Application of potential constants: Electronic chemical potentials of polyatomic molecules—VIII

A new approach for the calculation of electronic chemical potentials of polyatomic systems is developed by applying the quadratic potential (force) constants which are available from normal coordinate analyses using spectroscopic data. The approach is constructed within the framework of density-functional theory into which the simple bond-charge model is incorporated. To evaluate the utility of such an approach, we have calculated electronic chemical potentials for various kinds of polyatomic molecules, and the calculated results have been compared favorably with experimental values as well as those obtained from ab initio SCF calculations. It seems that this approach offers the possibility of chemical potential calculations for polyatomic molecules whose quadratic stretching force constants are obtained by normal coordinate analyses.     

The multiconfiguration time-dependent Hartree-Fock method for quantum chemical calculations

We apply the multiconfiguration time-dependent Hartree-Fock method to electronic structure calculations and show that quantum chemical information can be obtained with this explicitly time-dependent approach. Different equations of motion are discussed, as well as the numerical cost. The two-electron integrals are calculated using a natural potential expansion, of which we describe the convergence behavior in detail.     

Natural bond orbital analysis in the ONETEP code: Applications to large protein systems

First principles electronic structure calculations are typically performed in terms of molecular orbitals (or bands), providing a straightforward theoretical avenue for approximations of increasing sophistication, but do not usually provide any qualitative chemical information about the system. We can derive such information via post‐processing using natural bond orbital (NBO) analysis, which produces a chemical picture of bonding in terms of localized Lewis‐type bond and lone pair orbitals that we can use to understand molecular structure and interactions. We present NBO analysis of large‐scale calculations with the ONETEP linear‐scaling density functional theory package, which we have interfaced with the NBO 5 analysis program. In ONETEP calculations involving thousands of atoms, one is typically interested in particular regions of a nanosystem whilst accounting for long‐range electronic effects from the entire system. We show that by transforming the Non‐orthogonal Generalized Wannier Functions of ONETEP to natural atomic orbitals, NBO analysis can be performed within a localized region in such a way that ensures the results are identical to an analysis on the full system. We demonstrate the capabilities of this approach by performing illustrative studies of large proteins—namely, investigating changes in charge transfer between the heme group of myoglobin and its ligands with increasing system size and between a protein and its explicit solvent, estimating the contribution of electronic delocalization to the stabilization of hydrogen bonds in the binding pocket of a drug‐receptor complex, and observing, in situ, the n → π* hyperconjugative interactions between carbonyl groups that stabilize protein backbones. © 2012 Wiley Periodicals, Inc.     

Mapping the electronic structure of the blue copper site in plastocyanin by NMR relaxation

The biological function of metalloproteins stems from the electronic and geometric structures of their active sites. Thus, in blue copper proteins such as plastocyanins, an unusual electronic structure of the metal site is believed to contribute to the rapid, long-range electron-transfer reactivity that characterizes these proteins. To clarify this structure-function relationship, numerous quantum chemical calculations of the electronic structure of the blue copper proteins have been made. However, the obtained structures depend strongly on the applied model. Experimental approaches based on ENDOR spectroscopy and X-ray absorption have also been used to elucidate the electronic structure of the blue copper site. Still, the determination of the electronic structure relies on a calibration with quantum chemical calculations, performed on small model complexes. Here we present an approach that allows a direct experimental mapping of the electron spin delocalization in paramagnetic metalloproteins using oxidized plastocyanin from Anabaena variabilis as an example. The approach utilizes the longitudinal paramagnetic relaxation of protons close to the metal site and relies on the dependence of these relaxations on the spatial distribution of the unpaired electron of the metal ion. Surprisingly it is found that the unpaired electron of the copper ion in plastocyanin is less delocalized than predicted by most of the quantum chemical calculations.     

Inverse molecular design in a tight-binding framework

The number of chemical species of modest molecular weight that can be accessed with known synthetic methods is astronomical. An open challenge is to explore this space in a manner that will enable the discovery of molecular species and materials with optimized properties. Recently, an inverse molecular design strategy, the linear combination of atomic potentials (LCAP) approach [J. Am. Chem. Soc. 128, 3228 (2006)] was developed to optimize electronic polarizabilities and first hyperpolarizabilities. Here, using a simple tight-binding (TB) approach, we show that continuous optimization can be carried out on the LCAP surface successfully to explore vast chemical libraries of 10(2) to 10(16) extended aromatic compounds. We show that the TB-LCAP optimization is not only effective in locating globally optimal structures based on their electronic polarizabilities and first hyperpolarizabilities, but also is straightforwardly extended to optimize transition dipole moments and HOMO-LUMO energy gaps. This approach finds optimal structures among 10(4) candidates with about 40 individual molecular property calculations. As such, for structurally similar molecular candidates, the TB-LCAP approach may provide an effective means to identify structures with optimal properties.     

Electronic Properties of Vinylene-Linked Heterocyclic Conducting Polymers: Predictive Design and Rational Guidance from DFT Calculations

The band structure and electronic properties in a series of vinylene-linked heterocyclic conducting polymers are investigated using density functional theory (DFT). In order to accurately calculate electronic band gaps, we utilize hybrid functionals with fully periodic boundary conditions to understand the effect of chemical functionalization on the electronic structure of these materials. The use of predictive first-principles calculations coupled with simple chemical arguments highlights the critical role that aromaticity plays in obtaining a low band gap polymer. Contrary to some approaches which erroneously attempt to lower the band gap by increasing the aromaticity of the polymer backbone, we show that being aromatic (or quinoidal) in itself does not ensure a low band gap. Rather, an iterative approach which destabilizes the ground state of the parent polymer toward the aromatic ? quinoidal level crossing on the potential energy surface is a more effective way of lowering the band gap in these conjugated systems. Our results highlight the use of predictive calculations guided by rational chemical intuition for designing low band gap polymers in photovoltaic materials.     

An algebraic operator approach to electronic structure

In this paper, we introduce an algebraic approach to electronic structure calculations. Our approach constructs a Jordan algebra based on the second-quantized electronic Hamiltonian. From the structure factor of this algebra, we show that we can calculate the energy of the ground electronic state of the Hamiltonian operator. We apply our method to several generalized Hubbard models and show that we can usually obtain a significant fraction of the correlation energy for low-to-moderate values of the electronic repulsion parameter while still retaining the O(L(3)) scaling of the Hartree-Fock algorithm. This surprising result, along with several other observations, suggests that our algebraic approach represents a new paradigm for electronic structure calculations which opens up many new directions for research.     

CASSCF/CAS-PT2 study of hole transfer in stacked DNA nucleobases

CASSCF and CAS-PT2 calculations are performed for the ground and excited states of radical cations consisting of two and three nucleobases. The generalized Mulliken-Hush approach is employed for estimating electronic couplings for hole transfer in the pi-stacks. We compare the CASSCF results with data obtained within Koopmans' approximation. The calculations show that an excess charge in the ground and excited states in the systems is quite localized on a single base both at the CASSCF level and in Koopmans' picture. However, the CASSCF calculations point to a larger degree of localization and, in line with this, smaller transition dipole moments. The agreement between the CAS-PT2 corrected energy gaps and the values estimated with Koopmans' theorem is better, with the CAS-PT2 calculations giving somewhat smaller gaps. Overall, both factors result in smaller CASSCF/CAS-PT2 couplings, which are reduced by up to 40% of the couplings calculated using Koopmans' approximation. The tabulated data can be used as benchmark values for the electronic couplings of stacked nucleobases. For the base trimers, comparison of the results obtained within two- and three-state models show that the multistate treatment should be applied to derive reliable estimates. Finally, the superexchange approach to estimate the donor acceptor electronic coupling in the stacks GAG and GTG is considered.     

Electron group functions for the analysis of the electronic structures of molecules

The electronic structure of a vast majority of molecular systems can be understood in terms of electron groups and their wave functions. They serve as a natural basis for bringing intuitive chemical and physical concepts into quantum chemical calculations. This article considers the general electron group functions formalism as well as its simple geminal version. We try to characterize the wave function with the group structure and its capabilities in actual calculations. For this purpose we implement a variational method based on the wave function in the form of an antisymmetrized product of strongly orthogonal group functions and perform a series of electronic structure calculations for small molecules and model systems. The most important point studied is the relation between the choice of electron groups and the results obtained. We consider energetic characteristics as well as optimal geometry parameters. In view of practical importance, the structure of variationally optimized local one-electron states is considered in detail as well as intuitive characteristics of chemical bonds.     

Electronic and vibrational second-order nonlinear optical properties of protein secondary structural motifs

A perturbation theory approach was developed for predicting the vibrational and electronic second-order nonlinear optical (NLO) polarizabilities of materials and macromolecules comprised of many coupled chromophores, with an emphasis on common protein secondary structural motifs. The polarization-dependent NLO properties of electronic and vibrational transitions in assemblies of amide chromophores comprising the polypeptide backbones of proteins were found to be accurately recovered in quantum chemical calculations by treating the coupling between adjacent oscillators perturbatively. A novel diagrammatic approach was developed to provide an intuitive visual means of interpreting the results of the perturbation theory calculations. Using this approach, the chiral and achiral polarization-dependent electronic SHG, isotropic SFG, and vibrational SFG nonlinear optical activities of protein structures were predicted and interpreted within the context of simple orientational models.     

Using semiclassical surface hopping for coupled partial wave calculations on systems with non-spherically symmetric potentials

It is shown that a semiclassical surface hopping (SH) approach provides a simple and efficient method for scattering calculations with non-spherically symmetric potentials. The calculations are performed by expanding the wave function in an angular momentum state basis. Since the potential is not spherically symmetric, the different angular states are coupled. The semiclassical SH method, which is typically used for problems with coupled electronic states, can, in principle, be employed for any coupled state problem. The particular SH method employed is known to provide highly accurate results for coupled electronic state problems. The method is tested on model two angular state problems using potential surfaces and couplings arising from a non-spherically symmetric scattering problem. The results for these model problems are in excellent agreement with exact quantum calculations. Full calculations, which are converged with regard to the number of angular basis states, are also performed for the non-spherically symmetric problem. It is shown that an approximation to the surface hopping amplitudes that simplifies the numerical implementation of the method provides results in excellent agreement with the full surface hopping calculation.     

Theoretical investigation of the dissociation dynamics of vibrationally excited vinyl bromide on an ab initio potential-energy surface obtained using modified novelty sampling and feed-forward neural networks

The reaction dynamics of vibrationally excited vinyl bromide have been investigated using classical trajectory methods on a neural network potential surface that is fitted to an ab initio database of 12 122 configuration energies obtained from electronic structure calculations conducted at the MP4(SDQ) level of theory using a 6-31G(d,p) basis set for the carbon and hydrogen atoms and Huzinaga's (43334334) basis set augmented with split outer s and p orbitals (4332143214) and a polarization f orbital with an exponent of 0.5 for the bromine atom. The sampling of the 12-dimensional configuration hyperspace of vinyl bromide prior to execution of the electronic structure calculations is accomplished by combining novelty-sampling methods, chemical intuition, and trajectory sampling on empirical and neural network surfaces. The final potential is obtained using a two-layer feed-forward neural network comprising 38 and 1 neurons, respectively, with hyperbolic tangent sigmoid and linear transfer functions in the hidden and output layers, respectively. The fitting is accomplished using the Levenberg-Marquardt algorithm with early stopping and Bayesian regularization methods to avoid overfitting. The interpolated potentials have a standard deviation from the ab initio results of 0.0578 eV, which is within the range generally regarded as "chemical accuracy" for the purposes of electronic structure calculations. It is shown that the potential surface may be easily and conveniently transferred from one research group to another. The files required for transfer of the vinyl bromide surface can be obtained from the Electronic Physics Auxiliary Publication Service. Total dissociation rate coefficients for vinyl bromide are obtained at five different excitation energies between 4.50 and 6.44 eV. Branching ratios into each of the six open reaction channels are computed at 24 vibrational energies in the range between 4.00 and 6.44 eV. The distribution of vibrational energies in HBr formed via three-center dissociation from vinyl bromide is determined and compared with previous theoretical and experimental results. It is concluded that the combination of ab initio electronic structure calculations, novelty sampling with chemical intuition and trajectories on empirical analytic surfaces, and feed-forward neural networks provides a viable framework in which to execute purely ab initio molecular-dynamics studies on complex systems with multiple open reaction channels.     

Towards a comprehensive electronic database of polycyclic aromatic hydrocarbons and its application in constraining the identities of possible carriers of the diffuse interstellar bands

A theoretical approach is developed to pre-select individual polycyclic aromatic hydrocarbons (PAHs) as possible carriers of the diffuse interstellar bands (DIBs). In this approach, a computer program is used to enumerate all PAH molecules with up to a specific number of fused benzene rings. Fast quantum chemical calculations are then employed to calculate the electronic transition energies, oscillator strengths, and rotational constants of these molecules. An electronic database of all PAHs with up to any specific number of benzene rings can be constructed this way. Comparison of the electronic transition energies, oscillator strengths, and rotational band contours of all PAHs in the database with astronomical spectra allows one to constrain the identities of individual PAHs as possible carriers of some of the intense narrow DIBs. Using the current database containing up to 10 benzene rings we have pre-selected 8 closed-shell PAHs as possible carriers of the famous lambda6614 DIB.     

Ab initio quality properties for macromolecules using the ADMA approach

We describe new developments of an earlier linear scaling algorithm for ab initio quality macromolecular property calculations based on the adjustable density matrix assembler (ADMA) approach. In this approach, a large molecule is divided into fuzzy fragments, for which quantum chemical calculations can easily be done using moderate-size "parent molecules" that contain all the local interactions within a selected distance. If greater accuracy is required, a larger distance is chosen. With the present extension of this approximation, properties of the large molecules, like the electron density, the electrostatic potential, dipole moments, partial charges, and the Hartree-Fock energy are calculated. The accuracy of the method is demonstrated with test cases of medium size by comparing the ADMA results with direct quantum chemical calculations.     

Independent trajectory implementation of the semiclassical Liouville method: application to multidimensional reaction dynamics

We describe an independent trajectory implementation of semiclassical Liouville method for simulating quantum processes using classical trajectories. In this approach, a single ensemble of trajectories describes all semiclassical density matrix elements of a coupled electronic state problem, with the ensemble evolving classically under a single reference Hamiltonian chosen on the basis of physical grounds. In this paper, we introduce an additional uncoupled trajectory approximation, allowing the members of the ensemble to evolve independently of one another and eliminating the major computational costs of our previous coupled trajectory implementation. The accuracy of the method is demonstrated for model one-dimensional problems. In addition, the approach is applied to the chemical reaction dynamics of a collinear triatomic system, yielding excellent agreement with exact calculations. This method allows molecular dynamics involving coupled electronic surfaces to be modeled with essentially the same effort as classical molecular dynamics and ensemble averaging.     

Nuclear quadrupole hyperfine structure in HC14N/H14NC and DC15N/D15NC isomerization: a diagnostic tool for characterizing vibrational localization

Large-amplitude molecular motions which occur during isomerization can cause significant changes in electronic structure. These variations in electronic properties can be used to identify vibrationally-excited eigenstates which are localized along the potential energy surface. This work demonstrates that nuclear quadrupole hyperfine interactions can be used as a diagnostic marker of progress along the isomerization path in both the HC14N/H14NC and DC15N/D15NC chemical systems. Ab initio calculations at the CCSD(T)/cc-pCVQZ level indicate that the hyperfine interaction is extremely sensitive to the chemical bonding of the quadrupolar 14N nucleus and can therefore be used to determine in which potential well the vibrational wavefunction is localized. A natural bonding orbital analysis along the isomerization path further demonstrates that hyperfine interactions arise from the asphericity of the electron density at the quadrupolar nucleus. Using the CCSD(T) potential surface, the quadrupole coupling constants of highly-excited vibrational states are computed from a one-dimensional internal coordinate path Hamiltonian. The excellent agreement between ab initio calculations and recent measurements demonstrates that nuclear quadrupole hyperfine structure can be used as a diagnostic tool for characterizing localized HCN and HNC vibrational states.     

Solvent effects on 195Pt and 205Tl NMR chemical shifts of the complexes [(NC)5Pt--Tl(CN)n]n- (n=0-3), and [(NC)5Pt--Tl--Pt(CN)5]3- studied by relativistic density functional theory

The 295Pt and 205Tl NMR chemical shifts of the complexes [(NC)5Pt-Tl(CN)n]n- n=0-3, and of the related system [(NC)5Pt--Tl--Pt(CN)5]3- have been computationally investigated. It is demonstrated that based on relativistically optimized geometries, by applying an explicit first solvation shell, an additional implicit solvation model to represent the bulk solvent effects (COSMO model), and a DFT exchange-correlation potential that was specifically designed for the treatment of response properties, that the experimentally observed metal chemical shifts can be calculated with satisfactory accuracy. The metal chemical shifts have been computed by means of a two-component relativistic density functional approach. The effects of electronic spin-orbit coupling were included in all NMR computations. The impact of the choice of the reference, which ideally should not affect the accuracy of the computed chemical shifts, is also demonstrated. Together with recent calculations by us of the Pt and Tl spin-spin coupling constants, all measured metal NMR parameters of these complexes are now computationally determined with sufficient accuracy in order to allow a detailed analysis of the experimental results. In particular, we show that interaction of the complexes with the solvent (water) must be an integral part of such an analysis.     

Electrostatic embedding in large-scale first principles quantum mechanical calculations on biomolecules

Biomolecular simulations with atomistic detail are often required to describe interactions with chemical accuracy for applications such as the calculation of free energies of binding or chemical reactions in enzymes. Force fields are typically used for this task but these rely on extensive parameterisation which in cases can lead to limited accuracy and transferability, for example for ligands with unusual functional groups. These limitations can be overcome with first principles calculations with methods such as density functional theory (DFT) but at a much higher computational cost. The use of electrostatic embedding can significantly reduce this cost by representing a portion of the simulated system in terms of highly localised charge distributions. These classical charge distributions are electrostatically coupled with the quantum system and represent the effect of the environment in which the quantum system is embedded. In this paper we describe and evaluate such an embedding scheme in which the polarisation of the electronic density by the embedding charges occurs self-consistently during the calculation of the density. We have implemented this scheme in a linear-scaling DFT program as our aim is to treat with DFT entire biomolecules (such as proteins) and large portions of the solvent. We test this approach in the calculation of interaction energies of ligands with biomolecules and solvent and investigate under what conditions these can be obtained with the same level of accuracy as when the entire system is described by DFT, for a variety of neutral and charged species.     

Ab initio calculations of surface electronic states in indium oxide

A slab approach in the framework of ab initio calculations was applied to study surface electronic states in In₂O₃ crystal. Density functional theory (DFT) calculations were carried out employing the WIEN 2k code and using the full potential method with Augmented Plane Waves + local orbitals (APW+lo) formalism. Total and partial DOS (Density of States) were calculated for In and O atoms in two upper (110) surface layers. Comparison of total and partial DOS allowed determining a contribution of electronic states of different In and O surface atoms into formation of surface electronic spectra and corresponding chemical bonds. A dominant ionic character of chemical bonds in In₂O₃ is found. Calculations were performed for three slab models with different geometry parameters. It was shown that an optimal ratio between the whole vertical size of a supercell and the vertical size of atomic cluster has to be chosen. The size of vacuum region in the slab model influences significantly on the reliability of calculated characteristics of the surface electronic structure. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Dynamical variational approach to non-adiabatic electronic structure

Studying non-adiabatic effects in molecular dynamics simulations and modeling their optical signatures in linear and non-linear spectroscopies calls for electronic structure calculations in a situation when the ground state is degenerate or almost degenerate. Such degeneracy causes serious problems in invoking single Slater determinant Hartree–Fock (HF) and density functional theory (DFT) methods. To resolve this problem, we develop a generalization of time-dependent (dynamical) variational approach which accounts for the degenerate or almost degenerate ground state structure. Specifically, we propose a ground state ansatz for the subspace of generalized electronic configurations spanned on the degenerate grounds state multi-electron wavefunctions. Further employing the invariant form of Hamilton dynamics we arrive with the classical equations of motion describing the time-evolution of this subspace in the vicinity of the stationary point. The developed approach can be used for accurate calculations of molecular excited states and electronic spectra in the degenerate case.