Evaluation of the Coulomb energy in relativistic self-consistent-field theory

 Computational schemes are presented with which to evaluate the electrostatic Coulomb energy in relativistic molecular electronic structure calculations using a basis of four-component Dirac spinor amplitudes. We demonstrate that algorithms may be constructed and implemented which differ only in minor details from those in common use in nonrelativistic quantum chemistry, and that the four-component formalism is neither as complicated nor as expensive as has been suggested recently in the literature. Spherically symmetrical atomic basis sets are presented which indicate that accurate representations of the Coulomb energy may be obtained using modest expansions of the electronic density in a scalar auxiliary basis set of spherical harmonic Gaussian-type functions. Received: 15 April 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002     

A singularity excluded approximate expansion scheme in relativistic density functional theory

 A singularity excluded approximate expansion (SEAX) scheme, which can be considered as one between Breit-Pauli expansion and RA expansion schemes, is proposed to expand the total energy of 4-component relativistic density functional theory. The one-electron equation can be derived variationally from the approximate total energy expression. The Hamiltonian of the one-electron equation is bounded from below and can be dealt with variationally, and the gauge dependency error in the ZORA method is essentially eliminated. It is easier to solve the SEAX equation than the IORA equation. The results related to the valence orbitals by solving the scalar SEAX equation agree very well with those by the scalar ZORA ESA method, and the results related to the inner-shell electrons of heavy elements by the two component SEAX calculations agree quite well with those by the 4-component relativistic density functional calculations. Received: 20 February 2002 / Accepted: 29 April 2002 / Published online: 8 July 2002     

Semiempirical QM/MM potential with simple valence bond (SVB) for enzyme reactions. Application to the nucleophilic addition reaction in haloalkane dehalogenase

 We present a method for the correction of errors in combined QM/MM calculations using a semiempirical Hamiltonian for enzyme reactions. Since semiempirical models can provide a reasonable representation of the general shape of the potential energy surface for chemical reactions, we introduce a simple valence bond-like (SVB) term to correct the energies at critical points on the potential energy surface. The present SVB term is not a stand-alone potential energy function, but it is used purely for introducing small energy corrections to the semiempirical Hamiltonian to achieve the accuracy needed for modeling enzymatic reactions. We show that the present coupled QM-SVB/MM approach can be parameterized to reproduce experimental and ab initio results for model reactions, and have applied the PM3-SVB/MM potential to the nucleophilic addition reaction in haloalkane dehalogenase. In a preliminary energy minimization study, the PM3-SVB/MM results are reasonable, suggesting that it may be used in free energy simulations to assess enzymatic reaction mechanism. Received: 1 November 2001 / Accepted: 6 September 2002 / Published online: 19 February 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: Lakshmi S. Devi-Kesavan e-mail: kesavan@chem.umn.edu Acknowledgments. The work is partially supported by the NIH and the NSF.     

The fundamental nature and role of the electrostatic potential in atoms and molecules

 A variety of atomic and molecular properties can be expressed in terms of the electrostatic potential. These include energies, covalent and anionic radii, electronegativities (chemical potentials) and a variety of properties that depend upon noncovalent interactons. We present a survey of such relationships, which may be exact or approximate; they may involve the potential in three-dimensional space, along the axes between bonded atoms, at nuclei or on molecular surfaces. Thus, the electrostatic potential, which is rigorously related to the electronic density by Poisson's equation, can be regarded as, effectively, another fundamental determinant of atomic and molecular properties. Received: 6 March 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002     

Variational calculations for the energy levels of confined two-electron atomic systems

An accurate variational calculation has been performed for the ground-state-energy values of confined two-electron isoelectronic series from He to Ar¹⁶⁺. The confinement is obtained by embedding the ion in an overall charge neutral environment like that of a plasma. The confinement potential is chosen as that of a screened Coulomb potential between charges, obtained from a Debye model. The wave function is expanded in terms of product basis sets involving interparticle coordinates. The energy levels are found to be less bound with an increase of the screening parameter and ultimately become unstable. One- and two-particle moments have been calculated for the first time under such screening. The study is expected to throw new light on the behavior of the energy levels of foreign atoms embedded in an overall neutral environment which can be treated like a plasma. Received: 1 May 2002 / Accepted: 4 September 2002 / Published online: 6 November 2002 Acknowledgements. P.K.M. thanks the Max Planck Institute for Astrophysics, Garching, for financial support of his research visit to the institute where part of the work was performed. He also thanks the Council of Scientific and Industrial Research, Government of India, for research grant no. (03)/(0888)/99/EMR II. Correspondence to: P.K. Mukherjee e-mail: sppkm@mahendra.iacs.res.in     

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     

Mechanism and control of molecular energy flow: a modeling perspective

 Vibrational energy flow in organic molecules occurs by a multiple-time-scale mechanism that can be modeled by a single exponential only in its initial stages. The mechanism is a consequence of the hierarchical structure of the vibrational Hamiltonian, which leads to diffusion of vibrational wavepackets on a manifold with far fewer than the 3N−6 dimensions of the full vibrational state space. The dynamics are controlled by a local density of states, which does not keep increasing with molecular size. In addition, the number of vibrational coordinates severely perturbed during chemical reaction is small, leading to preservation of the hierarchical structure at chemically interesting energies. This regularity opens up the possibility of controlling chemical reactions by controlling the vibrational energy flow. Computationally, laser control of intramolecular vibrational energy redistribution can be modeled by quantum-classical, or by purely quantum-mechanical models of the molecule and control field. Received: 26 July 2002 / Accepted: 30 September 2002 / Published online: 2 December 2002 Electronic Supplementary Material to this paper can be obtained by using the Springer Link server located at http://dx.doi.org/10.1007/s00214-002-0394-2. Acknowledgements. This work was supported by NSF grant CHE 9986670. Correspondence to: M. Gruebele e-mail: gruebele@scs.uiuc.edu     

Role of twisting and sliding on the solvation of a stacked cytosine dimer: an ab initio study

Ab initio calculations with inclusion of correlation effects at the MP2/6-31G* level have been used to predict the interaction energy of stacked cytosine dimer (C/C) as a function of twisting and sliding in the gas phase. Systematic calculations have also been carried out on the solvation free energies of various rotated and translated C/C dimers using a polarized continuum model approach at the HF/6-31G* level with a view to probe the role of various degrees of freedom on the free energy of solvation of the C/C dimer. The interaction energy of the C/C dimer decreases upon changing from a parallel to an antiparallel conformation in the gas phase. The 180°-rotated conformation has been found to be the most stable arrangement when compared to other rotated positions. The rotated and translated dimers exhibit lower solvation free energy than the parallel conformation. The decrease in the dipole moment upon rotation from the parallel to the antiparallel conformation indicates the cancellation of charge distribution upon rotation in the z direction of one cytosine base with respect to the other. The calculation reveals that the present approach could not yield association energy, ΔΔG _Asso, in a solvent medium. This may be due to the fact that in the case of floppy molecules the contribution from translational, rotational and vibrational free energies plays a significant role in the calculation of ΔΔG _Asso. Received: 13 December 2001 / Accepted: 25 March 2002 / Published online: 13 June 2002     

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     

Transition states from empirical force fields

 This is an overview of the use of empirical force fields in the study of reaction mechanisms. Empirical-valence-bond-type methods (including reactive force field and multiconfigurational molecular mechanics) produce full reaction surfaces by mixing, in the simplest case, known force fields describing reactants and products. The SEAM method instead locates approximate transition structures by energy minimization along the intersection of the component force fields. The transition-state force-field approach (including Q2MM) designs a new force field mimicking the transition structure as an energy minimum. The scope and applicability of the various methods are compared. Received: 17 April 2002 / Accepted: 26 July 2002 / Published online: 4 November 2002 Correspondence to: P.-O. Norrby e-mail: pon@kemi.dtu.dk     

Second-order Møller–Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals

 The second-order correlation energy of M?ller–Plesset perturbation theory is computed for the neon atom using a wave function that depends explicitly on the interelectronic coordinates (MP2-R12). The resolution-of-identity (RI) approximation, which is invoked in the standard formulation of MP2-R12 theory, is largely avoided by rigorously computing the necessary three-electron integrals. The basis-set limit for the second-order correlation energy is reached to within 0.1 mE _h. A comparison with the conventional RI-based MP2-R12 method shows that only three-electron integrals over s and p orbitals need to be computed exactly, indicating that the RI approximation can be safely used for integrals involving orbitals of higher angular momentum. Received: 9 May 2001 / Accepted: 31 October 2001 / Published online: 9 January 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     

Internal rotation in squaramide and related compounds. A theoretical ab initio study

The structural and energetic changes associated with C–N bond rotation in a squaric acid derivative as well as in formamide, 3-aminoacrolein and vinylamine have been studied theoretically using ab initio molecular orbital methods. Geometry optimizations at the MP2(full)/6-31+G* level confirmed an increase in the C–N bond length and a smaller decrease in the C=O length on going from the equilibrium geometry to the twisted transition state. Other geometrical changes are also discussed. Energies calculated at the QCISD(T)/6-311+G** level, including zero-point-energy correction, show barrier heights decreasing in the order formamide, squaric acid derivative, 3-aminoacrolein and vinylamine. The origin of the barriers were examined using the atoms-in-molecules approach of Bader and the natural bond orbital population analysis. The calculations agree with Pauling's resonance model, and the main contributing factor of the barrier is assigned to the loss of conjugation on rotating the C–N bond. Finally, molecular interaction potential calculations were used to study the changes in the nucleophilicity of N and O (carbonyl) atoms upon C–N rotation, and to obtain a picture of the abilities of the molecules to act in nonbonded interactions, in particular hydrogen bonds. The molecular interaction potential results confirm the suitability of squaramide units for acting as binding units in host–guest chemistry. Received: 13 March 2002 / Accepted: 23 June 2002 / Published online: 21 August 2002     

Band structure representations of the electronic structure of one-dimensional materials with helical symmetry

 The relationship between band structure and the topology of the orbital interactions between neighboring chemical units comprising several model one-dimensional polymers with helical (screw-axis) symmetry is analyzed. A perturbative model of orbital interactions based on a tight binding implementation of the extended Hückel method is developed. The model accounts for both the band topologies and the seemingly anomalous band extrema within the Brillouin zone constructed using the chemical repeat unit of the polymer. Received: 5 November 2001 / Accepted: 14 January 2002 / Published online: 3 May 2002     

A thermodynamic and kinetic study of the formation of C<Subscript>20</Subscript> compounds encapsulating H,He and Ne atoms

 Binding energies of helium, neon and atomic hydrogen encapsulated inside a C₂₀ cage were calculated using an ab initio method at the B3LYP/6-31+G⋆ level of theory. The standard equilibrium constants for the reactions of noble-gas atoms going into the C₂₀ molecular cage have also been studied. The transition states for the reactions of C₂₀ with hydrogen and helium were further obtained with an ab initio method at the B3LYP/6-31+G⋆ level and the rate constants were estimated by using conventional transition-state theory. It was found that the hydrogen and helium atoms are extremely difficult to put into the C₂₀ cage. Once inside the cage, a helium atom can hardly get out, while a hydrogen atom can easily escape from the cage. The results are expected to enrich fullerene science and be helpful for fullerene applications such as storage. Received: 2 November 2002 / Accepted: 19 December 2002 / Published online: 30 April 2003 Correspondence to: R. Q. Zhang, e-mail: aprqz@cityu.edu.hk Acknowledgements. The work described in this paper was jointly supported by a grant from the City University of Hong Kong (project no. 7001222) and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. 9040633/CityU, 1011/01P].     

Ab initio structure and vibrational frequencies of lithium aromatic sulfonyl imide salts

The structure and vibrational frequencies of an aromatic lithium sulfonyl imide, i.e., lithium bis(4-nitrophenylsulfonyl)imide (LiNPSI) has been studied using self-consistent ab initio Hartree–Fock and hybrid density functional methods. These calculations engender two linkage isomers, which correspond to the local minima on the potential-energy surface. In the lowest-energy isomer, the ligand binds to the metal ion through two oxygens, one from each of the different SO₂ groups on the central nitrogen and forms a six-membered ring. Another LiNPSI isomer, wherein the anion coordinates through oxygen and nitrogen atoms and which is 55.9 kJmol⁻¹ higher in energy, has also been obtained. The S–N–S bond angle in the free anion as well as in the LiNPSI complex turns out to be nearly 121°. A comparison of the vibrational spectra of the free NPSI anion and that of the LiNPSI complex reveals that the SO₂ stretching vibrations at 1,239 and 1,205 cm⁻¹ can be used to differentiate between the two linkage isomers of the complex. The stronger complexation ability of the NPSI anion, compared to that for (CF₃SO₂)₂N⁻ has been explained in terms of the charge density within the molecular electrostatic potential isosurface encompassing both SO₂ groups of the anion. Received: 20 February 2002 / Accepted: 25 March 2002 / Published online: 3 June 2002     

On the relation between a common gauge origin formulation and the GIAO formulation of the NMR shielding tensor

In this article the formal equivalence between the “gauge including atomic orbitals” (GIAO) and the simpler common gauge (cg) formulations of the nuclear magnetic resonance (NMR) shielding tensor is proven. To be able to give this proof, one has to assume exactly solved zeroth order quantum mechanical equations and complete basis sets. The proof of the equivalence has been known in the literature for some time (e.g. S.T. Epstein `The variation method in quantum chemistry', Academic Press, 1974). However, our approach has the advantage that, by comparing the GIAO and cg methods, it provides insight into the para- and diamagnetic contributions of the shielding. Thus, it yields justification for qualitative analysis schemes that have been used to explain trends in chemical shifts. Our formal proof is based on density functional theory. However, it is argued that very similar arguments should apply to other levels of theory as well. Received: 25 June 2002 / Accepted: 18 July 2002 / Published online: 15 October 2002 Acknowledgments. The author would like to acknowledge Tom Ziegler, Calgary, for numerous discussions on the subject. The reviewer is acknowledged for the insightful and detailed comments. Correspondence to: G. Schreckenbach e-mail: schrecke@alcor.concordia.ca     

Influence of diffuse and polarization functions on the second-order Møller–Plesset optimized dihedral angle of biphenyl

 Using 6-31G and 6-311G basis sets to which diffuse and polarization functions were added in a stepwise fashion (a total of 16 basis sets), Hartree–Fock (HF), MP2 and B3LYP geometry optimizations were performed on biphenyl. With the MP2 method, diffuse functions raise the dihedral angle φ, for example, from 46.3° for 6-31G to 54.1° for 6-311++G, while polarization functions lower it, for example, from 54.1° for 6-311++G to 42.1° for 6-311++G(2d,2p). For a single set of polarization functions, φ(MP2) lies close to or above φ(HF) (44–47°), but for a double set it is below φ(HF) and is close to B3LYP values (38–42°) which show little basis set dependence. The most reliable value for φ, 42.1° [MP2/6-311++G(2d,2p)], is expected to increase slightly by adding more diffuse functions. The corresponding best calculated energy barrier at 0° (coplanar conformation) is 2.83 kcal/mol, much higher than the experimental estimate (1.4 ± 0.5 kcal/mol). The barrier at 90° is 1.82 kcal/mol, in line with the experimental estimate (1.6 ± 0.5 kcal/mol) and with previous theoretical results. Received: 9 September 2002 / Accepted: 15 November 2002 / Published online: 1 April 2003 Correspondence to: Friedrich Grein e-mail: fritz@unb.ca Acknowledgement. The author would like to thank NSERC (Canada) for financial support.     

Accuracy assessment of semiempirical molecular electrostatic potential of proteins

 Accurate electrostatic maps of proteins are of great importance in research of protein interaction with ligands, solvent media, drugs, and other biomolecules. The large size of real-life proteins imposes severe limitations on computational methods one can use for obtaining the electrostatic map. Well-known accurate second-order M?ller–Plesset and density functional theory methods are not routinely applicable to systems larger than several hundred atoms. Conventional semiempirical tools, as less resource demanding ones, could be an attractive solution but they do not yield sufficiently accurate calculation results with reference to protein systems, as our analysis demonstrates. The present work performs a thorough analysis of the accuracy issues of the modified neglect of differential overlap type semiempirical Hamiltonians AM1 and PM3 on example of the calculation of the molecular electrostatic potential and the dipole moment of natural amino acids. Real capabilities and limitations of these methods with application to protein modeling are discussed. Received: 26 April 2002 / Accepted: 19 September 2002 / Published online: 14 February 2003