Calculation of local excitations in large systems by embedding wave-function theory in density-functional theory

We present a simple and efficient embedding scheme for the wave-function based calculation of the energies of local excitations in large systems. By introducing an embedding potential obtained from density-functional theory (DFT) it is possible to describe the effect of an environment on local excitations of an embedded system in wave-function theory (WFT) calculations of the excitation energies. We outline the implementation of such a WFT-in-DFT embedding procedure employing the ADF, Dalton and DIRAC codes, where the embedded subsystem is treated with coupled cluster methods. We then evaluate this procedure in the calculation of the solvatochromic shift of acetone in water and of the f-f spectrum of NpO(2)(2+) embedded in a Cs(2)UO(2)Cl(4) crystal and find that our scheme does effectively incorporate the environment effect in both cases. A particularly interesting finding is that with our embedding scheme we can model the equatorial Cl(-) ligands in NpO(2)Cl(4)(2-) quite accurately, compared to a fully wavefunction-based calculation, and this opens up the possibility of modeling the interaction of different ligands to actinyl species with relatively high accuracy but at a much reduced computational cost.     

Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde

A combined quantum mechanics/molecular mechanics (QM/MM) method is described, where the polarization between the solvent and solute is accounted for using a self-consistent scheme linear in the solvent polarization. The QM/MM method is implemented for calculation of energies and molecular response properties including the calculation of linear and quadratic response functions using the density-functional theory (DFT) and the Hartree-Fock (HF) theory. Sample calculations presented for ground-state energies, first-order ground-state properties, excitation energies, first-order excited state properties, polarizabilities, first-hyperpolarizabilities, and two-photon absorptions strengths of formaldehyde suggests that DFT may in some cases be a sufficiently reliable alternative to high-level theory, such as coupled-cluster (CC) theory, in modeling solvent shifts, whereas results obtained with the HF wave function deviate significantly from the CC results. Calculations carried out on water gives results that also are comparable with CC calculations in accuracy for ground-state and first-order properties. However, to obtain such accuracy an exchange-correlation functional capable of describing the diffuse Rydberg states must be chosen.     

A new method for direct calculation of total energy of protein

A new scheme is developed for efficient quantum mechanical calculation of total energy of protein based on a recently developed MFCC (molecular fractionation with conjugate caps) approach. In this scheme, the linear-scaling MFCC method is first applied to calculate total electron density of protein. The computed electron density is then employed for direct numerical integration in density functional theory (DFT) to yield total energy of protein, with the kinetic energy obtained by a proposed ansatz. Numerical studies are carried out to calculate torsional energies of two polypeptides using this approach and the energies are shown to be in good agreement with the corresponding full system DFT calculation.     

Frozen-density embedding-based many-body expansions

Fragmentation methods allow for the accurate quantum chemical (QC) treatment of large molecular clusters and materials. Here we explore the combination of two complementary approaches to the development of such fragmentation methods: the many-body expansion (MBE) on the one hand, and subsystem density-functional theory (DFT) or frozen-density embedding (FDE) theory on the other hand. First, we assess potential benefits of using FDE to account for the environment in the subsystem calculations performed within the MBE. Second, we use subsystem DFT to derive a density-based MBE, in which a many-body expansion of the electron density is used to calculate the system's total energy. This provides a correction to the energies calculated with a conventional energy-based MBE that depends only on the subsystem's electron densities. For the test case of clusters of water and of aspirin, we show that such a density-based MBE converges faster than the conventional energy-based MBE. For our test cases, truncation errors in the interaction energies are below chemical accuracy already with a two-body expansion. The density-based MBE thus provides a promising avenue for accurate QC calculation of molecular clusters and materials.     

Acceleration of catalyst discovery with easy,fast, and reproducible computational alchemy

The expense of quantum chemistry calculations significantly hinders the search for novel catalysts. Here, we provide a tutorial for using an easy and highly cost‐efficient calculation scheme, called alchemical perturbation density functional theory (APDFT), for rapid predictions of binding energies of reaction intermediates and reaction barrier heights based on the Kohn‐Sham density functional theory (DFT) reference data. We outline standard procedures used in computational catalysis applications, explain how computational alchemy calculations can be carried out for those applications, and then present benchmarking studies of binding energy and barrier height predictions. Using a single OH binding energy on the Pt(111) surface as a reference case, we use computational alchemy to predict binding energies of 32 variations of this system with a mean unsigned error of less than 0.05 eV relative to single‐point DFT calculations. Using a single nudged elastic band calculation for CH₄ dehydrogenation on Pt(111) as a reference case, we generate 32 new pathways with barrier heights having mean unsigned errors of less than 0.3 eV relative to single‐point DFT calculations. Notably, this easy APDFT scheme brings no appreciable computational cost once reference calculations are performed, and this shows that simple applications of computational alchemy can significantly impact DFT‐driven explorations for catalysts. To accelerate computational catalysis discovery and ensure computational reproducibility, we also include Python modules that allow users to perform their own computational alchemy calculations.     

Theoretical Study of Stability and Electronic Characteristics in Various Complexes of Psoralen as an Anticancer Drug in Gas Phase,Water and CCl4 Solutions

The present research employs density functional theory(DFT) computations to analyze the structure and energy of complexes formed by psoralen drug with alkali(Li⁺, Na⁺, K⁺) and alkaline earth(Be²⁺, Mg²⁺, Ca²⁺) metal cations. The computations are conducted on M06-2X/aug-cc-pVTZ level of theory in the gas phase and solution. The Atoms in Molecules(AIM) and natural bond orbital(NBO) analyses are applied to evaluating the characterization of bonds and the atomic charge distribution, respectively. The results show that the absolute values of binding energies decrease with going from the gas phase to the solution. Furthermore, the considered complexes in the water(as a polar solvent) are more stable than the CCl₄(as a non-polar solvent). The DFT based chemical reactivity indices, such as molecular orbital energies, chemical potential, hardness and softness are also investigated. The outcomes show that the considered complexes have high chemical stability and low reactivity from the gas phase to the solution. Finally, charge density distributions and chemical reactive sites of a typical complex explored in this study are obtained by molecular electrostatic potential surface.     

The merits of the frozen-density embedding scheme to model solvatochromic shifts

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n-->pi(*) excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20-0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.     

Robust and accurate method for free-energy calculation of charged molecular systems

A new approach is presented to eliminate the problem of creation and/or annihilation of atoms in free-energy calculations of charged molecular systems. The method employs a damping potential in the Ewald summation scheme, which is an exact solution of the electrostatics for three-dimensional periodic systems. The proposed method enables entire molecules to be mutated from a noninteracting (ideal) state in an efficient and robust way, thus providing a means by which accurate absolute free energies of structurally complex molecules can be determined. This methodology will enable chemical and phase equilibria to be determined for large molecular species with significant charge distributions, e.g., biomolecules and drugs.     

ER-BOC calculations of crystal bulk properties from smallest-cluster models

Ab initio calculation of bulk properties of crystals with a high accuracy, which is a long-time goal of solid chemistry and physics, is still difficult and expensive because a large cluster is required as a crystal structure model. This article proposes a model based on density functional theory (DFT) quantum chemistry calculations and the assumption that the bond order of a given atom with its nearest atoms in a compound is conserved over the entire range from its diatomic molecules to clusters and further to crystals. This entire range bond order conservation (ER-BOC) provides an effective way to correlate bulk properties of crystals with those of the corresponding molecules and small clusters. By combining this ER-BOC principle with hybrid DFT quantum chemistry calculations, accurate predictions of the bulk bond lengths of a crystal can be made using calculations on small clusters.     

The effective fragment potential: small clusters and radial distribution functions

The effective fragment potential (EFP) method for treating solvent effects provides relative energies and structures that are in excellent agreement with the analogous fully quantum [i.e., Hartree-Fock (HF), density functional theory (DFT), and second order perturbation theory (MP2)] results for small water clusters. The ability of the method to predict bulk water properties with a comparable accuracy is assessed by performing EFP molecular dynamics simulations. The resulting radial distribution functions (RDF) suggest that as the underlying quantum method is improved from HF to DFT to MP2, the agreement with the experimental RDF also improves. The MP2-based EFP method yields a RDF that is in excellent agreement with experiment.     

Polarization charge densities provide a predictive quantification of hydrogen bond energies

A systematic density functional theory based study of hydrogen bond energies of 2465 single hydrogen bonds has been performed. In order to be closer to liquid phase conditions, different from the usual reference state of individual donor and acceptor molecules in vacuum, the reference state of donors and acceptors embedded in a perfect conductor as simulated by the COSMO solvation model has been used for the calculation of the hydrogen bond energies. The relationship between vacuum and conductor reference hydrogen bond energies is investigated and interpreted in the light of different physical contributions, such as electrostatic energy and dispersion. A very good correlation of the DFT/COSMO hydrogen bond energies with conductor polarization charge densities of separated donor and acceptor atoms was found. This provides a method to predict hydrogen bond strength in solution with a root mean square error of 0.36 kcal mol(-1) relative to the quantum chemical dimer calculations. The observed correlation is broadly applicable and allows for a predictive quantification of hydrogen bonding, which can be of great value in many areas of computational, medicinal and physical chemistry.     

Optical properties and delocalization of excess negative charges on oligo(phenylenevinylene)s: a quantum chemical study

A quantum chemical study of the electronic structure of negatively charged phenylenevinylene (PV) oligomers and methoxy-substituted derivatives is presented. The geometries of the PV oligomers were optimized using density functional theory. The geometry deformations are found to be delocalized along the entire oligomer chain without indication of polaron formation. The optical absorption spectra of the negatively charged PVs were calculated using both time-dependent density functional theory (TDDFT) and the singly excited configuration interaction method with an intermediate neglect of differential overlap reference wave function (INDO/s-CIS). The available experimental optical absorption energies are reproduced by the calculations. Introduction of methoxy substituents reduces the transition energies, while this does not have a strong effect on the charge distribution along the chain. DFT calculations yield a more delocalized excess negative charge than that of INDO/s-CIS calculations.     

Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning

Accurate and fast evaluation of electrostatic interactions in molecular systems is still one of the most challenging tasks in the rapidly advancing field of macromolecular chemistry, including molecular recognition, protein modeling and drug design. One of the most convenient and accurate approaches is based on a Buckingham-type approximation that uses the multipole moment expansion of molecular/atomic charge distributions. In the mid-1980s it was shown that the pseudoatom model commonly used in experimental X-ray charge density studies can be easily combined with the Buckingham-type approach for calculation of electrostatic interactions, plus atom-atom potentials for evaluation of the total interaction energies in molecular systems. While many such studies have been reported, little attention has been paid to the accuracy of evaluation of the purely electrostatic interactions as errors may be absorbed in the semiempirical atom-atom potentials that have to be used to account for exchange repulsion and dispersion forces. This study is aimed at the evaluation of the accuracy of the calculation of electrostatic interaction energies with the Buckingham approach. To eliminate experimental uncertainties, the atomic moments are based on theoretical single-molecule electron densities calculated at various levels of theory. The electrostatic interaction energies for a total of 11 dimers of alpha-glycine, N-acetylglycine and L-(+)-lactic acid structures calculated according to Buckingham with pseudoatom, stockholder and atoms-in-molecules moments are compared with those evaluated with the Morokuma-Ziegler energy decomposition scheme. For alpha-glycine a comparison with direct "pixel-by-pixel" integration method, recently developed Gavezzotti, is also made. It is found that the theoretical pseudoatom moments combined with the Buckingham model do predict the correct relative electrostatic interactions energies, although the absolute interaction energies are underestimated in some cases. The good agreement between electrostatic interaction energies computed with Morokuma-Ziegler partitioning, Gavezzotti's method, and the Buckingham approach with atoms-in-molecules moments demonstrates that reliable and accurate evaluation of electrostatic interactions in molecular systems of considerable complexity is now feasible.     

First-principles calculation of electronic spectra of light-harvesting complex II

We report on a fully quantum chemical investigation of important structural and environmental effects on the site energies of chlorophyll pigments in green-plant light-harvesting complex II (LHC II). Among the tested factors are technical and structural aspects as well as effects of neighboring residues and exciton couplings in the chlorophyll network. By employing a subsystem time-dependent density functional theory (TDDFT) approach based on the frozen density embedding (FDE) method we are able to determine site energies and electronic couplings separately in a systematic way. This approach allows us to treat much larger systems in a quantum chemical way than would be feasible with a conventional density functional theory. Based on this method, we have simulated a series of mutagenesis experiments to investigate the effect of a lack of one pigment in the chlorophyll network on the excitation properties of the other pigments. From these calculations, we can conclude that conformational changes within the chlorophyll molecules, direct interactions with neighboring residues, and interactions with other chlorophyll pigments can lead to non-negligible changes in excitation energies. All of these factors are important when site energies shall be calculated with high accuracy. Moreover, the redistribution of the oscillator strengths due to exciton coupling has a large impact on the calculated absorption spectra. This indicates that modeling mutagenesis experiments requires us to consider the entire set of chlorophyll molecules in the wild type and in the mutant, rather than just considering the missing chlorophyll pigment. An analysis of the mixing of particular excitations and the coupling elements in the FDEc calculation indicates that some pigments in the chlorophyll network act as bridges which mediate the interaction between other pigments. These bridges are also supported by the calculations on the "mutants" lacking the bridging pigment.     

Bonding and excitation in COCu(001) from a cluster model and density functional treatments

The bonding properties and charge distributions of the COCu(001) system have been studied within density functional theory (DFT) with several density functionals. A Cu18(9,4,5)CO three layer cluster was found to give bond distances and energies in agreement with previous experimental and theoretical results for low coverage systems, provided the atomic basis set includes diffuse orbitals and d-orbitals at the Cu atoms. Charge distributions give insight on the nature of the localized adsorbate bonding. Time-dependent DFT results on excitation energies and on transition and average electric dipoles, relevant to photodesorption, are also presented.     

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

An explicit quantum chemical method for modeling large solvation shells applied to aminocoumarin C151

The absorption spectra of aminocoumarin C151 in water and n-hexane solution are investigated by an explicit quantum chemical solvent model. We improved the efficiency of the frozen-density embedding scheme, as used in a former study on solvatochromism (J. Chem. Phys. 2005, 122, 094115) to describe very large solvent shells. The computer time used in this new implementation scales approximately linearly (with a low prefactor) with the number of solvent molecules. We test the ability of the frozen-density embedding to describe specific solvent effects due to hydrogen bonding for a small example system, as well as the convergence of the excitation energy with the number of solvent molecules considered in the solvation shell. Calculations with up to 500 water molecules (1500 atoms) in the solvent system are carried out. The absorption spectra are studied for C151 in aqueous or n-hexane solution for direct comparison with experimental data. To obtain snapshots of the dye molecule in solution, for which subsequent excitation energies are calculated, we use a classical molecular dynamics (MD) simulation with a force field adapted to first-principles calculations. In the calculation of solvatochromic shifts between solvents of different polarity, the vertical excitation energy obtained at the equilibrium structure of the isolated chromophore is sometimes taken as a guess for the excitation energy in a nonpolar solvent. Our results show that this is, in general, not an appropriate assumption. This is mainly due to the fact that the solute dynamics is neglected. The experimental shift between n-hexane and water as solvents is qualitatively reproduced, even by the simplest embedding approximation, and the results can be improved by a partial polarization of the frozen density. It is shown that the shift is mainly due to the electronic effect of the water molecules, and the structural effects are similar in n-hexane and water. By including water molecules, which might be directly involved in the excitation, in the embedded region, an agreement with experimental values within 0.05 eV is achieved.     

Molecular dynamics simulation with a continuum electrostatic model of the solvent

The accuracy and simplicity of the Poisson-Boltzmann electrostatics model has led to the suggestion that it might offer an efficient solvent model for use in molecular mechanics calculations on biomolecules. We report a successful merger of the Poisson-Boltzmann and molecular dynamics approaches, with illustrative calculations on the small solutes dichloroethane and alanine dipeptide. The algorithm is implemented within the program UHBD. Computational efficiency is achieved by the use of rather coarse finite difference grids to solve the Poisson-Boltzmann equation. Nonetheless, the conformational distributions generated by the new method agree well with reference distributions obtained as Boltzmann distributions from energies computed with fine finite difference grids. The conformational distributions also agree well with the results of experimental measurements and conformational analyses using more detailed solvent models. We project that when multigrid methods are used to solve the finite difference problem and the algorithm is implemented on a vector supercomputer, the computation of solvent electrostatic forces for a protein of modest size will add only about 0.1 s computer time per simulation step relative to a vacuum calculation. © 1995 by John Wiley & Sons, Inc.     

高精度的非相对论与完全相对论密度泛函理论计算方法和程序

介绍非相对论与完全相对论密度泛函理论计算方法和相应的计算程序（ＮＲ／Ｒ－ＤＦＴ）的结构和功能。本程序是目前用密度泛函理论方法计算完全相对论总能量能达到最高精度的程序。利用本程序可以高精度地计算含重元素体系的总能量、分子轨道能级、原子化能、键合能、偶极矩，分析化学键性质等。