Semiempirical Hamiltonian Research Articles

Theoretical study of the second-order nonlinear optical properties of [N]helicenes and [N]phenylenes.

The second-order nonlinear optical properties of helicenes and phenylenes have been theoretically investigated at the time-dependent Hartree-Fock level using the Austin model 1 semiempirical Hamiltonian. Both the antisymmetric isotropic component of the first hyperpolarizability (beta) and its projection on the dipole moment (beta(parallel)) have been determined for increasingly large helical systems as well as for their analogs substituted by donor/acceptor pairs. It is found that (i) in nonsubstituted helicenes and phenylenes, beta increases monotonically with the size of the system and slightly depends on the nature of the helix; (ii) the corresponding beta(parallel) is mostly determined by the radial component of the first hyperpolarizability vector; (iii) in helicenes, beta(parallel) is positive and presents quasiperiodic oscillations with the helix; (iv) in phenylenes, beta(parallel) depends upon the size of the helix and it can be either positive or negative as a result of the differences in evolution with N of the radial components of the dipole moment and first hyperpolarizability. Substituting the helicenes and phenylenes by the prototypical NH2/NO2 donor/acceptor pair provides a diversity of effects on beta and beta(parallel) that encompasses decrease, increase, and change in sign.

Crossed beams and theoretical studies of the O(3P)+CH4-->H+OCH3 reaction excitation function.

The excitation function for the reaction, O(3P)+CH4-->H+OCH3, has been measured in a crossed molecular beams experiment and determined with direct dynamics calculations that use the quasiclassical trajectory method in conjunction with a recently developed semiempirical Hamiltonian. Good agreement is found between experiment and theory, enabling us to address two fundamental issues for the O(3P)+CH4 reaction that arise for all O(3P)+saturated hydrocarbon reactions: (1) the importance of triplet excited states that correlate adiabatically to ground-state reactants and products and (2) the importance of intersystem crossing processes involving the lowest singlet surface [corresponding to reaction with O(1D)]. Our results indicate that the first excited triplet surface contributes substantially to the cross section when the collision energy exceeds the reaction barrier (approximately 2 eV) by more than 0.5 eV. Although triplet-singlet crossings may occur at all energies, we have found that their effect on the excitation function is negligible for the collision energies studied-up to 1.5 eV above threshold.

A direct classical trajectory study of the acetone photodissociation on the triplet surface

Product energy distributions (PEDs) for the photodissociation of acetone at 266, 248, and 193 nm were evaluated by direct classical trajectory calculations on the lowest triplet potential energy surface. CASSCF(8,7) and MRCI+Q calculations were first performed to obtain a set of high-level ab initio data with which the semiempirical parameters were refined. The trajectories were initiated at the barrier, using two different microcanonical sampling methods. The results obtained for the excess energies corresponding to excitation at 266 and 248 nm are in good agreement with the experimental product energy partitioning, supporting a dissociation event taking place on the T1 surface after intersystem crossing from the initially exited S1 state. At 193 nm, the results obtained with the two sampling methods show significant discrepancies. The PEDs calculated with the anharmonic sampling procedure appear to be consistent with the experimental data.

Semiempirical QM/MM method for studying HCl adsorption on ice

AbstractThe combined QM/MM method, where the QM forces are obtained from a fitted PM3 semiempirical Hamiltonian, is used to study HCl adsorption at an ice surface ledge defect site. The PM3‐SSP (PM3 with system‐specific parameters) Hamiltonian allows for multidimensional molecular dynamics simulations that are computationally inexpensive while still providing valid reaction dynamics. The simulations reveal that, depending on the initial position of the HCl above the ledge and the number and positions of dangling surface hydrogens, adsorption may be molecular or dissociative. HCl binding energies and geometries at the ice defect site are similar to those for adsorption at crystalline hexagon sites. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Quantum mechanical study of the shape and stability ofSnO2nanocrystalline grains

The purpose of this study is to get insight into the instability which is observed, under operative conditions, in ${\mathrm{SnO}}_{2}$ nanocrystalline materials. To this purpose, the binding and fragmentation energies of ${\mathrm{SnO}}_{2}$ crystalline grains have been evaluated quantum mechanically at the semiempirical level using the extended Debye-H\"uckel approximation. The grain structure is assumed to be an unreconstructed rutile lattice, as in the parent solid. The grain size and shape are variable, and a parametric search has been carried out on both quantities. Ab initio calculations of the binding energies of small oxygen and tin clusters have been also performed in order to test the accuracy of the semiempirical Hamiltonian and to offer a simple description of the properties of O-O, Sn-Sn, and Sn-O bonds. It has been found that a primary role in the grain stability arises from the interplay of the grain composition and shape, rather than from its size. Furthermore, the functional dependence of each of the characteristic energies on these parameters is qualitatively similar. However, the quantitative differences are not secondary. These features represent a central difference with respect to the known properties of pure clusters whose energetics is uniquely dictated by the cluster size.

Molecular crystals: the crystal field effect on molecular electronic structure.

The effect of crystal packing on the electronic structure of organic molecules was modeled by incorporation of the external electrostatic potential into the semiempirical Hamiltonian of the molecule. An empirical correction procedure was devised in order to compensate for systematic errors in the charge distribution typical of semiempirical methods. The model was applied to 79 crystal structures belonging to various syngonies and space groups. The effect of the crystal field is subject to wide variations depending on the crystal packing motif. The difference between the effect of the crystal field on the molecular electronic structure and the solvent effect modeled with COSMO is highlighted. The effect of intermolecular hydrogen bonds on the molecular electronic structure and electronic spectra was modeled with this approach, and it does not predominate over the effect of long-range electrostatic interactions. INDO/S calculations employing the crystal electrostatic potential give an insight into the origin of crystallochromy, in particular, they properly predict color difference for several groups of polymorphs.

Theoretical Studies of the O(3P) + Ethane Reaction

The O( 3 P) + C 2 H 6 reaction has been studied at two levels of theory. First, we have carried out high-level ab initio calculations of the various asymptotes and stationary points that are relevant to collision energies associated with low Earth orbit (LEO) conditions. CCSD(T)/cc-pVTZ calculations indicate that C-C breakage can occur with energies well below those encountered in LEO and that the barrier for this reaction is the lowest energy other than that for H abstraction to generate OH. Second, we have performed extensive direct dynamics calculations employing the MSINDO semiempirical Hamiltonian and density functional theory (B3LYP/6-31G*) at various collision energies relevant to LEO. OH abstraction is the dominant process at all energies, but other products are also important. Among these, H-atom elimination to give OC 2 H 5 + H is the most important, although other products such as H 2 O + C 2 H 4 , OC 2 H 4 + 2H, and OCH 3 + CH 3 are also generated at high collision energies. Analysis of product energy distributions reveals the expected trends for H abstraction and H elimination, with the behavior for OCH 3 + CH 3 being closer to that for abstraction. Angular distributions for OH under LEO conditions show forward scattering, whereas those for H elimination and C-C breakage are sideways and backward peaked, respectively. Detailed analysis of the dynamical information will hopefully lead to a better understanding of the microscopic reaction mechanisms of the fundamental processes that contribute to LEO materials erosion.

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 Moller–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.

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.

Quantum Mechanical Characterization of Nucleic Acids in Solution: A Linear-Scaling Study of Charge Fluctuations in DNA and RNA

Atom-centered point charges are a convenient and computationally efficient way to approximately represent the electrostatic properties of biological macromolecules. Atomic charges are routinely used in molecular modeling applications such as molecular simulations, molecular recognition, and ligand binding studies and for determining quantitative structure activity relationships. In the present paper a divide-and-conquer linear-scaling semiempirical method combined with a conductor-like screening model is applied to the calculation of charge distributions of solvated DNA and RNA duplexes in canonical A- and B-forms. The atomic charges on A-DNA, B-DNA, and A-RNA duplex decamers are analyzed to characterize the convergence of the linear-scaling method, and the effects of the charge model and semiempirical Hamiltonian. Furthermore, the inter- and intramolecular charge variations on DNA and RNA duplex 72-mers are investigated to gain insight into the influence of conformation, base stacking, and solvent polari...

Spectroscopic studies and dynamics of Nd 3+ ions in RbY 2Cl 7 single crystals. Part II. Crystal-field analysis

Crystal-field energy levels of Nd 3+ ions doped in the two slightly inequivalent sites of the RbY 2Cl 7 host crystal were assigned and fitted to the parameters of a semiempirical Hamiltonian representing the combined atomic and crystal-field interactions. Using the one-electron crystal-field formalism 151 levels of the Nd(1) site and 156 levels of the Nd(2) site were assigned with a r.m.s. deviation of 17.5 and 15.4 cm −1 , respectively. Including correlation crystal-field terms into the semiempirical Hamiltonian we could obtain an improvement of the r.m.s. deviation for the Nd(1) and Nd(2) site up to 11.4 and 10.3 cm −1 , respectively, as well as the elimination of major discrepancies between the calculated and observed energy levels within the anomalous 2 H(2) 11/2 and 2 F(2) 5/2 multiplets.

Sodium Parameters for AM1 and PM3 Optimized Using a Modified Genetic Algorithm

Sodium is very important as a counterion in biology. However, when used with the most common semiempirical Hamiltonians, such as AM1 or PM3, sodium is modeled as a point charge that can accept no electron density, called a “sparkle”. To better model sodium, we derived two sets of sodium parameters, which treat sodium on the same footing as other atoms parametrized in semiempirical methods. One set is compatible with the AM1 parameter set, while the second is compatible with PM3. These parameters were derived using a modified genetic algorithm with a diverse set of 71 compounds. The average unsigned error for the heats of formation was 10.3 kcal/mol for AM1 and 10.5 kcal/mol for PM3.

Solvent dependence of structure and electronic properties in the ground and first excited singlet state of 4-dimethylamino-4 ′-nitrostilbene (DANS) – semiempirical calculations

Ground and excited state properties of trans-4-dimethylamino-4 ′-nitrostilbene (DANS) in different solvents are calculated with the semiempirical SAM1 Hamiltonian. The solvent is treated as a continuum with the conductor-like screening model. Singlet excited-state conformations at various stages of relaxation, their optical transitions, and triplet states for these geometries are reported for the first time. Relaxation pathways are suggested which may be distinguished by characteristic optical spectra and which explain why fluorescence, intersystem crossing, and internal conversion strongly depend on the solvent.

Geometry Relaxation of Photoexcited States in Conjugated Molecules

The random phase approximation combined with semiempirical Hamiltonians is applied to compute and analyze electronic structure and excited state adiabatic potentials of several conjugated molecules. Calculated excited state energies and parameters of molecular adiabatic surfaces characterize the coupled dynamics of vibrational and electronic degrees of freedom. The analysis identifies the specific torsional and bond-stretching nuclear motions that dominate the excited state relaxation and lead to self-localized excitations. This approach is an inexpensive and numerically efficient method of computing molecular excited state adiabatic surfaces and modeling femto-to-pico second time-dependent photoexcitation processes along chosen trajectories.

A semiempirical study of the optimized ground and excited state potential energy surfaces of retinal and its protonated Schiff base

The electronic ground and first excited states of retinal and its Schiff base are optimized for the first time using the semiempirical AM1 Hamiltonian. The barrier for rotation about the C 11–C 12 double bond is characterized by variation of both the twist angle δ(C 10–C 11–C 12–C 13) and the bond length d(C 11–C 12). The potential energy surface is obtained by varying these two parameters. The calculated ground state rotational barrier is equal to 15.6 kcal/mol for retinal and 20.5 kcal/mol for its Schiff base. The all- trans conformation is more stable by 3.7 kcal/mol than the 11- cis geometry. For the first excited state, S 1, the 90° twisted geometry represents a saddle point for retinal with the rotational barrier of 14.6 kcal/mol. In contrast, this conformation is an energy minimum for the Schiff base. It can be easily reached at room temperature from the planar minima since it is separated from them by a barrier of only 0.6 kcal/mol. The 90° minimum conformation is more stable than the all- trans by 8.6 kcal/mol. We are thus able to present a reaction path on the S 1 surface of the retinal Schiff base with an almost barrierless geometrical relaxation into a twisted minimum geometry, as observed experimentally. The character of the ground and first excited singlet states underscores the need for the inclusion of double excitations in the calculations.

Collective electronic oscillator/semiempirical calculations of static nonlinear polarizabilities in conjugated molecules

The collective electronic oscillator (CEO) approach based on the time-dependent Hartree–Fock approximation is combined with INDO/S, MNDO, AM1, and PM3 semiempirical Hamiltonians. This technique is applied to compute and analyze the static nonlinear polarizabilities of a series of donor/acceptor substituted oligomers. To mimic the experimental conditions, polarizabilities in substituted molecules are calculated for the isolated complex and in a dielectric medium, wherein the solvent contributions are incorporated using the self-consistent reaction field approach. The dielectric environment significantly increases second and third order static polarizabilities and considerably improves the agreement with experimental data. We find that calculated spectroscopic observables agree well with experimental values. We conclude that the CEO/semiempirical approach is an inexpensive and numerically efficient method of computing nonlinear molecular properties.

Direct Molecular Dynamics Using Quantum Chemical Hamiltonians: C60 Impact on a Passive Surface

Quantum chemical Hamiltonians of the semiempirical type potentially provide a more reliable description of a potential energy surface for large scale molecular dynamics than does the tight-binding (TB) Hamiltonian, a reparametrized extended Hückel Hamiltonian including a short range repulsion. Their performance is tested here and compared with results from TB simulations. The methods considered are from the zero differential overlap family of semiempirical Hamiltonians, these are the intermediate neglect of differential overlap (INDO) method and three parametrizations of the neglect of differential diatomic overlap (NDDO) method, AM1, PM3, and MNDO. The collision of the C60 molecule with a passive surface at two collision energies is the test problem, where the higher energy leads to shattering of the molecule. The NDDO Hamiltonians are found to give a better qualitative description than the INDO Hamiltonian at both energies and further studies to reparametrize the NDDO form for direct MD are indicated.

New electronic states close to the Fermi edge in the c(2×2) MnCu(1 0 0) surface alloy

In the present study we investigate the electronic structure of the c(2×2)Mn/Cu(100) surface alloy which is formed by adsorption of 0.5 ML of Mn on Cu(100) at room temperature. We show that the electronic structure of the MnCu surface alloy is very different to that of the clean Cu(100) surface. We focus our investigation on the electronic structure related to electronic states close to the Fermi edge. The experimental synchrotron ultraviolet photoemission spectroscopy results are compared with theoretical calculations based on the surface Green's function matching technique, using a semiempirical tight-binding hamiltonian. The theoretical results are in very good agreement with the experimental ones and confirm the surface origin of the observed new spectral features.

Fragmentation of Sn clusters by a dynamical, semi-empirical Hartree–Fock method

A time-dependent Hartree–Fock (HF) method, with a semi-empirical (SE) Hamiltonian, has been applied to study fragmentation of tin clusters of size N⩽40. Calculations of the cluster ground state have also been carried out. These calculations serve as a benchmark for the SE Hamiltonian and are analyzed in the light of theoretical and experimental results available in the literature. Fragmentation is obtained by increasing the kinetic energy E k of the nuclear system. From the simulation of fragmentation transient we obtain the minimum E k needed for fragmentation and the size of the fragments in dependence of the size N of the parent cluster. These data are compared with the emission energies evaluated for the stationary state.

Absorption Spectra and Geometries of ArN+ (N = 30−60)

We report finite temperature simulations of (N = 30−60) using a semiempirical model Hamiltonian. We calculate the photoabsorption spectra and analyze the charge distribution in both ground and excited states. The maximum photoabsorption wavelength for this set of clusters is in good agreement with experimental data. We analyze the average position of the atoms and the finite temperature distribution of the positive charge over the cluster. We find the charge localized on three atoms in the ground state and over the first two solvation spheres in the excited states. The extent of delocalization in the excited states can be correlated with the shift in the maximum photoabsorption wavelength.