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Density-functional-theory-based chemical reactivity indicators are formulated for degenerate and near-degenerate ground states. For degenerate states, the functional derivatives of the energy with respect to the external potential do not exist, and must be replaced by the weaker concept of functional variation. The resultant reactivity indicators depend on the specific perturbation. Because it is sometimes impractical to compute reactivity indicators for a specific perturbation, we consider two special cases: point-charge perturbations and Dirac delta function perturbations. The Dirac delta function perturbations provide upper bounds on the chemical reactivity. Reactivity indicators using the common used 'average of degenerate states approximation' for degenerate states provide a lower bound on the chemical reactivity. Unfortunately, this lower bound is often extremely weak. Approximate formulas for the reactivity indicators within the frontier-molecular-orbital approximation and special cases (two or three degenerate spatial orbitals) are presented in the supplementary material. One remarkable feature that arises in the frontier molecular orbital approximation, and presumably also in the exact theory, is that removing electrons sometimes causes the electron density to increase at the location of a negative (attractive) Dirac delta function perturbation. That is, the energetic response to a reduction in the external potential can increase even when the number of electrons decreases. [ABSTRACT FROM AUTHOR]

This paper is a logical continuation of the 22 parameter, localized orbital correction (LOC) methodology that we developed in previous papers [R. A. Friesner et al., J. Chem. Phys. 125, 124107 (2006); E. H. Knoll and R. A. Friesner, J. Phys. Chem. B 110, 18787 (2006).] This methodology allows one to redress systematic density functional theory (DFT) errors, rooted in DFT’s inherent inability to accurately describe nondynamical correlation. Variants of the LOC scheme, in conjunction with B3LYP (denoted as B3LYP-LOC), were previously applied to enthalpies of formation, ionization potentials, and electron affinities and showed impressive reduction in the errors. In this paper, we demonstrate for the first time that the B3LYP-LOC scheme is robust across different basis sets [6-31G*, 6-311++G(3df,3pd), cc-pVTZ, and aug-cc-pVTZ] and reaction types (atomization reactions and molecular reactions). For example, for a test set of 70 molecular reactions, the LOC scheme reduces their mean unsigned error from 4.7 kcal/mol [obtained with B3LYP/6-311++G(3df,3pd)] to 0.8 kcal/mol. We also verified whether the LOC methodology would be equally successful if applied to the promising M05-2X functional. We conclude that although M05-2X produces better reaction enthalpies than B3LYP, the LOC scheme does not combine nearly as successfully with M05-2X than with B3LYP. A brief analysis of another functional, M06-2X, reveals that it is more accurate than M05-2X but its combination with LOC still cannot compete in accuracy with B3LYP-LOC. Indeed, B3LYP-LOC remains the best method of computing reaction enthalpies. [ABSTRACT FROM AUTHOR]

Our purpose is to identify a computational level sufficiently dependable and affordable to assess trends in the interaction of a variety of radical or closed shell unsaturated hydro-carbons A adsorbed on soot platelet models B. These systems, of environmental interest, would unavoidably have rather large sizes, thus prompting to explore in this paper the performances of relatively low-level computational methods and compare them with higher-level reference results. To this end, the interaction of three complexes between non-polar species, vinyl radical, ethyne, or ethene (A) with benzene (B) is studied, since these species, involved themselves in growth processes of polycyclic aromatic hydrocarbons (PAHs) and soot particles, are small enough to allow high-level reference calculations of the interaction energy ΔEAB. Counterpoise-corrected interaction energies ΔEAB are used at all stages. (1) Density Functional Theory (DFT) unconstrained optimizations of the A-B complexes are carried out, using the B3LYP-D, ωB97X-D, and M06-2X functionals, with six basis sets: 6-31G(d), 6-311 (2d,p), and 6-311++G(3df,3pd); aug-cc-pVDZ and aug-cc-pVTZ; N07T. (2) Then, unconstrained optimizations by Mo\ller-Plesset second order Perturbation Theory (MP2), with each basis set, allow subsequent single point Coupled Cluster Singles Doubles and perturbative estimate of the Triples energy computations with the same basis sets [CCSD(T)//MP2]. (3) Based on an additivity assumption of (i) the estimated MP2 energy at the complete basis set limit [EMP2/CBS] and (ii) the higher-order correlation energy effects in passing from MP2 to CCSD(T) at the aug-cc-pVTZ basis set, ΔECC-MP, a CCSD(T)/CBS estimate is obtained and taken as a computational energy reference. At DFT, variations in ΔEAB with basis set are not large for the title molecules, and the three functionals perform rather satisfactorily even with rather small basis sets [6-31G(d) and N07T], exhibiting deviation from the computational reference of less than 1 kcal mol-1. The zero-point vibrational energy corrected estimates Δ(EAB+ZPE), obtained with the three functionals and the 6-31G(d) and N07T basis sets, are compared with experimental D0 measures, when available. In particular, this comparison is finally extended to the naphthalene and coronene dimers and to three π-π associations of different PAHs (R, made by 10, 16, or 24 C atoms) and P (80 C atoms). [ABSTRACT FROM AUTHOR]

This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms. [ABSTRACT FROM AUTHOR]

Accurate predictions of molecular acidity using ab initio and density functional approaches are still a daunting task. Using electronic and reactivity properties, one can quantitatively estimate pKa values of acids. In a recent paper [S. B. Liu and L. G. Pedersen, J. Phys. Chem. A 113, 3648 (2009)], we employed the molecular electrostatic potential (MEP) on the nucleus and the sum of valence natural atomic orbital (NAO) energies for the purpose. In this work, we reformulate these relationships on the basis of conceptual density functional theory and compare the results with those from the thermodynamic cycle method. We show that MEP and NAO properties of the dissociating proton of an acid should satisfy the same relationships with experimental pKa data. We employ 27 main groups and first to third row transition metal-water complexes as illustrative examples to numerically verify the validity of these strong linear correlations. Results also show that the accuracy of our approach and that of the conventional method through the thermodynamic cycle are statistically similar. [ABSTRACT FROM AUTHOR]

A recently developed analysis method [J. Chem. Phys. 127, 124106 (2007)] for NMR spin-spin coupling constants employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic natural localized molecular orbitals (NLMOs) and natural bond orbitals (NBOs) has been extended for analyzing NMR shielding tensors. Contributions from a field-dependent basis set (gauge-including atomic orbitals) have been included in the formalism. The spin-orbit NLMO/NBO nuclear magnetic shielding analysis has been applied to methane, plumbane, hydrogen iodide, tetracholoplatinate(II), and hexachloroplatinate(IV). [ABSTRACT FROM AUTHOR]

The common density functionals for the exchange-correlation energy make serious self-interaction errors in the molecular dissociation limit when real or spurious noninteger electron numbers N are found on the dissociation products. An “M-electron self-interaction-free” functional for positive integer M is one that produces a realistic linear variation of total energy with N in the range of M-1≤Na=M, and so can avoid these errors. This desideratum is a natural generalization to all M of the more familiar one of one-electron self-interaction freedom. The intent of this paper is not to advocate for any functional, but to understand what is required for a functional to be M-electron self-interaction-free and thus correct even for highly stretched bonds. The original Perdew-Zunger self-interaction correction (SIC) and our scaled-down variant of it are exactly one- and nearly two-electron self-interaction-free, but only the former is nearly so for atoms with M>2. Thus all these SIC’s produce an exact binding energy curve for H2+, and an accurate one for He2+, but only the unscaled Perdew-Zunger SIC produces an accurate one for Ne2+, where there are more than two electrons on each fragment Ne+0.5. We also discuss LiH+, which is relatively free from self-interaction errors. We suggest that the ability of the original and unscaled Perdew-Zunger SIC to be nearly M-electron self-interaction-free for atoms of all M stems in part from its formal resemblance to the Hartree-Fock theory, with which it shares a sum rule on the exchange-correlation hole of an open system. [ABSTRACT FROM AUTHOR]

The numerical solution of the electronic structure problem in Kohn-Sham density functional theory may in certain cases yield fractional occupancy of the single-particle orbitals. In this paper, we propose a quadratically convergent approach for simultaneous optimization of orbitals and occupancies in systems with fractional occupation numbers (FONs). The starting guess for orbitals and FONs is obtained via the relaxed constraint algorithm. Numerical results are presented for benchmark cases. [ABSTRACT FROM AUTHOR]

In this paper we present new formulas related to the parametrization of molecular orbitals by exponential transformations. We show that it is not necessary to use series expansions of the exponentials and that the first derivative of the energy with respect to independent parameters can be calculated at arbitrary positions in an efficient manner. These formulas can be implemented such that computational costs are of order N2M and storage requirements of order NM, where N is the number of occupied orbitals and M the size of the basis set. We discuss possible applications to Hartree–Fock calculations and ab initio molecular dynamics. [ABSTRACT FROM AUTHOR]

This paper presents density functional calculations of structural and electronic properties of molecules by the use of ab initio pseudopotentials and the linear combination of Gaussian-type orbitals optimized by simulated annealing. A comprehensive study was carried out for various molecules whose constituent atoms cover a major portion of the Periodic Table from H to Po except for atoms in the lanthanum group. Bond distances, vibrational frequencies, and binding energies are obtained and compared with available experimental results and all-electron calculations. We find that, in general, pseudopotential bond distances are within 0.1 Å of experimental and all-electron results, and relative uncertainties of vibrational frequencies are, on the average, less than 12%. For binding energies, pseudopotential results agree well with corresponding all-electron results. For most cases, nonlocal gradient corrections to the local density approximation significantly improve both pseudopotential and all-electron binding energies. [ABSTRACT FROM AUTHOR]

Herein, we present a new method to efficiently calculate electronically excited states in large molecular assemblies, consisting of hundreds of molecules. For this purpose, we combine the long-range corrected tight-binding density functional fragment molecular orbital method (FMO-LC-DFTB) with an excitonic Hamiltonian, which is constructed in the basis of locally excited and charge-transfer configuration state functions calculated for embedded monomers and dimers and accounts explicitly for the electronic coupling between all types of excitons. We first evaluate both the accuracy and efficiency of our fragmentation approach for molecular dimers and aggregates by comparing it with the full LC-TD-DFTB method. The comparison of the calculated spectra of an anthracene cluster shows a very good agreement between our method and the LC-TD-DFTB reference. The effective computational scaling of our method has been explored for anthracene clusters and for perylene bisimide aggregates. We demonstrate the applicability of our method by the calculation of the excited state properties of pentacene crystal models consisting of up to 319 molecules. Furthermore, the participation ratio of the monomer fragments to the excited states is analyzed by the calculation of natural transition orbital participation numbers, which are verified by the hole and particle density for a chosen pentacene cluster. The use of our FMO-LC-TDDFTB method will allow for future studies of excitonic dynamics and charge transport to be performed on complex molecular systems consisting of thousands of atoms. [ABSTRACT FROM AUTHOR]

Nonadiabatic excited state molecular dynamics underpin many photophysical and photochemical phenomena, such as exciton dynamics, and charge separation and transport. In this work, we present an efficient nonadiabatic molecular dynamics (NAMD) simulation method based on time-dependent density functional tight-binding (TDDFTB) theory. Specifically, the adiabatic electronic structure, an essential NAMD input, is described at the TDDFTB level. The nonadiabatic effects originating from the coupled motions of electrons and nuclei are treated by the trajectory surface hopping algorithm. To improve the computational efficiency, nonadiabatic couplings between excited states within the TDDFTB method are derived and implemented using an analytical approach. Furthermore, the time-dependent nonadiabatic coupling scalars are calculated based on the overlap between molecular orbitals rather than the Slater determinants to speed up the simulations. In addition, the electronic decoherence scheme and a state reassigned unavoided crossings algorithm, which has been implemented in the NEXMD software, are used to improve the accuracy of the simulated dynamics and handle trivial unavoided crossings. Finally, the photoinduced nonadiabatic dynamics of a benzene molecule are simulated to demonstrate our implementation. The results for excited state NAMD simulations of benzene molecule based on TDDFTB method compare well to those obtained with numerically expensive time-dependent density functional theory. The proposed methodology provides an attractive theoretical simulation tool for predicting the photophysical and photochemical properties of complex materials. [ABSTRACT FROM AUTHOR]

We propose a direct method for reducing the dimension of the space of orbital products that occur, for example, in the calculation of time dependent density functional theory linear response and in Hedin’s GW approximation to the electron propagator. We do this by defining, within the linear space of orbital products, a subspace of dominant directions that are associated with a certain eigenvalue problem. These directions span the entire linear space of products with an error that decreases approximately exponentially with their number. Our procedure works best for atomic orbitals of finite range and it avoids the use of extra sets of auxiliary fit functions. [ABSTRACT FROM AUTHOR]

The common density functionals for the exchange-correlation energy make serious self-interaction errors in the molecular dissociation limit when real or spurious noninteger electron numbers N are found on the dissociation products. An “M-electron self-interaction-free” functional for positive integer M is one that produces a realistic linear variation of total energy with N in the range of M-1≤Na=M, and so can avoid these errors. This desideratum is a natural generalization to all M of the more familiar one of one-electron self-interaction freedom. The intent of this paper is not to advocate for any functional, but to understand what is required for a functional to be M-electron self-interaction-free and thus correct even for highly stretched bonds. The original Perdew-Zunger self-interaction correction (SIC) and our scaled-down variant of it are exactly one- and nearly two-electron self-interaction-free, but only the former is nearly so for atoms with M>2. Thus all these SIC’s produce an exact binding energy curve for H2+, and an accurate one for He2+, but only the unscaled Perdew-Zunger SIC produces an accurate one for Ne2+, where there are more than two electrons on each fragment Ne+0.5. We also discuss LiH+, which is relatively free from self-interaction errors. We suggest that the ability of the original and unscaled Perdew-Zunger SIC to be nearly M-electron self-interaction-free for atoms of all M stems in part from its formal resemblance to the Hartree-Fock theory, with which it shares a sum rule on the exchange-correlation hole of an open system. [ABSTRACT FROM AUTHOR]

Density functional theory has been used to investigate the binding of propene to small Ag clusters in the gas phase. The binding mechanism based on frontier orbital theory, which we used previously to describe the binding between propene and the Au clusters, works for the pure Ag clusters as well. Among other things, it explains the trends of the desorption energy of propene as a function of the Ag cluster size. We show that one can predict the binding site of propene by examining the shape of the lowest unoccupied molecular orbitals (LUMOs) of the bare clusters and correlate the strength of the bond to the orbital energies of the LUMOs of the bare cluster. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We propose a machine-learned correlation model that is built using the regression between density variables such as electron density and correlation energy density. The correlation energy density of coupled cluster singles, doubles, and perturbative triples [CCSD(T)] is derived based on grid-based energy density analysis. The complete basis set (CBS) limit is estimated using the composite method, which has been reported to calculate the total correlation energy. The numerical examination revealed that the correlation energy density of the CCSD(T)/CBS level is appropriate for the response variable of machine learning. In addition to the density variables used in the exchange-correlation functionals of the density functional theory, the Hartree−Fock (HF) exchange energy density and electron density based on the fractional occupation number of molecular orbitals were employed as explanatory variables. Numerical assessments confirmed the accuracy and efficiency of the present correlation model. Consequently, the present protocol, namely, learning the CCSD(T)/CBS correlation energy density using density variables obtained by the HF calculation with a small basis set, yields an efficient correlation model. [ABSTRACT FROM AUTHOR]

The key characteristics of electronic excitations of many-electron systems, the excitation energies ωα and the oscillator strengths fα, can be obtained from linear response theory. In one-electron models and within the adiabatic approximation, the zeros of the inverse response matrix, which occur at the excitation energies, can be obtained from a simple diagonalization. Particular cases are the eigenvalue equations of time-dependent density functional theory (TDDFT), time-dependent density matrix functional theory, and the recently developed phase-including natural orbital (PINO) functional theory. In this paper, an expression for the oscillator strengths fα of the electronic excitations is derived within adiabatic response PINO theory. The fα are expressed through the eigenvectors of the PINO inverse response matrix and the dipole integrals. They are calculated with the phase-including natural orbital functional for two-electron systems adapted from the work of Lowdin and Shull on two-electron systems (the phase-including Löwdin-Shull functional). The PINO calculations reproduce the reference fα values for all considered excitations and bond distances R of the prototype molecules H2 and HeH+ very well (perfectly, if the correct choice of the phases in the functional is made). Remarkably, the quality is still very good when the response matrices are severely restricted to almost TDDFT size, i.e., involving in addition to the occupied-virtual orbital pairs just (HOMO+1)-virtual pairs (R1) and possibly (HOMO+2)-virtual pairs (R2). The shape of the curves fα(R) is rationalized with a decomposition analysis of the transition dipole moments. [ABSTRACT FROM AUTHOR]

Recently, we introduced a new density-functional theory (DFT) approach for the calculation of NMR shielding constants. First, a hybrid DFT calculation (using 5% exact exchange) is performed on the molecule to determine Kohn-Sham orbitals and their energies; second, the constants are determined as in nonhybrid DFT theory, that is, the paramagnetic contribution to the constants is calculated from a noniterative, uncoupled sum-over-states expression. The initial results suggested that this semiempirical DFT approach gives shielding constants in good agreement with the best ab initio and experimental data; in this paper, we further validate this procedure, using London orbitals in the theory, having implemented DFT into the ab initio code DALTON. Calculations on a number of small and medium-sized molecules confirm that our approach produces shieldings in excellent agreement with experiment and the best ab initio results available, demonstrating its potential for the study of shielding constants of large systems. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Recently, an approximate theoretical framework was introduced, called local reduced density matrix functional theory (local-RDMFT), where functionals of the one-body reduced density matrix (1-RDM) are minimized under the additional condition that the optimal orbitals satisfy a single electron Schrödinger equation with a local potential. In the present work, we focus on the character of these optimal orbitals. In particular, we compare orbitals obtained by local-RDMFT with those obtained with the full minimization (without the extra condition) by contrasting them against the exact NOs and orbitals from a density functional calculation using the local density approximation (LDA). We find that the orbitals from local-RMDFT are very close to LDA orbitals, contrary to those of the full minimization that resemble the exact NOs. Since local RDMFT preserves the good quality of the description of strong static correlation, this finding opens the way to a mixed density/density matrix scheme, where Kohn-Sham orbitals obtain fractional occupations from a minimization of the occupation numbers using 1-RDM functionals. This will allow for a description of strong correlation at a cost only minimally higher than a density functional calculation. [ABSTRACT FROM AUTHOR]

Meta-generalized gradient approximation (meta-GGA) exchange-correlation density functionals depend on the Kohn-Sham (KS) orbitals through the kinetic energy density. The KS orbitals in turn depend functionally on the electron density. However, the functional dependence of the KS orbitals is indirect, i.e., not given by an explicit expression, and the computation of analytic functional derivatives of meta-GGA functionals with respect to the density imposes a challenge. The practical solution used in many computer implementations of meta-GGA density functionals for ground-state calculations is abstracted and generalized to a class of density functionals that is broader than meta-GGAs and to any order of functional differentiation. Importantly, the TDDFT working equations for meta-GGA density functionals are presented here for the first time, together with the technical details of their computer implementation. The analysis presented here also uncovers the implicit assumptions in the practical solution to computing functional derivatives of meta-GGA density functionals. The connection between the approximation that is invoked in taking functional derivatives of density functionals, the non-uniqueness with respect to the KS orbitals, and the non-locality of the resultant potential is also discussed. [ABSTRACT FROM AUTHOR]

Whereas a density functional that incorporates dispersion interaction has remained elusive to date, we demonstrate that in principle the dispersion energy can be obtained from a density matrix functional. In density matrix functional theory one tries to find suitable approximations to the two-particle reduced density matrix (2RDM) in terms of natural orbitals (NOs) and natural orbital occupation numbers (ONs). The total energy is then given as a function(al) of the NOs and ONs, i.e., as an implicit functional of the 1RDM. The left-right correlation in a (dissociating) bond, as well as various types of dynamical correlation, can be described accurately with a NO functional employing only J and K integrals (JK-only functional). We give a detailed analysis of the full CI wavefunction of the He2 dimer, from which the dispersion part of the two-particle density matrix is obtained. It emerges that the entirely different physics embodied in the dispersion interaction leads to an essentially different type of exchange-correlation orbital functional for the dispersion energy (non-JK). The distinct NO functionals for the different types of correlation imply that they can be used in conjunction without problems of double counting. Requirements on the (primitive) basis set for Van der Waals bonding appear to be more modest than for other types of correlation. [ABSTRACT FROM AUTHOR]

To better understand the nature of alkyl intermediates often invoked in reactions involving hydrocarbon reactants and products, the adsorption of linear and branched C1-C4 alkyls on Cu(111) at 1/4 ML and 1/9 ML coverages was studied using density functional theory. The adsorption energy and site preference are found to be coverage-dependent, and both direct alkyl-alkyl interactions and changes in the Cu electronic structure play a role in these trends. It was found that methyl strongly prefers the hollow sites, the branched alkyls strongly prefer the top site, and the linear C2-C4 alkyls have weak site preferences that change with coverage. To explain these differences, rationalize alkyl adsorption trends, and predict the binding energy of other alkyls, a simple model was developed in which the binding energy is fit as a linear function of the number of C-Cu and C-H-Cu interactions as well as the C-H bond energy in the corresponding alkane. Site preference can be understood as a compromise between C-Cu interactions and C-H-Cu interactions. Density of states analysis was used to gain a molecular-orbital understanding of the bonding of alkyls to Cu(111). [ABSTRACT FROM AUTHOR]

The conventional analysis of Perdew and Levy, and Sham and Schlüter shows that the functional derivative discontinuity of the exchange-correlation density functional plays a critical role in the correct prediction of bandgaps, or the chemical hardness. In a recent work by the present authors, explicit expressions for bandgap prediction with all common types of exchange-correlation functionals have been derived without invoking the concept of exchange-correlation energy functional derivative discontinuity at all. We here analyze the two approaches and establish their connection and difference. The present analysis further leads to several important results: (1) The lowest unoccupied molecular orbital (LUMO) in DFT has as much meaning in describing electron addition as the highest occupied molecular orbital (HOMO) in describing electron removal. (2) Every term in the total energy functional contributes to the energy gap because of the discontinuity of the derivative of the density (or density matrix) with respect to the number of electrons, ((∂ρs(r′,r))/∂N)vs, at integers. (3) Consistent with the Perdew-Levy-Sham-Schlüter conclusion that the exact Kohn-Sham energy gap differs from the fundamental bandgap by a finite correction due to the functional derivative discontinuity of the exchange-correlation energy, we show that the exchange-correlation functional cannot be an explicit and differentiable functional of the electron density, either local or nonlocal. The last result is further strengthened when we consider Mott insulators. There, the exact exchange-correlation functional needs to have an explicitly discontinuous (nondifferentiable) dependence on the density or the density matrix. (4) We obtain exact conditions on the derivatives of total energy with respect to the spin-up and spin-down number of electrons. [ABSTRACT FROM AUTHOR]

In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H2 and N2, and twisted ethylene, while performing similar to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are 'challenging problems' for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets. [ABSTRACT FROM AUTHOR]

Theory and implementation of the analytical nuclear gradient is presented for orbital optimized scaled opposite-spin perturbation theory (O2). Evaluation of the O2 analytical gradient scales with the 4th power of molecular size, like the O2 energy. Since the O2 method permits optimization of the orbitals in the presence of wavefunction-based electron correlation, it is suitable for problems where correlation effects determine the competition between localization and delocalization of an odd electron, or hole. One such problem is the description of a neutral soliton defect on an all-trans polyacetylene chain with an odd number of carbon atoms. We show that the results of the O2 method compare well to benchmark values for small polyenyl radicals. O2 is also efficient enough to be applied to longer chains where benchmark coupled cluster methods are unfeasible. For C41H43, unrestricted orbital O2 calculations yield a soliton length of about 9 carbon atoms, while other unrestricted orbital methods such as Hartree-Fock, and the B3LYP and ωB97X-D density functionals, delocalize the soliton defect over the entire chain. The O2 result is about half the width inferred experimentally. [ABSTRACT FROM AUTHOR]

Adsorption of O2 molecule on Al surface has been a long standing puzzle for the first principles calculation. We have studied the adsorption of O2 molecule on the Al(111) surface using hybrid functionals. In contrast to the previous local-density approximation/gradient-corrected approximation, the present calculations with hybrid functionals successfully predict that O2 molecule can be absorbed on the Al(111) surface with a barrier around 0.2-0.4 eV, which is in good agreement with experiments. Our calculations predict that the lowest unoccupied molecular orbital of O2 molecule is higher than the Fermi level of the Al(111) surface, which is responsible for the barrier of the O2 adsorption. [ABSTRACT FROM AUTHOR]

We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. [ABSTRACT FROM AUTHOR]

A study of differently polarized structures relevant to the H-bonded antiferroelectric (AFE) compound NH4H2PO4 (ADP) is performed by first-principles calculations in the framework of the density functional theory. The calculated structures for the AFE and paraelectric (PE) phases are found in general good agreement with the available experimental data. We study the energetics and relative stability of different polarized clusters embedded in a PE matrix of ADP. We find that local ferroelectric and AFE clusters are stable and may coexist in the PE phase, which explains the coexistence of both type of microregions determined by electron spin probe measurements above the AFE-PE transition temperature. The dependency with the O-H···O bridge length of the energy barrier heights for proton transfer is studied for coordinated proton displacements along the bridges within clusters of different sizes. This dependency may have implications for the geometric isotopic effects on Tc. We analyze Mulliken orbital and bond populations which confirm the existence of a charge flow within the NH4+ ion, an essential fact for the stabilization of the AFE phase over other possible polarized structures. This charge transfer is correlated with the optimization of the N-H···O bridges and with distortions of the NH4+ group. [ABSTRACT FROM AUTHOR]

We analyze the pentacene/Au(111) interface by means of density functional theory (DFT) calculations using a new hybrid functional; in our approach we introduce, in a local-orbital formulation of DFT, a hybrid exchange potential, and combine it with a calculation of the molecule charging energy to properly describe the transport energy gap of pentacene on Au(111). Van der Waals forces are taken into account to obtain the adsorption geometry. Interface dipole potentials are also calculated; it is shown that the metal/pentacene energy level alignment is determined by the potential induced by the charge transfer between the metal surface and the organic material, as described by the induced density of interface states model. Our results compare well with the experimental data. [ABSTRACT FROM AUTHOR]

Threshold photoelectron spectra (TPESs) were obtained for naphthalene, anthracene, pyrene, 1,2-dihydronaphthalene, and 9,10-dihydroanthracene using imaging photoelectron photoion coincidence spectroscopy, from threshold to a photon energy of ∼20 eV. Outer valence Green's function calculations at the OVGF/cc-pVTZ level of theory were used to assign molecular orbitals to the observed TPES features. There is generally good agreement between the predicted and observed bands. Threshold regions for each molecule exhibit vibrational structure which is readily assigned based on previous PES studies. While the measured adiabatic ionization energies (IEa) for naphthalene, anthracene, and pyrene are in good agreement with previous works, new values are reported for the two dihydro species (1,2-dihydronaphthalene, 8.010 ± 0.010 eV and 9,10-dihydroanthracene, 8.335 ± 0.010 eV). A comparison is also made with the G3//B3LYP composite method, which consistently overestimates the IE values by 0.06-0.09 eV. The double ionization energies for anthracene and pyrene have been measured to be 19.3 ± 0.2 and 19.8 ± 0.2 eV, respectively. [ABSTRACT FROM AUTHOR]

Using density functional theory calculations, we have investigated the interactions between hydrogen molecules and metalloporphyrins. A metal atom, such as Ca or Ti, is introduced for incorporation in the central N4 cavity. Within local density approximation (generalized gradient approximation), we find that the average binding energy of H2 to the Ca atom is about 0.25 (0.1) eV/H2 up to four H2 molecules, whereas that to the Ti atom is about 0.6 (0.3) eV per H2 up to two H2 molecules. Our analysis of orbital hybridization between the inserted metal atom and molecular hydrogen shows that H2 binds weakly to Ca-porphyrin through a weak electric polarization in dihydrogen, but is strongly hybridized with Ti-porphyrin through the Kubas interaction. The presence of d orbitals in Ti may explain the difference in the interaction types. [ABSTRACT FROM AUTHOR]

In this study, the conformational preferences and photochemistry of acrylic acid (AA, CH2=CHCOOH) monomer isolated in cryogenic argon and krypton matrices were interpreted, based on results of quantum chemical calculations. Natural bond orbital analysis allowed to shed light on the main electronic effects determining the relative stability of the conformers of the molecule in the ground electronic state. The conformational isomerization taking place upon UV-irradiation of the matrix-isolated compound (λ ∼ 243 nm) was explained, based on theoretical complete active space self-consistent field/complete active space with second order perturbation theory (CASSCF/CASPT2) and time-dependent density functional theory (TD-DFT) results, allowing to rationalize the nearly equal populations of the two lowest energy conformers of the molecule observed in the photostationary state. Besides, details of the infrared spectra of the compound were reinterpreted based on the calculated spectra for the two most stable conformers of the molecule. In particular, the assignments for the out-of-plane A″ symmetry vibrations were revised. [ABSTRACT FROM AUTHOR]

Influence of acrylic acid grafting of isotactic polypropylene on the dielectric properties of the polymer is investigated using density functional theory (DFT) calculations, both in the molecular modeling and three-dimensional (3D) bulk periodic system frameworks. In our molecular modeling calculations, polarizability volume, and polarizability volume per mass which reflects the permittivity of the polymer, as well as the HOMO-LUMO gap, one of the important measures indicating the electrical breakdown voltage strength, were examined for oligomers with various chain lengths and carboxyl mixture ratios. When a polypropylene oligomer is grafted with carboxyl groups (cf. acrylic acid), our calculations show that the increase of the polarizability volume α′ of the oligomer is proportional to the increase of its mass m, while the ratio α′/ m decreases from the value of a pure polymer when increasing the mixture ratio. The decreasing ratio of α′/ m under carboxyl grafting indicates that the material permittivity might also decrease if the mass density of the material remains constant. Furthermore, our calculations show that the HOMO-LUMO gap energy decreases by only about 15% in grafting, but this decrease seems to be independent on the mixture ratio of carboxyl. This indicates that by doping polymers with additives better dielectric properties can be tailored. Finally, using the first-principles molecular DFT results for polarizability volume per mass in connection with the classical Clausius-Mossotti relation, we have estimated static permittivity for acrylic acid grafted polypropylene, assuming the structural density keeping constant under grafting. The computed permittivity values are in a qualitative agreement with the recent experiments, showing increasing tendency of the permittivity as a function of the grafting composition. In order to validate our molecular DFT based approach, we have also carried out extensive three-dimensional bulk periodic first-principles total-energy calculations in the frameworks of the density functional theory and density functional perturbation theory (DFPT) for crystalline acrylic acid grafted polypropylene. Interestingly, the computed electronic and dielectric properties behave very similarly between the simplified molecular DFT modeling and the more realistic 3D bulk periodic DFPT method. In particular, the static permittivity values [[variant_greek_epsilon]r(0)] from the molecular DFT-Clausius-Mossotti modeling are in excellent agreement with the high-frequency dielectric constant values ([variant_greek_epsilon]∞) from the DFPT method. This obviously implies that the chain-to-chain interaction to dielectric and electronic properties of acrylic acid polypropylene, to a first approximation, can be neglected, therefore justifying the usage of molecular DFT modeling in our calculations. [ABSTRACT FROM AUTHOR]

Dissociative electron attachment to dialanine and alanine anhydride has been studied in the gas phase utilizing a double focusing two sector field mass spectrometer. We show that low-energy electrons (i.e., electrons with kinetic energies from near zero up to 13 eV) attach to these molecules and subsequently dissociate to form a number of anionic fragments. Anion efficiency curves are recorded for the most abundant anions by measuring the ion yield as a function of the incident electron energy. The present experiments show that as for single amino acids (M), e.g., glycine, alanine, valine, and proline, the dehydrogenated closed shell anion (M-H)- is the most dominant reaction product. The interpretation of the experiments is aided by quantum chemical calculations based on density functional theory, by which the electrostatic potential and molecular orbitals are calculated and the initial electron attachment process prior to dissociation is investigated. [ABSTRACT FROM AUTHOR]

The effect of a finite size model for both the nuclear charge and magnetic moment distributions on calculated EPR hyperfine structure have been studied using a relativistic four-component method based on density functional theory. This approach employs a restricted kinetically balanced basis (mDKS-RKB) and includes spin-polarization using noncollinear spin-density exchange-correlation functionals in the unrestricted fashion. Benchmark calculations have been carried out for a number of small molecules containing Zn, Cd, Ag, and Hg. The present results are compared with those obtained at the Douglas-Kroll-Hess second order (DKH-2) method. The dependence of the results on the quality of the orbital and auxiliary basis sets has been studied. It was found that some basis sets contain irregularities that deteriorate the results. Especial care has to be taken also on the construction of the auxiliary basis for fitting the total electron and spin-densities. [ABSTRACT FROM AUTHOR]

Starting from the equation of motion in the density matrix formulation, we reformulate the analytical gradient of the excited-state energy at the time-dependent density functional theory level in the nonorthogonal Gaussian atom-centered orbital (AO) basis. Analogous to the analytical first derivative in molecular-orbital (MO) basis, a Z-vector equation has been derived with respect to the reduced one-electronic density matrix in AO basis, which provides a potential possibility to exploit quantum locality of the density matrix and avoids the matrix transformation between the AO and the MO basis. Numerical tests are finished for the excited-state geometry optimization and adiabatic excitation energy calculation of a series of small molecules. The results demonstrate the computational efficiency and accuracy of the current AO-based energy gradient expression in comparison with the MO-based scheme. [ABSTRACT FROM AUTHOR]

The implementation of fewest-switches surface-hopping (FSSH) within time-dependent Kohn-Sham (TDKS) theory [Phys. Rev. Lett. 95, 163001 (2005)] has allowed us to study successfully excited state dynamics involving many electronic states in a variety of molecular and nanoscale systems, including chromophore-semiconductor interfaces, semiconductor and metallic quantum dots, carbon nanotubes and graphene nanoribbons, etc. At the same time, a concern has been raised that the KS orbital basis used in the calculation provides only approximate potential energy surfaces [J. Chem. Phys. 125, 014110 (2006)]. While this approximation does exist in our method, we show here that FSSH-TDKS is a viable option for computationally efficient calculations in large systems with straightforward excited state dynamics. We demonstrate that the potential energy surfaces and nonadiabatic transition probabilities obtained within the TDKS and linear response (LR) time-dependent density functional theories (TDDFT) agree semiquantitatively for three different systems, including an organic chromophore ligating a transition metal, a quantum dot, and a small molecule. Further, in the latter case the FSSH-TDKS procedure generates results that are in line with FSSH implemented within LR-TDDFT. The FSSH-TDKS approach is successful for several reasons. First, single-particle KS excitations often give a good representation of LR excitations. In this regard, DFT compares favorably with the Hartree-Fock theory, for which LR excitations are typically combinations of multiple single-particle excitations. Second, the majority of the FSSH-TDKS applications have been performed with large systems involving simple excitations types. Excitation of a single electron in such systems creates a relatively small perturbation to the total electron density summed over all electrons, and it has a small effect on the nuclear dynamics compared, for instance, with thermal nuclear fluctuations. In such cases an additional, classical-path approximation can be made. Third, typical observables measured in time-resolved experiments involve averaging over many initial conditions. Such averaging tends to cancel out random errors that may be encountered in individual simulated trajectories. Finally, if the flow of energy between electronic and nuclear subsystems is insignificant, the ad hoc FSSH procedure is not required, and a straightforward mean-field, Ehrenfest approach is sufficient. Then, the KS representation provides rigorously a convenient and efficient basis for numerically solving the TDDFT equations of motion. [ABSTRACT FROM AUTHOR]

Transition states and reaction paths for a hydrogen molecule dissociating on small aluminum clusters have been calculated using density functional theory. The two lowest spin states have been taken into account for all the Aln clusters considered, with n=2-6. The aluminum dimer, which shows a 3Πu electronic ground state, has also been studied at the coupled cluster and configuration interaction level for comparison and to check the accuracy of single determinant calculations in this special case, where two degenerate configurations should be taken into account. The calculated reaction barriers give an explanation of the experimentally observed reactivity of hydrogen on Al clusters of different size [Cox et al., J. Chem. Phys. 84, 4651 (1986)] and reproduce the high observed reactivity of the Al6 cluster. The electronic structure of the Aln-H2 systems was also systematically investigated in order to determine the role played by interactions of specific molecular orbitals for different nuclear arrangements. Singlet Aln clusters (with n even) exhibit the lowest barriers to H2 dissociation because their highest doubly occupied molecular orbitals allow for a more favorable interaction with the antibonding σu molecular orbital of H2. [ABSTRACT FROM AUTHOR]

Segmented contracted basis sets for 4d, 5d, 5s, and 6s elements of split (double zeta) valence to quadruple zeta valence quality optimized for Dirac-Fock effective core potentials (ECPs) are presented. They were obtained from previous bases optimized for Wood-Boring ECPs by comparably small modifications and reoptimizations. Additionally extensions for two-component self-consistent-field treatments accounting for spin-orbit (SO) coupling were designed and optimized. Reliability for chemical applications was assessed by comparing results to those obtained with a very large (19s16p17d7f6g) reference basis for a set of more than 80 representatively chosen 5s-5d compounds. Moreover, the effect of different types of ECPs and that of the SO-coupling at the basis set limit of density functional theory is documented for the above set of molecules extended by 40 5p-6p compounds. [ABSTRACT FROM AUTHOR]

We study a time-dependent semiempirical method to determine excitation energies, TD-PM3. This semiempirical method allows large molecules to be treated. A Linear-response Chebyshev approach yields the TD-PM3 spectrum very efficiently. Spectra and excitation energies were tested by comparing it with the results obtained using TD-DFT (Time Dependent-Density Functional Theory), using both small and large basis sets. They were also compared to PM3-CI, Time Dependent-Hartree Fock using the STO-3G basis set, and to experiment. TD-PM3 results generally match better the large-basis set calculations than the small-basis TD-DFT do; excitation energies are almost always accurate to within about 20% or less, except for a few small molecules. Accuracy improves as the molecules get larger. [ABSTRACT FROM AUTHOR]

The electronic structure of single and multiple layers of C60 molecules deposited on a Rh(100) surface is investigated by means of valence photoemission spectroscopy and density functional theory calculations. The binding of the fullerene monolayer to the metal surface yields the appearance of a new state in the valence band spectrum crossing the Fermi level. Insight into the metallization of the metal/fullerene interface is provided by the calculated electronic structure that allows us to correlate the measured interface state with a strong hybridization between the Rh metal states and the highest and lowest molecular orbitals. This results in a net charge transfer of ≈0.5e–0.6e from the metal to the p states of the interfacial C atoms. The charge transfer is shown to be very short range, involving only the C atoms bound to the metal. The electronic structure of the second C60 layer is already insulating and resembles the one measured for C60 multilayers supported by the same substrate or calculated for fullerenes isolated in vacuum. The discussion of the results in the context of other C60/metal systems highlights the distinctive electronic properties of the molecule/metal interface determined by the Rh support. [ABSTRACT FROM AUTHOR]

Time-dependent density functional theory (TD-DFT) calculations of the electronic response of molecular and bulk liquid water based on a very accurate orbital-dependent ground-state exchange-correlation potential, the statistical average of (model) orbital potentials (SAOP), and on the adiabatic local density approximation (ALDA) for the exchange-correlation kernel are described. The quality of the calculated excitation energies, both in the molecule and in the liquid, is assessed by comparison to hybrid TD-DFT calculations and experimental data. A combination of classical molecular dynamics simulations and TD-DFT calculations sampling several disordered configurations of a small liquid sample is then used to simulate the optical absorption spectrum in the region of 0–15 eV. The resulting room-temperature absorption profile is discussed in connection with previous TD-DFT calculations as well as with results from Green’s function theory and experiment. [ABSTRACT FROM AUTHOR]

A recently developed relativistic four-component density functional method for calculation of nuclear magnetic resonance (NMR) shielding tensors using restricted magnetically balanced basis sets for the small component (mDKS-RMB) was extended to incorporate the gauge including atomic orbitals (GIAO) approach. The combined method eliminates a strong dependence of the results, calculated with a finite basis set, on the choice of the gauge origin for the magnetic potential of a uniform external magnetic field. Benchmark relativistic calculations have been carried out for xenon dimer and the HX series (X=F, Cl, Br, I), where spin-orbit effects are known to be very pronounced for hydrogen shieldings. Our results clearly demonstrate that shieldings calculated at the four-component level with a common gauge (i.e., without GIAO, IGLO, or similar methods to treat the gauge problem) depend dramatically on the choice of the common gauge. The GIAO approach solves the problem in fully relativistic calculations as it does in the nonrelativistic case. [ABSTRACT FROM AUTHOR]

Localized molecular orbital energy decomposition analysis and symmetry-adapted perturbation theory (SAPT) calculations are used to analyze the two- and three-body interaction energies of four low-energy isomers of (H2O)6 in order to gain insight into the performance of several popular density functionals for describing the electrostatic, exchange-repulsion, induction, and short-range dispersion interactions between water molecules. The energy decomposition analyses indicate that all density functionals considered significantly overestimate the contributions of charge transfer to the interaction energies. Moreover, in contrast to some studies that state that density functional theory (DFT) does not include dispersion interactions, we adopt a broader definition and conclude that for (H2O)6 the short-range dispersion interactions recovered in the DFT calculations account about 75% or more of the net (short-range plus long-range) dispersion energies obtained from the SAPT calculations. [ABSTRACT FROM AUTHOR]

Photoelectron spectra of cold aluminum cluster anions Aln- have been measured in the size range n=13–75 and are compared to the results of density functional theory calculations. Good agreement between the measured spectra and the calculated density of states is obtained for most sizes, which gives strong evidence that the correct structures have been found. In particular the results confirm the occurrence of rather different structural motifs in this size range, from fcc-like stacks over fragments of decahedrons to disordered structures. An analysis of the density of states of representatives of the different structural motifs shows that the electronic structure is strongly influenced by the cluster geometry, and that a clear jelliumlike electron shell structure is present only in some exceptional cases. [ABSTRACT FROM AUTHOR]

It is found that for closed-l-shell atoms, the exact local exchange potential vx(r) calculated in the exchange-only Kohn–Sham (KS) scheme of the density functional theory (DFT) is very well represented within the region of every atomic shell by each of the suitably shifted potentials obtained with the nonlocal Fock exchange operator for the individual Hartree–Fock (HF) orbitals belonging to this shell. This newly revealed property is not related to the well-known steplike shell structure in the response part of vx(r), but it results from specific relations satisfied by the HF orbital exchange potentials. These relations explain the outstanding proximity of the occupied HF and exchange-only KS orbitals as well as the high quality of the Krieger–Li–Iafrate and localized HF (or, equivalently, common-energy-denominator) approximations to the DFT exchange potential vx(r). Another highly accurate representation of vx(r) is given by the continuous piecewise function built of shell-specific exchange potentials, each defined as the weighted average of the shifted orbital exchange potentials corresponding to a given shell. The constant shifts added to the HF orbital exchange potentials, to map them onto vx(r), are nearly equal to the differences between the energies of the corresponding KS and HF orbitals. It is discussed why these differences are positive and grow when the respective orbital energies become lower for inner orbitals. [ABSTRACT FROM AUTHOR]

Equation of motion coupled-cluster singles and doubles (EOM-CCSD) is one of the most accurate computational methods for the description of one-electron vertical transitions. However, its O(N6) scaling, where N is the number of basis functions, often makes the study of molecules larger than 10–15 heavy atoms prohibitive. In this work we investigate how accurately less expensive methods can approximate the EOM-CCSD results. We focus on our own N-layer integrated molecular orbital molecular mechanics (ONIOM) hybrid scheme, where the system is partitioned into regions which are treated with different levels of theory. For our set of benchmark calculations, the comparison of conventional configuration interaction singles (CIS), time-dependent Hartree–Fock (TDHF), and time-dependent density functional theory (TDDFT) methods and ONIOM (with different low level methods) showed that the best accuracy-computational time combination is obtained with ONIOM(EOM:TDDFT), which has a rms of the error with respect to the conventional EOM-CCSD of 0.06 eV, compared with 0.47 eV of the conventional TDDFT. [ABSTRACT FROM AUTHOR]

Occupied-orbital dependent (OOD) exchange-correlation functionals hold a particularly prominent place in current developments of density functional theory. Their self-consistent implementation is complicated by the fact that their orbital-dependent parts are not explicit but only implicit functionals of electron density, and the exchange-correlation potential may not be obtained straightforwardly by taking the functional derivative with respect to the density. A two-step procedure is required, in which initially the functional derivatives with respect to the orbitals (FDOs) are obtained, which may then be transformed into local and multiplicative potentials by techniques of the optimized-effective potential. In view of the rather large variety of OOD functionals under current study, we report here general, systematic, and transparent expressions of the FDOs of a generalized OOD functional and additionally a matrix-element version in a basis set of atomic orbitals. Explicit FDOs are for the first time derived and numerically tested for one of the currently most complex examples of an OOD functional, Becke’s real-space model of nondynamical correlation (B05 functional) [J. Chem. Phys. 122, 064101 (2005)]. [ABSTRACT FROM AUTHOR]

First principles studies on the geometry, electronic structure, and magnetic properties of neutral and anionic Fe2Sin, Co2Sin, and Ni2Sin (1≤n≤8) clusters have been carried out within a gradient corrected density functional framework. It is shown that these clusters display a variety of magnetic species with varying magnetic moment and different magnetic coupling between the two transition metal atoms. While Fe2Sin clusters are mostly ferromagnetic with large moments, Ni2Sin clusters are mostly nonmagnetic. Our studies of the variation of the binding energy upon addition of successive Si atoms and the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital indicate that many of the motifs are quite stable and could be suitable as building blocks for generating magnetic cluster assembled materials. The studies also reveal motifs that could be used in molecular electronic devices to generate spin polarized currents or large magnetoresistance. [ABSTRACT FROM AUTHOR]

We show that, at least for the ground electronic state of systems treated using semilocal density functionals (like in local density or generalized gradient approximations), a calculation of the entire extended nonperiodic system consisting of several well distinguished parts (e.g., a collection of molecules) can be replaced with a finite set of calculations on specifically chosen smaller subsystems that overlap with each other. Every subsystem is terminated with link (or pseudo) atoms (or groups of atoms) to reduce the effect of the termination. However, because of the particular choice of the subsystems, the effect of the link atoms is largely compensated in the final total energy if the subsystems are chosen sufficiently large. In fact, we prove that the proposed method should result in nearly the same total energy, electronic density and atomic forces as a single (considered as a reference) density functional calculation on the entire system. Our method, however, should be much more efficient due to unfavorable scaling of the modern electronic structure methods with the system size. The method is illustrated on examples of serine water, lysine-water and lysine dimer systems. We also discuss possible approximate applications of our method for quantum-classical calculations of extended systems, when, as compared to widely used quantum-mechanical/molecular-mechanical methods, the problem of the quantum cluster boundary can be eliminated to a large degree. [ABSTRACT FROM AUTHOR]