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     

The inclusion of electron correlation in intermolecular potentials: applications to the formamide dimer and liquid formamide

A test of the quality of the electrostatic properties and polarizabilities used in the nonempirical molecular orbital (NEMO) potential is carried out for formamide by calculating the molecular dipole moment and polarizability at the second-order M?ller–Plesset (MP2) level of theory. The molecular dipole moment is 11% lower at the MP2 level than at the Hartree–Fock (HF) level, whereas the isotropic part of the polarizability is increased by 36% by adding electron correlation and using a considerably larger basis set. The atomic charges, dipole moments and polarizabilities obtained at the HF level are rescaled to get the correct molecular properties at the MP2 level. The potential minimum for the cyclic dimer of formamide is −17.50 kcal/mol with the MP2-scaled properties and is significantly lower than other potentials give. Two intermolecular potentials are constructed and used in subsequent molecular dynamics simulations: one with the regular NEMO potential and the other with the rescaled MP2 properties. A damping of the electrostatic field at short intermolecular distances is included in the present NEMO model. The average energies for liquid formamide are lower for the MP2-scaled model and are in good agreement with experimental results. The lowering of the simulation energy for the MP2-scaled potential indicates the strong dispersive interactions in liquid formamide. Received: 20 March 2000 / Accepted: 18 April 2000 / Published online: 18 August 2000     

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     

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     

Investigation of the S<Subscript>0</Subscript>S<Subscript>1</Subscript> excitation in bacteriorhodopsin with the ONIOM(MO:MM) hybrid method

 We have investigated the S₀ and S₁ electronic states in bacteriorhodopsin using a variety of QM/MM levels. The decomposition of the calculated excitation energies into electronic and electrostatic components shows that the interaction of the chromophore with the protein electric field increases the excitation energy, while polarization effects are negligible. Therefore, the experimentally observed reduction in excitation energy from solution phase to protein environment (the Opsin shift) does not come from the electrostatic interaction with the protein environment, but from either the interaction ofthe chromophore with the solvent or counter ion, or structural effects. Our high-level ONIOM(TD– B3LYP:Amber) calculation predicts the excitation energy within 8 kcal/mol from experiment, the discrepancy probably being caused by the neglect of polarization of the protein environment. In addition, we have shown that the level of optimization is extremely critical for the calculation of accurate excitation energies in bacteriorhodopsin. Received: 13 October 2001 / Accepted: 6 September 2002 / Published online: 3 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: K. Morokuma e-mail: morokuma@emory.edu     

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     

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     

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].     

An overlap criterion for selection of core orbitals

 An overlap criterion is defined that connects the identification of core orbitals in a molecular system, which can be problematic, to that in isolated atoms, which is well defined. This approach has been tested on a variety of troublesome systems that have been identified in the literature, including molecules containing third-row main-group elements, and is shown to remove errors of up to 100 kcal/mol arising from an inconsistent treatment of core orbitals at different locations on a potential-energy surface. For some systems and choices of core orbitals, errors as large as 19 kcal/mol can be introduced even when consistent sets of orbitals are frozen, and the new method is shown to identify these cases of substantial core–valence mixing. Finally, even when there is limited core–valence mixing, the frozen-core approximation can introduce errors of more than 5 kcal/mol, which is much larger than the presumed accuracy of models such as G2 and CBS-QB3. The source of these errors includes interatomic core–core and core–valence dispersion forces. Received: 31 August 2001 / Accepted: 11 October 2001 / Published online: 9 January 2002     

Computational modeling of enzymatic keto-enol isomerization reactions

Catalysis of proton abstraction from nonacidic carbon atoms adjacent to a carbonyl or carboxylate group is a fundamental reaction in enzymology that has been extensively studied during the last few decades. Enzymes catalyzing these reactions, which normally involve labile enolic intermediates, need to overcome large pK _a differences between the reacting groups as well as high intrinsic free-energy barriers. Here, we present an overview of results from recent computer simulation studies of keto-enol isomerization reactions catalyzed by the enzymes glyoxalase I, triosephopsphate isomerase and ketosteroid isomerase. For all three enzymes it is found that electrostatic stabilization of the transient enolate intermediates, either by charge–charge interactions or by hydrogen bonding, accounts for the main part of the activation free-energy barrier reduction. Another catalytic effect observed in all cases is the reduction of the reorganization energy by the enzyme active site. Some other factors that have been proposed to be important for these reactions are also discussed and evaluated. Received: 3 January 2002 / Accepted: 13 May 2002 / Published online: 29 July 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     

Unified analytical treatment of one-electron two-center integrals with noninteger n Slater-type orbitals

A unified treatment of one-electron two-center integrals over noninteger n Slater-type orbitals is described. Using an appropriate prolate spheroidal coordinate system with the two atomic centers as foci, all the molecular integrals are expressed by a single analytical formula which can be readily and compactly programmed. The analysis of the numerical performance of the computational algorithm is also presented. Received: 1 April 1999 / Accepted: 2 July 1999 / Published online: 2 November 1999     

Electron localization function for transition-metal compounds

 The analysis of the electron localization function of molecules and solids needs to involve the atomic core regions as well to reveal a more detailed insight into the bonding situation. Received: 20 February 2002 /Accepted: 14 June 2002 /Published online: 19 August 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     

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