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.     

Electron-pairing analysis from localization and delocalization indices in the framework of the atoms-in-molecules theory

This article presents an overview of recent advances in the study of electron pairing through the use of localization and delocalization indices obtained from double integration over atomic basins of the exchange–correlation density in the framework of the atoms-in-molecules theory. These localization and delocalization indices describe the intra- and interatomic distribution of the electron pairs in a molecule. The main results of the application of these second-order indices to the analysis of molecular structure and chemical reactivity are briefly reviewed. It is shown that localization and delocalization indices represent a powerful tool to describe the electron-pair structure of molecules, which, in turn, provides deeper insight into relevant chemical phenomena such as electron correlation effects and the formation of localized α, β electron pairs. Received: 8 April 2002 / Accepted: 26 June 2002 / Published online: 6 September 2002 Acknowledgements. Financial help was furnished by the Spanish DGES projects no. PB98-0457-C02-01 and BQU2002-04112-C02-02. J.P. thanks the Departament d'Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya for benefiting from a doctoral fellowship, no. 2000FI-00582. M.S. is indebted to the Departament d'Universitats, Recerca i Societat de la Informació of the Generalitat de Catalunya for financial support through the Distinguished University Research Promotion, 2001. We also thank the Centre de Supercomputació de Catalunya for providing us with computing facilities. Correspondence to: M. Solà e-mail: miquel.sola@udg.es     

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     

Partial Hessian vibrational analysis: the localization of the molecular vibrational energy and entropy

The partial Hessian vibrational analysis (PHVA), in which only a subblock of the Hesssian matrix is diagonalized to yield vibrational frequencies for partially optimized systems, is extended to the calculation of vibrational enthalpy and entropy changes for chemical reactions. The utility of this method is demonstrated for various deprotonation reactions by reproducing full HVA values to within 0.1–0.4 kcal/mol, depending on the number atoms included in the PHVA. When combined with the hybrid effective fragment potential method [Gordon MS, et al. (2001) J Phys Chem A 105:293–307], the PHVA method can provide (harmonic) free-energy changes for localized chemical reactions in very large systems. Received: 21 September 2001 / Accepted: 30 October 2001 / Published online: 22 March 2002     

Comments on “Some fundamental problem with zero flux partitioning of electron densities”

 The article by P. Cassam-Chena? and D. Jayatilaka (Theor Chem Acc (2001) 105: 213) is critically analyzed. Received: 18 April 2001 / Accepted: 9 September 2001 / Published online: 3 June 2002     

Molecular structure and Bader's theory

 It is shown that a supposed catastrophe of Bader's theory of atoms in molecules, suggested by Cassam-chena? and Jayatilaka [Theor Chem Acc (2001) 105: 213] is merely a consequence of the approximate character of the adiabatic Born–Oppenheimer theory of molecular structure, and that nonadiabatic approaches could be in accordance with Bader's ideas. Received: 4 April 2001 / Accepted: 5 September 2001 / Published online: 3 June 2002     

Uncertainty Quantification of Reactivity Scales**

According to Mayr, polar organic synthesis can be rationalized by a simple empirical relationship linking bimolecular rate constants to as few as three reactivity parameters. Here, we propose an extension to Mayr's reactivity method that is rooted in uncertainty quantification and transforms the reactivity parameters into probability distributions. Through uncertainty propagation, these distributions can be transformed into uncertainty estimates for bimolecular rate constants. Chemists can exploit these virtual error bars to enhance synthesis planning and to decrease the ambiguity of conclusions drawn from experimental data. We demonstrate the above at the example of the reference data set released by Mayr and co-workers [J. Am. Chem. Soc. 2001 , 123, 9500; J. Am. Chem. Soc. 2012 , 134, 13902]. As by-product of the new approach, we obtain revised reactivity parameters for 36 π-nucleophiles and 32 benzhydrylium ions.     

A genetic algorithm for the structural optimization of Morse clusters

This article describes the application of a genetic algorithm for the structural optimization of 19–50-atom clusters bound by medium-range and short-range Morse pair potentials. The GA is found to be efficient and reliable for finding the geometries corresponding to the previously published global minima [Doye JPK, Wales DJ (1997) J Chem Soc Faraday Trans 93: 4233]. Using the genetic algorithm, only a relatively small number of energy evaluations and minimizations are required to find the global minima. By contrast, a simple random search algorithm often cannot find the global minima of the larger clusters, even after many thousands of searches. Received: 27 October 1999 / Accepted: 7 December 1999 / Published online: 19 April 2000     

Rotational Dynamics of Adamantanecarboxylic Acid in Complex with β-cyclodextrin

The reorientation of 1-adamantanecarboxylic acid (AdCA) within the β-cyclodextrin (β-CD) cavity is investigated by means of multiple-field ¹³C NMR relaxation. The dissociation constant describing the complexation equilibrium is determined using translational diffusion measurements for the guest during a titration by the host in D₂O/DMSO solvent mixture. The changes in apparent diffusion properties of AdCA during the titration are at 25 °C well described assuming the formation of a 1:1 complex, whereas at 0 °C the data indicate the presence of a 2:1 (guest:host) complex. The ¹³C NMR relaxation parameters for the AdCA molecule bound inside the β-CD cavity are extracted. Despite the high association constant, indicating a strong interaction between the two molecules, the guest molecule is quite mobile. The reorientation of the bound AdCA at 25 °C can be described by either the Lipari–Szabo or the axially symmetric rotational diffusion model. The motion is extremely anisotropic: the adamantyl group rotates fast around the β-CD symmetry axis, inside its cylindrical cavity. At lower temperature, the relaxation properties are no longer possible to explain using these models. Instead, the data are analyzed using extended, three-step spectral density of Clore et al. [J. Am. Chem. Soc. 112, 4989 (1990)].     

Rydberg character of the higher excited states of free-base porphin

 The Rydberg character of the excited states of free-base porphin (FBP) has been investigated by the ab initio configuration interaction singles (CIS) method and the state-averaged complete-active-space self-consistent-field method. Double-zeta basis sets augmented with s, p, and d Rydberg functions and d polarization functions have been employed. Two types of molecular orbitals sets, the restricted Hartree–Fock molecular orbitals obtained for the ground state (¹A _g ) and for the cation state (²A _u ), have been used in the CIS calculations. All the calculations show that Rydberg-type excitations play important roles especially in the N bands. In this article we propose applying the model of a perturbed Rydberg series to interpret the excited states of FBP. By using this model, we have succeeded in analyzing the characteristics of the excited states as well as the experimental oscillator strengths, which have considerable magnitude even in the higher excited states. Received: 27 November 2000 / Accepted: 11 April 2001 / Published online: 27 June 2001     

Ab initio calculations for the potential curves and spin–orbit coupling of Mg2

 The ground state and several low-lying excited states of the Mg₂ dimer have been studied by means of a combination of the complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) method and coupled-cluster with single and double excitations and perturbative contribution of connected triple excitations [CCSD(T)] scheme. Reasonably good agreement with experiment has been obtained for the CCSD(T) ground-state potential curve but the dissociation energy of the only experimentally known A¹Σ _u ⁺ excited state of Mg₂ is somewhat overestimated at the CASSCF/CASPT2 level. The spectroscopic constants D _e, R _e and ω_e deduced from the calculated potential curves for other states are also reported. In addition, some spin–orbit matrix elements between the excited singlet and triplet states of Mg₂ have been evaluated as a function of internuclear separation. Received: 10 May 2001 / Accepted: 15 August 2001 / Published online: 30 October 2001     

A proposed modification of CBS-4M model chemistry for application to molecules of increasing molecular size

 In order to calculate more accurately the enthalpies of formation, ΔH _f°(298 K), for large molecules using the CBS-4M method, a new formulation of the empirical higher-level correction to the energy is proposed: ΔE=a|S|² _{i i} I _{i i} +b(n _α+n _β)+cΔ<S ²>+Σn _i d _{i .} The new methodology (CBS-4MB) applied to a set of 114 molecules of different size significantly decreases the mean absolute deviation from 3.78 to 2.06 kcal/mol. Received: 7 February 2001 / Accepted: 5 April 2001 / Published online: 13 June 2001     

Maxwell–Cartesian spherical harmonics in multipole potentials and atomic orbitals

 The nature of the Maxwell–Cartesian spherical harmonics S ⁽ⁿ⁾ _K and their relation to tesseral harmonics Y _nm is examined with the help of “tricorn arrays” that display the components of a totally symmetric Cartesian tensor of any rank in a systematic way. The arrays show the symmetries of the Maxwell–Cartesian harmonic tensors with respect to permutation of axes, the traceless properties of the tensors, the linearly independent subsets, the nonorthogonal subsets, and the subsets whose linear combinations produce the tesseral harmonics. The two families of harmonics are related by their connection with the gradients of 1/r, and explicit formulas for the transformation coefficients are derived. The rotational transformation of S ⁽ⁿ⁾ _K functions is described by a relatively simple Cartesian tensor method. The utility of the Maxwell–Cartesian harmonics in the theory of multipole potentials, where these functions originated in the work of Maxwell, is illustrated with some newer applications which employ a detracer exchange theorem and make use of the partial linear independence of the functions. The properties of atomic orbitals whose angular part is described by Maxwell–Cartesian harmonics are explored, including their angular momenta, adherence to an Uns?ld-type spherical symmetry relation, and potential for eliminating an angular momentum “contamination” problem in Cartesian Gaussian basis sets. Received: 9 July 2001 / Accepted: 7 September 2001 / Published online: 19 December 2001     

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     

The effect of basis set superposition error on the convergence of interaction energies

 For the intermolecular interaction energies of ion-water clusters [OH⁻(H₂O) _n (n=1,2), F⁻(H₂O), Cl⁻(H₂O), H₃O⁺(H₂O) _n (n=1,2), and NH₄ ⁺(H₂O) _n (n=1,2)] calculated with correlation-consistent basis sets at MP2, MP4, QCISD(T), and CCSD(T) levels, the basis set superposition error is nearly zero in the complete basis set (CBS) limit. That is, the counterpoise-uncorrected intermolecular interaction energies are nearly equal to the counterpoise-corrected intermolecular interaction energies in the CBS limit. When the basis set is smaller, the counterpoise-uncorrected intermolecular interaction energies are more reliable than the counterpoise-corrected intermolecular interaction energies. The counterpoise-uncorrected intermolecular interaction energies evaluated using the MP2/aug-cc-pVDZ level is reliable. Received: 14 March 2001 / Accepted: 25 April 2001 / Published online: 9 August 2001     

Radial electron-pair densities in momentum space and shell structure of atoms

 The radial electron-pair intracule (relative motion) H(u) and extracule (center-of-mass motion) D(R) densities in position space were known to reveal four types of maxima which are related to the four inner electron shells, K, L, M, and N, of atoms. The corresponding radial electron-pair intracule Hˉ(v) and extracule Dˉ(P) densities in momentum space are studied for the 102 atoms from He (atomic number Z=2) to Lr (Z=103). The densities Hˉ(v) and Dˉ(P) are found to have either one maximum or two maxima, and the numbers of maxima in Hˉ(v) and Dˉ(P) are the same for 98 atoms. For these atoms, the locations υ _max and P _max and the heights Hˉ _max and Dˉ _max of the corresponding maxima satisfy the approximate relations υ _max ≅ 2P _max and Hˉ _max ≅Dˉ _max /2. On the basis of their Z-dependence, the maxima in Hˉ(v) and Dˉ(P) of the 102 atoms are classified into five types. Shell-pair decompositions of the radial densities show that these maxima reflect five outer electron shells of atoms. Received: 24 January 2001 / Accepted: 12 March 2001 / Published online: 13 June 2001     

Calculations of the geometries, electronic structures and nonlinear second-order optical susceptibilities of spiroannelated quinone-type methanofullerenes

 The equilibrium geometries, electronic structures and UV–vis spectra of a series of spiroannelated quinone-type methanofullerenes have been determined by using Zerner's intermediate neglect of differential overlap method. The results show that between fullerene and the addend there exists a special interaction, “periconjugation”, which results in through-space orbital interactions. The calculated UV–vis spectra are in good agreement with experiments. On the basis of the electronic spectra, the β values are calculated. The results show that spiroannelated quinone-type methanofullerenes have quite large β values. We attribute the large β values to both the charge transfer from C₆₀ to benzoquinone and on the C₆₀ three-dimensional conjugated sphere. Received: 17 December 2000 / Accepted: 16 March 2001 / Published online: 13 June 2001     

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