NMR chemical shifts in the low–pH form of a-chymotrypsin. A QM/MM and ONIOM–NMR study

 The relationship between hydrogen bonding and NMR chemical shifts in the catalytic triad of low-pH α-chymotrypsin is investigated by combined use of the effective fragment potential [(2001) J Phys Chem A 105:293] and ONIOM–NMR [(2000) Chem Phys Lett 317:589] methods. Our study shows that while the His57 N^δ1−H bond is stretched by a relatively modest amount (to about 1.060 ?) this lengthening, combined with the polarization due to the molecular environment, is sufficient to explain the experimentally observed chemical shifts of 18.2 ppm. Furthermore, the unusual down-field shift of H^ɛ1 (9.2 ppm) observed experimentally is reproduced and shown to be induced by interactions with the C=O group of Ser214 as previously postulated. The free-energy cost of moving H^δ1 from His57 to Asp102 is predicted to be 5.5 kcal/mol. Received: 26 September 2001 / Accepted: 6 September 2002 / Published online: 21 January 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: J. H. Jensen e-mail: jan-jensen@uiowa.edu Acknowledgements. This work was supported by a Research Innovation Award from the Research Corporation and a type G starter grant from the Petroleum Research Fund. The calculations were performed on IBM RS/6000 workstations obtained through a CRIF grant from the NSF (CHE-9974502) and on supercomputers at the National Center for Supercomputer Applications at Urbana-Champaign. The authors are indebted to Visvaldas Kairys for help with the CHARMM program, and to Daniel Quinn for many helpful discussions.     

Average inner product sums of electron linear momenta for atoms and ions

From the second moments of the electron-pair densities in momentum space, accurate Hartree–Fock values of the average inner product sum 〈∑ _i<j p _i ·p _j 〉 of electron linear momenta are evaluated for the 102 neutral atoms from He to Lr, the 53 singly charged cations from Li⁺ to Cs⁺, and the 43 stable anions from H⁻ to I⁻ in their experimental ground states. The present results are new for 38 species and improve the literature values for 68 species. Received: 18 July 2002 / Accepted: 4 September 2002 / Published online: 8 November 2002 Acknowledgement. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan. Correspondence to: H. Matsuyama e-mail: hisashi@mmm.muroran-it.ac.jp     

Correlating basis sets for the H atom and the alkali-metal atoms from Li to Rb

 Contracted Gaussian-type function sets are developed for correlating p, d, and f functions for a valence electron of the hydrogen atom and alkali-metal atoms from Li to Rb. A segmented contraction scheme is used for its compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from the K orbitals of the atoms. The present basis sets yield an accuracy comparable to the correlation-consistent basis set for the hydrogen atom and also give a similar high accuracy for the alkali-metal atoms. In the calculations of spectroscopic constants of alkali hydrides, the decontraction of the p function plays an important role, especially for LiH. The contributions of d and f functions are nontrivial for KH and RbH. Received: 6 September 2002 / Accepted: 13 November 2002 / Published online: 19 March 2003 Acknowledgements. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan. Correspondence to: T. Noro e-mail: tashi@sci.hokudai.ac.jp     

An atom-in-molecules and electron-localization-function study of the interaction between O2 and VxOy+/VxOy (x = 1, 2, y = 1–5) clusters

 The most stable structures of V _x O _y ⁺/V _x O _y (x=1, 2, y=1–5) clusters and their interaction with O₂ are determined by density functional calculations, the B3LYP functional with the 6-31G* basis set. The nature of the bonding of these clusters and the interaction with O₂ have been studied by topological analysis in the framework of both the atoms-in-molecules theory of Bader and the Becke–Edgecombe electron localization function. Bond critical points are localized by means of the analysis of the electron density gradient field, ∇ρ(r), and the electron localization function gradient field, ∇η(r). The values of the electron density properties, i.e., electron density, ρ(r), Laplacian of the electron density, ∇²ρ(r), and electron localization function, η(r), allow the nature of the bonds to be characterized, and linear correlation is found for the results obtained in both gradient fields. Vanadium-oxygen interactions are characterized as unshared-electron interactions, and linear correlation is observed between the electron density properties and the V–O bond length. In contrast, O₂ units involve typical shared-electron interactions, as for the dioxygen molecule. Four different vanadium–oxygen interactions are found and characterized: a molecular O₂ interaction, a peroxo O₂ ²⁻ interaction, a superoxo O₂ ⁻ interaction and a side-on O₂ ⁻ interaction. Received: 15 October 2001 / Accepted: 30 January 2002 / Published online: 24 June 2002     

Formulas and numerical table for the radial part of overlap integrals with the same screening parameters of Slater-type orbitals

 The numerical properties of the radial part of overlap integrals with the same screening parameters in the form of polynomials in p = ξR over Slater-type orbitals have been studied and obtained by using three different methods. For that purpose, the characteristics of auxiliary functions were used first, then Fourier transform convolution theorem, and recurrence relations for the basic coefficients of A ^s _{n l λ, n ′ l ′λ} were used. The calculations of the radial part of overlap integrals with the same screening parameters were made in the range 1 ≤ n ≤ 75, 1 ≤ n′ ≤ 75, and 10⁻⁶ ≤ p. Received: 18 January 2001 / Accepted: 5 April 2001 / Published online: 27 June 2001     

Solvent effects on the electronic absorption spectrum of formamide studied by a sequential Monte Carlo/quantum mechanical approach

Sequential Monte Carlo/quantum mechanical calculations are performed to study the solvent effects on the electronic absorption spectrum of formamide (FMA) in aqueous solution, varying from hydrogen bonds to the outer solvation shells. Full quantum-mechanical intermediate neglect of differential overlap/singly excited configuration interaction calculations are performed in the supermolecular structures generated by the Monte Carlo simulation. The largest calculation involves the ensemble average of 75 statistically uncorrelated quantum mechanical results obtained with the FMA solute surrounded by 150 water solvent molecules. We find that the n → π* transition suffers a blueshift of 1,600 cm⁻¹ upon solvation and the π → π* transition undergoes a redshift of 800 cm⁻¹. On average, 1.5 hydrogen bonds are formed between FMA and water and these contribute with about 20% and about 30% of the total solvation shifts of the n → π* and π → π* transitions, respectively. The autocorrelation function of the energy is used to sample configurations from the Monte Carlo simulation, and the solvation shifts are shown to be converged values. Received: 14 March 2002 / Accepted: 3 April 2002 / Published online: 24 June 2002     

Ab initio study of bonding trends for f0 actinide oxyfluoride species

 Fully relativistic, four-component Dirac–Fock calculations and quasirelativistic pseudopotential calculations at different ab initio levels are used to study the bonding trends among the naked, triatomic [OAnO] ^q+ groups or the oxyfluorides [AnO _n F _m ] ^q with f ⁰ configurations. The triatomic f ⁰ series is suggested to range from the bent ThO₂ via the linear OPaO⁺ to at least NpO₂ ³⁺, a possible new gas-phase species. The neutral oxyfluoride molecules include the experimentally unknown NpO₂F₃ and PuO₂F₄. The latter is a candidate for the so far unknown oxidation state Pu(VIII), which is found to lie considerably above Pu(VI), but to be locally stable. Their all-oxygen isoelectronic analogues are NpO₅ ³⁻, known in the solid state, and the unknown PuO₆ ⁴⁻. Further possible candidates for Pu(VIII) are PuO₄(D _4h ) and the cube-shaped PuF₈(O _h ). Isoelectronic UF₈ ²⁻ is calculated to be D _4d , in agreement with experiment. Received: 18 May 2001 / Accepted: 21 June 2001 / Published online: 11 October 2001     

Conformational Properties of (Z,Z)-, (E,Z)-, and (E,E)-Cycloocta-1,4-dienes

Summary.  Ab initio calculations at the HF/6-31G^* level of theory for geometry optimization and the MP2/6-31G^*//HF/6-31G^* level for a single point total energy calculation are reported for (Z,Z)-, (E,Z)-, and (E,E)-cycloocta-1,4-dienes. The C ₂-symmetric twist-boat conformation of (Z,Z)-cycloocta-1,4-diene was calculated to be by 3.6 kJ·mol⁻¹ more stable than the C _S-symmetric boat-chair form; the calculated energy barrier for ring inversion of the twist-boat conformation via the C _S-symmetric boat-boat geometry is 19.1 kJ·mol⁻¹. Interconversion between twist-boat and boat-chair conformations takes place via a half-chair (C ₁) transition state which is 43.5 kJ·mol⁻¹ above the twist-boat form. The unsymmetrical twist-boat-chair conformation of (E,Z)-cycloocta-1,4-diene was calculated to be by 18.7 kJ·mol⁻¹ more stable than the unsymmetrical boat-chair form. The calculated energy barrier for the interconversion of twist-boat-chair and boat-chair is 69.5 kJ·mol⁻¹, whereas the barrier for swiveling of the trans-double bond through the bridge is 172.6 kJ·mol⁻¹. The C _S symmetric crown conformation of the parallel family of (E,E)-cycloocta-1,4-diene was calculated to be by 16.5 kJ·mol⁻¹ more stable than the C _S-symmetric boat-chair form. Interconversion of crown and boat-chair takes place via a chair (C _S) transition state which is 37.2 kJ·mol⁻¹ above the crown conformation. The axial- symmetrical twist geometry of the crossed family of (E,E)-cycloocta-1,4-diene is 5.9 kJ·mol⁻¹ less stable than the crown conformation. Corresponding author. E-mail: isayavar@yahoo.com Received March 25, 2002; accepted April 3, 2002     

Density functional computation of 55Mn NMR parameters

Gradient-corrected (GGA) and hybrid variants of density functional theory are used to compute geometries and ⁵⁵Mn chemical shifts of MnO₄ ⁻, Mn(CO)₆ ⁺, Mn₂(CO)₁₀, Mn(CO)₅ X [X=H, Cl, C(O)Me], Mn(CO)₅ ⁻, Mn(NO)₃(CO), and Mn(C₅H₅)L _x [L _x =(CO)₃, C₆H₆, C₇H₈]. For this set of compounds, substituent effects on δ(⁵⁵Mn) are significantly underestimated with the pure GGA functional BPW91 and are well described with hybrid functionals such as mPW1PW91 and, in particular, B3LYP. The computed data provide evidence for solvent and counterion effects on δ(⁵⁵Mn) of MnO₄ ⁻ and Mn(CO)₆ ⁺, respectively. The latter, in the presence of Cl⁻, may be described as highly fluxional Mn(CO)₅C(O)Cl. Electric field gradients computed with the B3LYP functional can be used for a qualitative rationalization of observed trends in ⁵⁵Mn NMR line widths. Electronic supplementary material to this paper can be obtained by using the Springer LINK server located at http://dx.doi.org/10.1007/s002140020338x Received: 17 January 2002 / Accepted: 13 March 2002 / Published online: 3 June 2002     

A DFT study of pyramidalized alkenes: 7-oxasesquinorbornenes and 7,7′-dioxasesquinorbornenes

  DFT calculations of 7′–oxasesquinorbornenes and 7,7′-dioxasesquinorbornenes using the B3LYP/6–31G* method are reported. All the investigated structures (syn- and anti- derivatives) showed significant non-planarity of the central double bond, with the exception of those anti-derivatives possessing symmetrical structures. The influence of the replacement of the methylene groups at position 7- of the norbornene fragment with oxygen and the introduction of second and third (peripheral) double bonds and benzene rings on the molecular and electronic structures of these molecules have also been investigated. Received: 11 November 2002 / Accepted: 6 June 2002 / Published online: 29 April 2003     

The calculation of electron localization and delocalization indices at the Hartree–Fock, density functional and post-Hartree–Fock levels of theory

 Localization, λ(A), and delocalization indices, δ(A,B), as defined in the atoms in molecules theory, are a convenient tool for the analysis of molecular electronic structure from an electron-pair perspective. These indices can be calculated at any level of theory, provided that first- and second-order electron densities are available. In particular, calculations at the Hartree–Fock (HF) and configuration interaction (CI) levels have been previously reported for many molecules. However, λ(A) and δ(A,B) cannot be calculated exactly in the framework of Kohn–Sham (KS) density functional theory (DFT), where the electron-pair density is not defined. As a practical workaround, one can derive a HF-like electron-pair density from the KS orbitals and calculate approximate localization and delocalization indices at the DFT level. Recently, several calculations using this approach have been reported. Here we present HF, CI and approximate DFT calculations of λ(A) and δ(A,B) values for a number of molecules. Furthermore, we also perform approximate CI calculations using the HF formalism to obtain the electron-pair density. In general, the approximate DFT and CI results are closer to the HF results than to the CI ones. Indeed, the approximate calculations take into account Coulomb electron correlation effects on the first-order electron density but not on the electron-pair density. In summary, approximate DFT and CI localization and delocalization indices are easy to calculate and can be useful in the analysis of molecular electronic structure; however, one should take into account that this approximation increases systematically the delocalization between covalently bonded atoms, with respect to the exact CI results. Received: 13 February 2002 / Accepted: 24 April 2002 / Published online: 18 June 2002     

Dipole–reaction field interaction model for the solvent reorganization energy and its application to the benzoquinone–benzoquinone anion radical system

 Based on the spherical cavity approximation and the Onsager model, a dipole–reaction field interaction model has been proposed to elucidate the solvent reorganization energy of electron transfer (ET). This treatment only needs the cavity radius and the solute dipole moment in the evaluation of the solvent reorganization energy, and fits spherelike systems well. As an application, the ET reaction between p-benzoquinone and its anion radical has been investigated. The inner reorganization energy has been calculated at the level of MP2/6–31+G, and the solvent reorganization energies of different conformations have been evaluated by using the self-consistent reaction field approach at the HF/6–31+G level. Discussions have been made on the cavity radii and the values are found to be reasonable when compared with the experimental ones of some analogous intramolecular ET reactions. The ET matrix element has been determined on the basis of the two-state model. The fact that the value of the ET matrix element is about 10 times larger than RT indicates that this ET reaction can be treated as an adiabatic one. By invoking the classical Marcus ET model, a value of 4.9 × 10⁷M⁻¹s⁻¹ was obtained for the second-order rate constant, and it agrees quite well with the experimental one. Received: 19 October 2001 / Accepted: 17 January 2002 / Published online: 3 May 2002     

Relativistic and nonrelativistic finite nucleus optimized double zeta basis sets for the 4p, 5p and 6p elements (Theor Chem Acc (1998) 99:366-371): addendum

 The coefficients of the atomic Foldy-Wout-huysen transformed large component, which can be used in scalar relativistic calculations, are provided in an internet archive for the relativistic double zeta basis sets for the 4p, 5p and 6p elements previously published by the author. Published online: 14 November 2002 Correspondence to: K.G. Dyall e-mail: dyall@schrodinger.com     

Structures and stability of N9, N9 − and N9 + clusters

 Ab initio molecular orbital calculations for N₉, N⁻ ₉ and N⁺ ₉ isomers were carried out at the HF/ 6-31G*, B3PW91/6-31G*, B3LYP/6-31G* and MP2/ 6-31G* levels of theory. Stable equilibrium geometric structures were determined by harmonic vibrational frequency analyses at the HF/6-31G*, B3PW91/6-31G* and B3LYP/6-31G* levels of theory. The most stable free-radical N₉ cluster is structure 1 with C _{2 v} symmetry and that of anion N⁻ ₉ is structure 3 with C _s symmetry. Only one stable structure of the N⁺ ₉ cation with C _{2 v} symmetry was predicted. Their potential application as high-energy-density materials has been examined. Received: 15 June 1999 / Accepted: 11 October 1999 / Published online: 14 March 2000     

A correlation-consistent basis set for Fe

 A series of correlation-consistent basis sets are developed for Fe. Our best computed ⁵F–⁵D separation in the Fe atom is in excellent agreement with experiment. Our best estimate for the FeCO D ₀ value is in good agreement with experiment. The ⁵Σ⁻–³Σ⁻ separation in FeCO has an error of 3.6 kcal/mol; while the origin of this error is not clear, it is probably not due to the basis set. Received: 5 March 2001 / Accepted: 2 May 2001 / Published online: 9 August 2001     

Physical analysis of the diatomic “chemical” energy components

 The recent “chemical energy component analysis” permits the total energy of a molecule to be presented approximately but to good accuracy as a sum of atomic and diatomic energy contributions. Here the diatomic energy components are further decomposed into terms of different physical origin: electrostatics (in point-charge approximation and the distributed charge corrections), exchange effects, diatomic overlap and atomic basis extension terms. This analysis may provide us with a deeper insight into the factors influencing both the chemical bonds and the nonbonded interatomic interactions. Received: 6 May 2002 / Accepted: 13 November 2002 / Published online: 19 March 2003 Acknowledgements. The authors are indebted to the Hungarian Scientific Research Fund for partial financial support (grant no. OTKA T29716). Correspondence to: I. Mayer e-mail: mayer@chemres.hu