSD(T) approach for the determination of spectroscopical parameters, vibration-rotation interaction constants were calculated for the ground (1²Π) and first electronically excited (1²Σ) states of the NCO and NCS radicals. In addition, harmonic vibrational frequencies for both states, the Renner-Teller parameter for the ground state, as well as the 1²Π→1²Σ excitation energy are reported. While the computed values are in good agreement with reliable experimental information for NCO, most of the data presented for NCS are predictions of quantities not well known from experiment. Received: 4 May 1998 / Accepted: 27 July 1998 / Published online: 12 October 1998     

Density functional study of ethylene oxidation on an Ag(111) surface

The mechanism of ethylene epoxidation on Ag surfaces has been investigated using the density functional method and Ag _n clusters (n = 3 to 10) modeling the Ag(111) surface. The adsorption energy of O₂ to the Ag clusters was strongly dependent on the HOMO level of the cluster, and the clusters with higher HOMO levels afforded larger O₂ adsorption energies. The energetics was investigated for both the molecular and atomic oxygen epoxidation mechanisms. For the atomic oxygen mechanism, epoxidation was found to proceed without an activation energy, whereas a small amount of activation energy (about 5 kcal/mol) was calculated for the molecular oxygen mechanism. Received: 2 July 1998 / Accepted: 9 September 1998 / Published online: 8 February 1999     

Counterpoise-corrected potential energy surfaces of simple H-bonded systems

Geometries and stabilization energies of various simple H-bonded complexes (water dimer, hydrogen fluoride dimer, formamide dimer, formic acid dimer) have been determined by a gradient optimization that eliminates the basis set superposition error (BSSE) by the counterpoise (CP) method in each gradient cycle as well as by the standard gradient optimization. Both optimization methods lead to different potential energy surfaces (PES). The difference depends on the theoretical level used and is larger if correlation energy is considered. Intermolecular distances from the CP-corrected PES are consistently longer, and this difference might be significant (∼0.1 ?); also angular characteristics determined from both surfaces differ significantly. Different geometries were obtained even when passing to larger basis sets (aug-cc-pVDZ). The standard optimization procedure can result in a completely wrong structure. For example, the “quasi-linear” structure of the (HF)₂ (global minimum) does not exist at the standard MP2/ 6-31G** PES (where only cyclic structure was detected) and is found only at the CP-corrected PES. Stabilization energies obtained from the CP-corrected PES are always larger than these from the standard PES where the BSSE is added only a posteriori for the final optimized structure; both energies converge only when passing to a larger basis set (aug-cc-pVDZ). Received: 11 March 1998 / Accepted: 19 June 1998 / Published online: 4 September 1998 RID=" ID=" <E6>Acknowledgements.</E6> The project was supported by the Grant Agency of the Czech Republic (Grant No. 203/98/1166). RID=" ID=" <E5>Correspondence to</E5>: P. Hobza     

Transition structures and exo/endo stereoselectivities of concerted [6 + 4] cycloadditions with density functional theory

Density functional theory transition structures were located for three concerted [6 + 4] cycloaddition reactions involving cis-hexatriene and butadiene, cyclopentadiene and cycloheptatriene, and cyclopentadiene and tropone. Geometries, energies, and entropies were computed at the Becke3LYP/6-31G* level. The activation energy of the concerted [6 + 4] cycloaddition of hexatriene and butadiene is 33.3 kcal/mol, about 8 kcal/mol above the activation energy of the butadiene plus ethylene [4 + 2] cycloaddition. The endo concerted [6 + 4] transition state is 1.1 kcal/mol higher than the exo. The [6 + 4] reaction of cyclopentadiene and cycloheptatriene has a barrier of 25.9 kcal/mol, while the cyclopentadiene–tropone barrier drops to 20.7 kcal/mol. Received: 3 December 1998 / Accepted: 18 February 1999 / Published online: 7 June 1999     

Equation for the direct determination of the density matrix: Time-dependent density equation and perturbation theory

The density equation proposed previously for the direct determination of the density matrix, i.e. for the wave mechanics without wave, is extended to a time-dependent case. The time-dependent density equation has been shown to be equivalent to the time-dependent Schr?dinger equation so long as the density matrix, included as a self-contained variable, is N-representable. Formally, it is obtainable from the previous time-independent equation by replacing the energy E with . The perturbation theory formulas for the density equation have also been given for both the time-dependent and time-independent cases. Received: 16 June 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

A direct ab initio dynamics study of the water-assisted tautomerization of formamide

Direct ab initio dynamics calculations based on a canonical variational transition-state theory with several multidimensional semiclassical tunneling approximations were carried out to obtain rate constants for the water-assisted tautomerization of formamide. The accuracy of the density functionals, namely, B-LYP, B3-LYP, and BH&H-LYP, were examined. We found that the BH&H-LYP method yields the most accurate transition-state properties when comparing it to ab initio MP2 and QCISD results, whereas B-LYP and B3-LYP methods predict barrier heights too low. Reaction path information was calculated at both the MP2 and nonlocal hybrid BH&H-LYP levels using the 6–31G(d,p) basis set. At the BH&H-LYP level, we found that the zero-point energy motion lowers the barrier to tautomerization in the formamide-water complex by 3.6 kcal/mol. When tunneling is considered, the activation energy at the BH&H-LYP level at 300 K is 17.1 kcal/mol. This is 3.4 kcal/mol below the zero-point-corrected barrier and 7.0 kcal/mol below the classical barrier. Excellent agreement between BH&H-LYP and MP2 rate constants further supports the use of BH&H-LYP for rate calculations of large systems. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 861–874, 1997     

Diatomic potential well depths from analyses of high-resolution electron energy spectra for autoionizing collision complexes

High-resolution energy spectra of electrons released in Penning ionization collisions of metastable rare gas atoms Rg*(ns) (Rg = He, Ne, Ar, Kr, Xe) with several open-shell and closed-shell atoms are analyzed to determine the well depth of the potential energy curve which describes the respective autoionizing collision complex. We thereby elucidate trends in the chemical interaction of Rg* with closed-shell target atoms A(ns ²) and establish a basis for detailed comparison with the respective interactions involving open-shell, ground state alkali atoms A(ns). From electron energy spectra due to␣associative ionization (RgH⁺ formation) in Rg* + H(1s) collisions, we determine binding energies for the RgH⁺(¹Σ) ground state potential (Rg = Ne, Ar, Kr, Xe) with uncertainties around 0.03 eV. Received: 30 June 1998 / Accepted: 5 August 1998 / Published online: 28 October 1998     

High-level ab initio versus DFT calculations on (H2O2)2 and H2O2–H2O complexes as prototypes of multiple hydrogen bond systems

The performance of B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91 density functionals to describe multiple hydrogen bond systems was studied. For this purpose we have chosen the dimers of hydrogen peroxide and the hydrogen peroxide–water complexes. The geometries and vibrational frequencies obtained with a 6-311+G(d,p) basis set were compared with those obtained at the MP2 level using the same basis set expansion. The corresponding dimerization energies were obtained using a 6-311+G(3df,2p) basis set and compared with those obtained using the G2(MP2) theory. Red shiftings of the OH donor stretching frequencies were predicted by all approaches investigated; however, in all cases, the DFT values were sizably larger than the MP2 ones. Similarly, the blue shifting of the torsion of the hydrogen peroxide subunit was larger when evaluated at the DFT level. All functionals reproduced the G2(MP2) relative stabilities of the different local minima quite well. With the exception of the B-LYP and B3-PW91 approaches, all functionals yielded binding energies which deviated from the G2(MP2) values by less than 0.5 kcal/mol, provided that G2-type basis sets were used and that the corresponding BSSE corrections were included. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1124–1135     

Density functional study on zerovalent lanthanide bis(arene)-sandwich complexes

Several zerovalent lanthanide bis(arene)-sandwich complexes, Ln(η⁶-C₆H₆)₂, Ln = La, Ce, Eu, Gd and Lu, have been studied by means of density functional theory. The calculated geometries are in good agreement with experiment. The calculated dissociation energies of the bond Ln-(η⁶-C₆H₆) may be considerably underestimated, but they correctly reveal the variation regularity. The bonding in these molecules can be described in terms of a relatively weak π-electron donation from benzene to Ln and a stronger electron back-donation from Ln 5d to the benzene π* orbitals. During bond formation, there is electron promotion from Ln 6s to 5d instead of from 4f to 5d, in opposition to the proposal of Anderson et al. The relativistic effect only slightly influences the molecular geometry, but decreases the bonding energy considerably through lowering the Ln 6s level and raising the 5d level. It enhances the trend of the bonding energy to decrease along the lanthanide series. Received: 22 June 1998 / Accepted: 9 September 1998 / Published online: 17 December 1998     

Inclusion of exact exchange for self-interaction corrected H3 density functional potential energy surface

The effect of the inclusion of the exact exchange into self-interaction corrected generalized gradient approximation density functional theory (GGA-DFT) for the simplest hydrogen abstraction reaction, H + H₂ → H₃ → H₂ + H, is presented using a triple-zeta augmented 6-311++G(d,3pd) basis set. The introduction of the self-interaction correction has a considerably larger effect on molecular geometry and vibrational frequencies than the inclusion of the exact exchange. We investigate the influence of the self-interaction error on the shape of the potential energy surface around the transition state of the hydrogen abstraction reaction. The decomposition of the self-interaction error into correlation and exchange parts shows that the exchange self-interaction error is the main component of the energy barrier error. The best agreements with the experimental barrier height were achieved by self-interaction corrected B3LYP, B-LYP and B3PW functionals with errors of 1.5, 2.9 and 3.0 kcal/mol, respectively. Received: 13 August 1997 / Accepted: 14 November 1997