Semiempirical Hamiltonian Research Articles

Mode assignment for linear phenyl acetylene sequence: phenylacetylene, di-phenylacetylene and 1,4-di(phenylethynyl)benzene

Normal mode derivation for a large molecule at the harmonic approximation level, is still, a demanding task for ab initio large-size basis or functional densities methods. Build in-process additive errors, affect the accuracy and often limit the applicability of such. It is argued here, that in cases, where point group symmetry of a large molecule is not lower then the symmetry of the related structural “building-block”, normal mode unfolding scheme could be effectively predicted from group theory considerations and the vibrational structure of the building block. A simple semiempirical Hamiltonian could be then utilized in order to obtain a mode assignment for the large molecule. In the present study, vibrational mode assignment for members of a poly-phenylacetylene linear chain: 1,4-di(phenylethynyl) benzene (DPB), diphenylacetylene (DPA) and phenyl acetylene (PA) is obtained. Their structure was calculated by means of the computationally efficient semiemprical RHF PM3 Hamiltonian. Raman and FTIR spectra were taken and assign with mutual correspondence for the three compounds. The remaining weak peaks observed in the spectra were successfully described as overtones and combinations. Few medium sized modes were identified as Fermi resonances. The overall, mode-unfolding scheme of the DPB, which was originated in the DPA, which in turn was originated in the PA, was established. The successive elements of the linear poly-phenylacetylene chain are all members of a same D 2h point group, except the phenyl acetylene which is of lower C 2v point group. It is argued here, that the same principle allows us to predict the unfolding scheme further for linear DPB…+PA, but not for the lower symmetry phenyl acetylene macro cycles.

Semiempirical implementation of strictly localized geminals for analysis of molecular electronic structure

AbstractApproximate electronic trial wave function taken as the antisymmetrized product of strictly localized geminals (APSLG) is implemented for semiempirical analysis of molecular electronic structure of “organic” compounds and for calculations of their heats of formation. This resulted in an O(N)‐scaling method. Using the MINDO/3 form of the semiempirical Hamiltonian with reparameterized βAB values in combination with the APSLG form of the wave function yields the computational procedure BF'98. Calculations on the heats formation and the equilibrium geometries for a wide range of molecules show that the APSLG‐MINDO/3 approach is more favorable than its self‐consistent field‐based counterpart. Also, the APSLG formalism allows to interpret molecular electronic wave function in chemically sensible terms. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 752–764, 2001

Franck–Condon spectra and electron-libration coupling in para-polyphenyls

Proceeding from quantum-chemical potential energy surfaces, we compute the absorption and fluorescence spectra of conventional and ladder-type para-phenylene oligomers (OPP and OLPP) with up to 7 benzene rings. Electronically excited states are addressed by means of extended configuration interaction within a standard molecular all-valence-electron semiempirical Hamiltonian. Adiabatic excitation energies, interstate distortions and normal modes are used to compute Franck–Condon band shapes with rigorous consideration of vibrational structure. Theoretical spectra agree with the experiment and rationalize the striking disparities in the linear optical response of OPP and OLPP. Whereas electron–phonon coupling in OLPP is essentially restricted to the carbon–carbon bond-stretching modes, photoexcitation, and emission processes in OPP are followed by significant relaxations in ring-torsional degrees of freedom. The broadening of spectra of OPP, especially pronounced in absorption, and the large Stokes shift between absorption and emission are traced back to the strong coupling of electronic excitations and low-frequency libration motions. The results highlight the importance of ring-torsional flexibility in conjugated polymers.

Reaction Dynamics of a Photochromic Fluorescing Dithienylethene

The interplay of photochromism and fluorescence was studied by attaching anthracene as chromophore to dithienylperfluorocyclopentene (1,2-bis[5-anthryl-2-methylthien-3-yl]perfluorocyclopentene, Ac-BMTFP). The blue fluorescence of the open isomer of Ac-BMTFP is suppressed by the ring-closure reaction. The spectroscopic properties and the reaction dynamics of this compound were characterized by measurements of the fluorescence yield and decay dynamics, and the quantum yields of the photochromic ring-closure and ring-opening reactions, as well as the spectra and time evolution of reaction intermediates. The data are analyzed in terms of a model potential and single-electron density matrices, which are calculated using the collective electronic oscillator (CEO) approach and the INDO/S semiempirical Hamiltonian. For the ring-opening reaction, single-exponential decays with a time constant of 8 ± 0.5 ps were determined for the photoinduced bleaching and absorption transients. In contrast, because of the presenc...

Direct Dynamic Studies on Tropospheric Reactivity of Fluorinated Ethanes: Scope and Limitations of the General Reaction Parameter Method

A direct dynamics study on the gas-phase reactions of OH radical with polyfluorinated ethanes has been carried out. Their thermal rate constants were calculated using canonical variational transition state theory augmented by multidimensional semiclassical small and large curvature tunneling approximations. The potential energy surface for the 1,1- and 1,2-difluoroethane reaction with hydroxyl radical was investigated with ab initio methods and a semiempirical PM3 Hamiltonian using specific reaction parameters (SRP). The reaction proceeds via hydrogen atom abstraction from both α and β carbon atoms with respect to fluorine substitution. In total, 26 stationary points were found, corresponding to the three and four reaction channels for 1,1- and 1,2-difluoroethane, respectively. Reactant molecules and product radicals, transition state structures, and pre-reactive complexes were characterized. Pre-reactive complexes are formed on both sides of the reaction path, directing the reaction to the different reac...

Ground-state tautomerism and rotational isomerization in 4,5-dimethyl-2-(2-hydroxyphenyl)imidazole in the gas phase and in polar solvents: a theoretical study of the aromaticity, intramolecular hydrogen-bond strength and differential solute–solvent interactions

Ground-state tautomerism and rotational isomerization in 4,5-dimethyl-2-(2-hydroxyphenyl)imidazole in the gas phase and in solution have been investigated by means of quantum mechanical calculations, NMR and steady-state fluorescence spectroscopy. In the gas phase, the cis-enol form is the most stable species, followed by the trans-enol and the keto forms. Several theoretical approaches were employed to characterize the electronic structure of the different isomers in the gas phase at the RB3LYP/6-31 + G* level of theory. The observed behavior could be rationalized according to the different weights of the resonance and the hydrogen-bond energies in the overall energy of each isomer. The hydroxyphenyl rings of the trans-enol and the cis-enol forms exhibit a nearly aromatic structure, whereas the electronic structure of the keto-form shows a higher degree of localization. In turn, it was found that the intramolecular hydrogen bond shows similar strength in the cis-enol and keto-forms, whereas this interaction is very weak in the trans-enol form. Polar solute–solvent non-specific interactions were modeled through the Onsager, SCI-PCM and COSMO methods based on ab initio and semiempirical Hamiltonians. In solution, the keto-form is stabilized by its much greater solute–solvent electrostatic interaction through its dipolar term and the aromatization of its phenyl ring. The trans-enol form is mainly stabilized by electrostatic interactions through higher multipolar terms than dipolar and specific solute–solvent interactions through the lone pair of the imidazole N3.

Simplified embedding schemes for the quantum-chemical description of neutral and charged point defects in SiO2 and related dielectrics

Embedding methods specifically designed to treat large molecules with bulky ligands or in polar solvents are used to describe the electronic structure of point defects in the covalently bonded solids SiO2, Si3N4, and Si2N2O. The mechanical relaxation of the lattice around a given defect, in particular an anion vacancy or interstitial, is described using the ONIOM approach where the system is partitioned in two regions, the local defect treated at the gradient corrected DFT level, and the surrounding matrix treated with a semiempirical Hamiltonian. In this way clusters of 100 atoms and more are used to describe a portion of the solid of 10–15 Å of diameter. The long-range lattice polarization induced by a charged defect, a charged oxygen vacancy or a proton bound to O or N atoms, is estimated by means of the isodensity polarized continuum model, IPCM, and compared with the approximate Born’s formula. The two simplified embedding schemes provide a simple way to improve cluster models of neutral and charged defects in covalent materials.

CEO/semiempirical calculations of UV–visible spectra in conjugated molecules

The collective electronic oscillators (CEO) approach based on the TDHF approximation is combined with INDO/S, MNDO, AM1, and PM3 semiempirical Hamiltonians. This technique is applied to compute and analyze the electronic structure of acceptor-substituted oligomers and conjugated polymers. Calculated excited-state energies and oscillator strengths agree well with the experimental data and with each other. In particular, the results using the Hamiltonians parameterized for ground-state calculations such as AM1 and PM3 agree well with the INDO/S results. In addition, a two-dimensional analysis of the corresponding transition density matrices provides an efficient way for tracing the origin of various optical transitions by identifying the underlying changes in charge densities and bond-orders.

A semi-empirical electrostatic potential in the studies of molecular crystals

A model based on incorporation of the external electrostatic potential into a semi-empirical Hamiltonian has been applied to explore the effect of crystal packing on the electronic structure of molecules within crystals. Different schemes for representation of charge distribution within a molecule are compared. The results obtained using this model were compared to the results of calculations carried out with the COSMO method. The effect of electrostatic potential is subject to wide variations, depending on the packing motif, and it may exceed the effect of very polar solvents. For three pairs of polymorphs, the incorporation of electrostatic potential into the INDO/S scheme allowed the rationalization of their difference in color.

Relaxation of Optically Excited p-Nitroaniline: Semiempirical Quantum-Chemical Calculations Compared to Femtosecond Experimental Results

p-Nitroaniline (pNA) was examined with the semiempirical SAM1 Hamiltonian in vacuo and in water. Geometry optimizations were performed in the ground and the lowest excited state along the −NH2 wagging and the −NO2 twisting coordinate. The latter is shown to play a key role in the spectroscopy and dynamics of pNA. The strong charge-transfer (CT) absorption band is conformationally broadened. Red-edge excitation prepares the CT state with a distribution of −NO2 conformations which is concentrated around the coplanar conformation with the benzene moiety. In water, C-amino and C-nitro stretching vibrations are also excited. The structural reorganization along those modes is assumed to occur on the same time scale as ultrafast polar solvation. In this case the relaxation dynamics in water after ∼100 fs consists mainly in an evolution of the −NO2 twist distribution toward a deep minimum at the perpendicular conformation; the dipole moment change during that process has an upper limit of 2 D. Stimulated emission...

Quantum mechanical/quantum mechanical methods. I. A divide and conquer strategy for solving the Schrödinger equation for large molecular systems using a composite density functional–semiempirical Hamiltonian

Herein we describe a new combined quantum mechanical/quantum mechanical (QM/QM) method for solving the Schrödinger equation for large molecular systems. The new method uses the divide and conquer (D&C) strategy to partition a large molecular system into subsystems and a composite density functional theory (DFT)–semiempirical (SEM) Hamiltonian to describe the molecular interactions. The DFT and SEM subsystems are coupled through the chemical potential and are equilibrated by exchanging electronic charge. Calculations performed with the DFT, SEM, and composite (DFT/SEM) methods on diatomic, triatomic, and polyatomic molecules show that as one moves away from the QM/QM boundary region the Mulliken charges converge to the values that would be obtained using the “pure” Hamiltonian. In other words, we find that the quality of each SEM and DFT wave function is largely conserved, which strongly suggests that this type of approach could be applied to study chemical reactivity much in the same way combined quantum mechanical/molecular mechanical (QM/MM) methods are presently utilized.

Properties of Polycrystalline Diamond: Multiscale Modeling Approach

Two modeling techniques to characterize fracture behavior of polycrystalline diamond films are discussed. The first technique is a multiscale modeling method in which first-principles local density approximation calculations on selected structures are combined with an analytic mesoscale model to obtain energies and cleavage fracture energies for symmetric ⟨001⟩ tilt grain boundaries (GBs) over the entire misorientation range. The second technique is large-scale atomistic simulation of the dynamics of failure in notched polycrystalline diamond samples under an applied strain. Electronic characteristics of selected ⟨001⟩ symmetrical tilt GBs calculated with a semiempirical tight-binding Hamiltonian are also presented, and the possible role of graphitic defects on field emission from polycrystalline diamond is briefly discussed.

The Influence of Protein Environment on the Low Temperature Electronic Spectroscopy of Zn-Substituted Cytochrome c

Low-temperature UV−vis absorption and Stark-effect hole-burning spectra of Zn substituted cytochrome c are studied experimentally and theoretically using quantum mechanical and Poisson−Boltzmann electrostatics models. Both the Q and Soret bands show resolved splitting at temperatures below ∼180 K. The trend observed in the splittings when comparing cytochromes from different species is found to be the same as that observed for the Q(0,0) band of ferrous cytochrome c. The relative magnitudes of the Q and Soret splittings are found to be consistent with predictions based on Gouterman's four orbital model. For horse heart and yeast cytochrome c, which show the greatest difference in the UV−visible band splittings, Stark effect measurements on persistent spectral holes in the Q(0,0) band indicate that the protein-induced polarization is distinctly different for these two species. Incorporation of the protein electrostatic field as virtual point charges into quantum mechanical calculations utilizing the INDO/s semiempirical Hamiltonian is used to demonstrate that the effects of the protein on the heme electronic structure can be considerably different for the two proteins, consistent with the experimental observations.

Electronic structure properties of solvated biomolecules: A quantum approach for macromolecular characterization

Linear-scaling electronic structure calculations of solvated biomolecules have been carried out using a semiempirical Hamiltonian and a new smooth solvation potential. These methods afford a new way of generating macromolecular properties that include quantum electronic structure. In addition to the widely used classical electrostatic potential maps based on empirically derived static point charges, now fully quantum mechanical electrostatic potentials that include electronic polarization are possible. Linear-scaling electronic structure methods provide a host of response properties of the electron density such as linear response functions, local hardness functions, and Fukui functions. It is the hope that these indices will extend insight into problems of biological macromolecular characterization. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1562–1571, 2000

Linear scaling molecular orbital calculations of biological systems using the semiempirical divide and conquer method

A “linear-scaling revolution” is occurring in quantum chemistry. This development is allowing for the first time the routine examination of large molecular assembles (e.g., proteins and DNA in water) using electronic structure methods. One of these approaches is the divide and conquer method and, in this article, we review the implementation of this approach for semiempirical Hamiltonians. This is then followed by brief reviews of three application areas. First, we will discuss the charge distribution of biological molecules in solution as described by quantum mechanics. In particular, the role polarization and charge transfer plays in affecting the charge distribution of proteins will be discussed. Next, we will examine the energetic consequences of charge transfer and polarization on biomolecular solvation. The final section will describe the computation of solvation free energies using a combined divide and conquer/Poisson–Boltzmann approach. The application of linear scaling quantum mechanical methods to biology is only just beginning, but the future is very bright, and it is our opinion that quantum mechanics will have a profound influence on our understanding of biological systems in the coming years. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1494–1504, 2000

Central bond vibrations in 1,1′-biadamantane

Raman (3100–10cm−1) and IR (3100–200cm−1) spectra of solid and dissolved 1,1′-biadamantane were recorded. The molecular structure and vibrational normal modes were calculated using the semi-empirical AM1 Hamiltonian. The distortions from the tetrahedral geometry induced by linking two adamantane units are discussed. The potential barrier of 19.3kJmol−1 for internal rotation of two adamantyl cages around the central bond was determined by calculations of heat of formation for fully relaxed structures at different dihedral angles. The final scaled vibrational force field was obtained by transferring the scale factors from parent adamantane. The normal mode displacements are described in terms of adamantane normal mode displacements using the generalised harmonic mode scrambling approach. The central bond stretching, torsion around the central bond and CCC deformations involving the central bond are genuine 1,1′-biadamantane vibrations. The semi-rigid molecular model is qualitatively applied on lattice dynamics of 1,1′-biadamantane in order to assign two Raman bands observed below 100cm−1.

Electronic screening in second order optical polarizabilities of elongated Donor/Acceptor polyenes

Optical polarizabilities of a family of donor/acceptor substituted polyenes are calculated using collective electronic normal modes obtained by solving equations of motion for the single-electron density matrix combined with the INDO/S semiempirical hamiltonian. Size-scaling of static polarizabilities χ= α, β, γ is analyzed using the exponents b χ ≡dln χ/dln n where n is the number of repeat units. We find that for long chains b α and b γ tend to 1 whereas b β approaches 0. Two-dimensional plots of the dominant collective electronic modes show that α and γ are generated along the entire chain whereas β only originates from the donor and acceptor chain regions. Electronic screening makes these regions neutral. The size of this boundary screening region is ∼15–17 double bonds, and β saturates at ∼30–40 double bonds, depending on the type of donor/acceptor substitution.

Reaction dynamics of photochromic dithienylethene derivatives

The reaction dynamics of the photochromic ring-opening reaction of 1,2-bis(5-formyl-2-methyl-thien-3-yl)perfluorocyclopentene (CHO-BMTFP) in dichloromethane solution was investigated using femtosecond transient absorption spectroscopy. The data were analyzed in terms of a model potential and single-electron density matrices, which were calculated using the collective electronic oscillator (CEO) approach and the INDO/S semiempirical Hamiltonian. The S 0–S 1 and S 0–S 2 transitions of the closed isomer were resonantly excited using 120 fs pump pulses at 610 and 410 nm, respectively. A temporally delayed white light continuum probe pulse monitors the decay of the S 1 or S 2 state as well as the recovery of the S 0 state. Within the first picosecond after excitation, CHO-BMTFP was observed to undergo a fast structural relaxation along the S 1 potential energy surface into a minimum constituting a precursor of the ring-opening process. The rather long lifetime of the precursor, τ 2=13 ps, was consistent with the calculated potential barrier in front of the conical intersection with the S 0 potential energy surface, which may arise from stabilization of the nearly planar closed isomer by an efficiently delocalized π-electron system.

An Implementation of Configuration Interaction in a General Purpose Semiempirical Context

We illustrate here an efficient approach to the implementation of configuration interaction (CI) methodologies in the case of general purpose semiempirical Hamiltonians such as MINDO/3, MNDO, PM3, AM1, and SAM1. The strategy described here has been implemented in the commercial program AMPAC and successfully blends well-known and tested algorithms. The primary purpose is to derive a reliable method for determining a CI solution with minimal user input. The success and intrinsic accuracy of the approach is discussed.

Rapid single- and multiple-scattering EXAFS Debye-Waller factor calculations on active sites of metalloproteins.

This paper describes recent results using our approach to calculating self-consistently single (SS) and multiple-scattering (MS) DebyeWaller factors (DWF) on active sites of metalloproteins. The calculation of MS DWF, together with the Feff7 program allows us to simulate ab-initio EXAFS spectra for a given temperature systems with no adjustable parameters. In our latest report (Dimakis N., and Bunker G., 1998) we calculate, using density functional and semiempirical approaches, the SS and MS DWF for small molecules and compared them to Raman, infrared and EXAFS spectra. In this report calculation of DWFs is done for tetrahedral Zn imidazole, a complex containing thirty two atoms that is similar in certain respects to active sites of many metalloproteins. Ab-initio calculation, although it is a more accurate and reliable scheme, it is not at present practical on desktop computers; computation times are weeks. Therefore as an alternative we have tried the semiempirical MNDO Hamiltonian, which is at least three orders of magnitude faster than ab-initio, and can be expected to be of reasonable accuracy because it is parameterized for organic compounds. Our approaches take advantage of commercially available molecular orbital programs. We have written additional programs which, using normal mode calculations, calculate the MS paths, and transparently interface with Fef-f'/to produce the EXAFS spectra. Results are in very good agreement with experimental data tested.