Stationary points on the H2CO potential energy surface: dependence on theoretical level

A total of 36 stationary points have been located on the H₂CO potential energy surface by means of gradient extremal following. These 36 points are believed to represent all the important stationary points on this surface. There is no indication that the structure of the surface becomes less complicated as the size of the basis set is enlarged at the Hartree-Fock level of theory, but many of the second- and third-order saddle points disappear when electron correlation is introduced. Of the ten first-order saddle points (transition structures) located, the majority have reaction paths entering the associated minima in a side-on approach, i.e. these cannot be located by uphill walking from the minimum. Received: 5 February 1998 / Accepted: 21 May 1998 / Published online: 29 July 1998     

Computation of stationary points via a homotopy method

A homotopy method is presented that locates both minimizers and saddle points of energy functions in an efficient manner. In contrast to other methods, it makes possible the exploration of large parts of potential energy surfaces. Along a homotopy path stationary points of odd and even order occur alternately. A path tracing procedure requiring only gradients and at most one evaluation of the Hessian matrix is given. Test results on a model potential and three MINDO/3 potentials are reported. Received: 6 May 1996 / Accepted: 2 April 1998 / Published online: 23 June 1998     

A new look at the reduced-gradient-following path

 The mathematical structure of the reduced-gradient-following (RGF) path introduced by Quapp et al. (1988 J. Comput. Chem. 19:1087) is reviewed and analyzed. We report two new algorithms to evaluate the RGF path. The RGF path is also compared mathematically and computationally with the gradient extremals path. An example of the evaluation of the RGF path is also reported. Received: 21 May 2001 / Accepted: 27 September 2001 / Published online: 9 January 2002     

The spin-forbidden reaction CH(2∏) + N2→ HCN + N(4S) revisited I. Ab initio study of the potential energy surfaces

High-level ab initio electronic structure theories have been applied to investigate the detailed reaction mechanism of the spin-forbidden reaction CH(²∏) + N₂ → HCN + N(⁴S). The G2M(RCC) calculations provide accurate energies for the intermediates and transition states involved in the reaction, whereas the B3LYP/6-311G(d,p) method overestimates the stability of some intermediates by as much as about 10 kcal/mol. A few new structures have been found for both the doublet and quartet electronic states, which are mainly involved in the dative pathways. However, due to the higher energies of these structures, the dominant mechanism remains the one involving the C ₂ intersystem-crossing step. The C ₂ minima on the seam of crossing (MSX) structures and the spin-orbit coupling between the doublet and quartet electronic states are rather close to those found in previous studies. Vibrational frequencies orthogonal to the normal of the seam which have been applied in a separate publication to calculate the rate of the CH(²∏) + N₂ → HCN + N(⁴S) reaction with a newly proposed nonadiabatic transition-state theory for spin-forbidden reactions have been calculated at the MSX from first principles. Received: 23 June 1998 / Accepted: 21 September 1998 / Published online: 8 February 1999     

Vibrational softening of diatomic molecules

An analysis of a model molecular oscillator is presented: a vibrating diatomic molecule carrying N ₀ electrons. The energy derivatives over the number of electron (N) and the deformation (Q), ∂ ⁿ /∂N ⁿ and ∂ ⁿ /∂Q ⁿ have been analyzed up to second order (n=2), including the appropriate mixed derivatives. The effect of coupling between distortion of the electron density induced by ΔN and the vibrational deformation of the molecule has been studied. Anharmonicity of the oscillator has been shown to be a possible result of that coupling; new relations between the parameters characterizing the anharmonicity of the oscillator and the energy derivatives at density functional theory level have been obtained. Ab initio calculations for a set of diatomic molecules have been performed, yielding values for all the derivatives discussed and demonstrating the effect of coupling with vibrations. Received: 1 June 2000 / Accepted: 20 October 2000 / Published online: 21 March 2001     

The hierarchy of localization basins: a tool for the understanding of chemical bonding exemplified by the analysis of the VOx and VOx+ (x=1–4) systems

The hierarchy of the electron localization basins is a powerful tool of analysis of the bonding in molecules and solids within the “elfological” framework. It is a generalization of the molecular isodensity contour analysis originally proposed by Mezey. In this approach the basins are ordered with respect to the electron localization function values at the critical points which determine the reduction of the reducible localization domains. The procedure enabling the corresponding tree diagrams to be built is described and it is shown how the method can be used as a generator of mathematical definitions of chemical concepts. The possibility offered by this simple tool is illustrated by a study of the VO _x and VO _x ⁺ (x=1–4) oxides in their ground state and in some excited states. Received: 20 July 2000 / Accepted: 20 October 2000 / Published online: 23 January 2001     

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     

A theoretical investigation of (−)-deprenyl (selegiline) as a radical scavenger

The chemical reactions between (−)-deprenyl and ·OH or ·OOH were studied using molecular orbital theory, with N,N-dimethylpropargylamine as a model. (−)-Deprenyl was confirmed to be a good radical scavenger. The active site was the acetylenic part and ·OH- or ·OOH was trapped on either acetylenic carbon. The activation energies were about 10–20 kcal/mol. The resulting ·OH- or ·OOH-adducts, still radicals, trapped further radicals on the remaining carbon of the acetylenic part. The final double trapping products were at extraordinarily lower energy levels than the original reactants by 50–70 kcal/mol. The secondary transition states were not detected, suggesting that the reactions occurred at once or in a cascade. Some results with the model system were verified by the results with the real (−)-deprenyl system. Received: 6 October 1999 / Accepted: 5 March 2000 / Published online: 21 June 2000     

The glycosyl C1′—N9 bond of deoxyadenosine and deoxyguanosine: response to electrophilic attacks on the purinic nitrogen atoms

Self-consistent-field computations shed light on two relevant conformations of deoxyadenosine (dA) and deoxyguanosine (dG): one with a pseudoequatorial C_1′N₉ glycosyl bond and the other, a slightly more stable one, with its C_1′N₉ bond in a bisectional orientation. In dA, both the N₃ and N₇ nitrogens are plausible sites for electrophilic attack, but only N₇ is a plausible site in dG. The addition of H⁺, CH₃ ⁺, C₂H₅ ⁺ or tert-C₄H₉ ⁺ onto N₇ does not provoke notable structural modifications and leaves the base of dA and dG in an antiperiplanar (or nearly antiperiplanar) position with respect to the sugar C_1′O_4′ bond, but N₃ additions cause the base to adopt a synperiplanar or strongly chiral position. This produces strong interactions between the purine and deoxyribose moieties, whose relief could aid the eventual cleavage of the glycosyl bond of dA. Addition of a radical cation onto N₇ reduces the dissociation energy of the glycosyl bond by an estimated 8 kcal mol⁻¹ in dA and 4 kcal mol⁻¹ in dG – a bond weakening likely to concur to a depurination of DNA induced by radical cations. Received: 13 September 1999 / Accepted: 3 February 2000 / Published online: 21 June 2000     

Domain-averaged Fermi holes – a new means of visualization of chemical bonds. Bonding in hypervalent molecules

The nature of bonding in several hypervalent molecules was analyzed at the ab initio SCF level using the recently proposed methodology based on the analysis of domain-averaged Fermi holes. The results of the analysis demonstrate that, for sufficiently flexible basis sets, the expansion of the valence shell does indeed take place for second row central atoms in PF₅, SF₄, and SF₆. On the other hand, no such expansion was observed for the first row N atom in NF₅. Received: 1 June 2000 / Accepted: 11 October 2000 / Published online: 23 January 2001     

Perspective on “An extended Hückel theory. I. Hydrocarbons”

 The size-consistent self-consistent matrix dressing method has been applied on an open-shell single-configuration reference state. Once the reference state is converged, several low-lying roots can be obtained for the dressed configuration interaction (CI) matrices of appropriate symmetry. The CI matrices were built with a complete-active-space singles and doubles CI method in order to deal properly with multiconfiguration excited states. The vertical ionization and ionization–excitation transitions are obtained from the difference to the closed shell ground-state energy of the neutral molecule. The method has been applied to NH⁺ ₃ and N⁺ ₂ using atomic natural orbital basis sets and state-average adapted molecular orbitals. Two ²A₁ states, very similar and showing great mixing of the (2a _l ⁻¹) and (3a _l ⁻²5a _l ¹) determinants, can be assigned to the broad asymmetric band at 27.6 ± 2 eV in the photoelectron spectrum of NH₃. The possible contribution of a ²Π _g (3σ _g ⁻²1π _g ¹) state to the A shake-up peak of N₂ at 24.6 eV is also discussed. Other states, doublets and quadruplets, are reported for both systems up to 30 eV for NH₃ and 37 eV for N₂. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Global geometry optimization of small silicon clusters at the level of density functional theory

By an application to small silicon clusters Si _N (with N = 4,5,7,10) it is shown that truly global geometry optimization on an ab initio or density functional theory level can be achieved, at a computational cost of approximately 1–5 traditional local optimization runs (depending on cluster size). This extends global optimization from the limited area of empirical potentials into the realm of ab initio quantum chemistry. Received: 24 February 1998 / Accepted: 6 March 1998 / Published online: 17 June 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     

Structures and stability of N7+ and N7− clusters

Ab initio molecular orbital theory and density functional theory have been used to study nine isomers of N₇ ionic clusters with low spin at the HF/6-31G*, MP2/6-31G*, B3LYP/6-31G*, and B3LYP/6-311(+)G* levels of theory. All stationary points are examined with harmonic vibrational frequency analyses. Four N₇ ⁺ isomers and five N₇ ⁻ isomers are determined to be local minima or very close to the minima on their potential-energy hypersurfaces, respectively. For N₇ ⁺ and N₇ ⁻, the energetically low lying isomers are open-chain structures (C _{2 v} and C _{2 v} or C₂). The results are very similar to those of other known odd-number nitrogen ions, such as N₅ ⁺, N₉ ⁺, and N₉ ⁻, for which the open-chain structures are also the global minima. This research suggests that the N₇ ionic clusters are likely to be stable and to be potential high-energy-density materials if they could be synthesized. Received: 16 July 2001 / Accepted: 8 October 2001 / Published online: 21 January 2002     

Analysis of the RGD sequence in protein structures: comparison to the conformations of the RGDW and DRGDW peptides determined by molecular dynamics simulations

Geometric properties of the RGD sequence in a data set of protein crystal and NMR structures deposited in the Protein Data Bank were examined to identify structural characteristics that are related to cell adhesion activity. Interatomic distances and dihedral angles are examined. These geometric measures are then used in an analysis of the conformations of the RGDW and _DRGDW peptides obtained from molecular dynamics simulations (Stote RH, et al. (2000) J Phys ChemB 104:1624). This analysis leads to the suggestion that differences in the accessible conformations contribute to the difference in biological activity between the RGDW and the _DRGDW peptides. Received: 15 August 2000 / Accepted: 4 October 2000 / Published online: 21 March 2001     

Prediction of DNA far-IR absorption spectra based on normal mode analysis

 We present a computational method which couples normal mode analysis in internal coordinates of a molecule with very far IR spectroscopy. The analytical expression for the dependence of IR absorption on frequency incorporates frequencies and optical activities of each normal mode. In order to predict far-IR spectra of a molecule we evaluate the optical activity of each normal mode. This optical activity is determined by the vibration amplitude of the dipole moment produced by a normal mode. We calculated normal modes of DNA double-helical fragments (dA)₁₂ · (dT)₁₂ and (dA-dT)₆ · (dA-dT)₆ and evaluated their optical activities. These were found to be very sensitive to the DNA base-pair sequence. The positions of the resonance peaks in the calculated absorption spectrum of (dA)₁₂ · (dT)₁₂ are in a good agreement with those obtained by Fourier transform IR spectroscopy (Powell JW et al. 1987 Phys Rev A 35: 3929–3939). Received: 20 June 2000 / Accepted: 5 January 2001/ Published online: 3 May 2001     

Transition structure selectivity in enzyme catalysis: a QM/MM study of chorismate mutase

Two different transition structures (TSs) have been located and characterized for the chorismate conversion to prephenate in Bacillus subtilis chorismate mutase by means of hybrid quantum-mechanical/molecular-mechanical (QM/MM) calculations. GRACE software, combined with an AM1/CHARMM24/TIP3P potential, has been used involving full gradient relaxation of the position of ca. 3300 atoms. These TSs have been connected with their respective reactants and products by the intrinsic reaction coordinate (IRC) procedure carried out in the presence of the protein environment, thus obtaining for the first time a realistic enzymatic reaction path for this reaction. Similar QM/MM computational schemes have been applied to study the chemical reaction solvated by ca. 500 water molecules. Comparison of these results together with gas phase calculations has allowed understanding of the catalytic efficiency of the protein. The enzyme stabilizes one of the TSs (TS_OHout) by means of specific hydrogen bond interactions, while the other TS (TS_OHin) is the preferred one in vacuum and in water. The enzyme TS is effectively more polarized but less dissociative than the corresponding solvent and gas phase TSs. Electrostatic stabilization and an intramolecular charge-transfer process can explain this enzymatically induced change. Our theoretical results provide new information on an important enzymatic transformation and the key factors responsible for efficient selectivity are clarified. Received: 25 March 2000 / Accepted: 7 August 2000 / Published online: 23 November 2000     

Bifurcation of reaction pathways: the set of valley ridge inflection points of a simple three-dimensional potential energy surface

This paper serves for the better understanding of the branching phenomenon of reaction paths of potential energy hypersurfaces in more than two dimensions. We apply the recently proposed reduced gradient following (RGF) method for the analysis of potential energy hypersurfaces having valley-ridge inflection (VRI) points. VRI points indicate the region of possible reaction path bifurcation. The relation between RGF and the so-called global Newton search for stationary points (Branin method) is shown. Using a 3D polynomial test surface, a whole 1D manifold of VRI points is obtained. Its relation to RGF curves, steepest descent and gradient extremals is discussed as well as the relation of the VRI manifold to bifurcation points of these curves. Received: 8 July 1998 / Accepted: 24 August 1998 / Published online: 23 November 1998     

Finding transition states using reduced potential-energy surfaces

 We propose a method to locate saddle points that is based on the interplay between the driving coordinate and the restricted quasi-Newton algorithm. The method locates the transition state using a reduced potential-energy surface. The reduced potential-energy surface is characterized by the set of driving coordinates. The proposed algorithm starts at a point on the surface that is slightly perturbed from either reactant or product and, in principle, converges to the transition state. Finally we give a special type of update Hessian matrix formula that should be applied in optimizations carried out on reduced potential-energy surfaces. Received: 29 September 2000 / Accepted: 3 January 2001 / Published online: 3 April 2001     

Anab initio quantum-chemical study of proton addition to F-, Ch3-, and CF3-substituted ethylene derivatives

Protonated forms of the molecules of ethylene derivatives with the general formula C₂X₂Y₂ (X=Y=H) (1), F (2), CH₃ (3) CH₃ (4); X=F, Y=H:cis-(5)trans- (6)) were calculated by theab initio MP2/6-31 G^* method with full geometry optimization. The minima and saddle points located on the potential energy surface (PES) of the protonated ethylene molecule correspond to the stationary states and transition states of proton migration, respectively. The stationary states are characterized by a nonclassical geometry of carbocations similar to that of π-complexes, whereas the transition states have a classical structure. Unlike1, the carbocations of molecules2–6 have the classical structure. The saddle points on the PES of the ethylene derivatives correspond to the structures of the π-complex type, which are the transition states of proton migration between the C atoms of the ethylene bond. The barrier to rotation about, the C−C bond depends essentially on the substituent nature. Published inIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1333–1337, August, 2000.