A density functional theory for studying ionization processes in water clusters

A generalized Kohn-Sham (GKS) approach to density functional theory (DFT), based on the Baer-Neuhauser-Livshits range-separated hybrid, combined with ab initio motivated range-parameter tuning is used to study properties of water dimer and pentamer cations. The water dimer is first used as a benchmark system to check the approach. The present brand of DFT localizes the positive charge (hole), stabilizing the proton transferred geometry in agreement with recent coupled-cluster calculations. Relative energies of various conformers of the water dimer cation compare well with previously published coupled cluster results. The GKS orbital energies are good approximations to the experimental ionization potentials of the system. Low-lying excitation energies calculated from time-dependent DFT based on the present method compare well with recently published high-level "equation of motion-coupled-cluster" calculations. The harmonic frequencies of the water dimer cation are in good agreement with experimental and wave function calculations where available. The method is applied to study the water pentamer cation. Three conformers are identified: two are Eigen type and one is a Zundel type. The structure and harmonic vibrational structure are analyzed. The ionization dynamics of a pentamer water cluster at 0 K shows a fast <50 fs transient for transferring a proton from one of the water molecules, releasing a hydroxyl radical and creating a protonated tetramer carrying the excess hole.     

A density functional theory formulation of the reaction field model of solvent effects

It is possible to reformulate the reaction field (RF ) model of continuum solvent effects, by considering an approximate expression describing the energy changes from one ground state to another, in the frame of density functional theory (DFT ). The energy functional for an arbitrary electronic system coupled to a spin-independent electrostatic external perturbation is used to derive the well-known Born expression giving the electrostatic component of the solvation energy of an atomic ion. The approximate RF –DFT model is illustrated for a series of representative singly positive and negatively charged atomic ions. A Kohn–Sham (KS )-like formalism is then proposed to compute solvation energies within a self-consistent field scheme. The extension of the RF -DFT model to molecular systems is also outlined. © 1995 John Wiley & Sons, Inc.     

Scaled density functional theory correlation functionals

We show that a simple one-parameter scaling of the dynamical correlation energy estimated by the density functional theory (DFT) correlation functionals helps increase the overall accuracy for several local and nonlocal functionals. The approach taken here has been described as the "scaled dynamical correlation" (SDC) method [Ramachandran, J. Phys. Chem. A 2006, 110, 396], and its justification is the same as that of the scaled external correlation (SEC) method of Brown and Truhlar. We examine five local and five nonlocal (hybrid) DFT functionals, the latter group including three functionals developed specifically for kinetics by the Truhlar group. The optimum scale factors are obtained by use of a set of 98 data values consisting of molecules, ions, and transition states. The optimum scale factors, found with a linear regression relationship, are found to differ from unity with a high degree of correlation in nearly every case, indicating that the deviation of calculated results from the experimental values are systematic and proportional to the dynamic correlation energy. As a consequence, the SDC scaling of dynamical correlation decreases the mean errors (signed and unsigned) by significant amounts in an overwhelming majority of cases. These results indicate that there are gains to be realized from further parametrization of several popular exchange-correlation functionals.     

eQE: An open‐source density functional embedding theory code for the condensed phase

In this work, we present the main features and algorithmic details of a novel implementation of the frozen density embedding (FDE) formulation of subsystem density functional theory (DFT) that is specifically designed to enable ab initio molecular dynamics (AIMD) simulations of large‐scale condensed‐phase systems containing 1000s of atoms. This code (available at http://eqe.rutgers.edu ) has been given the moniker of embedded Quantum ESPRESSO (eQE) as it is a generalization of the open‐source Quantum ESPRESSO (QE) suite of programs. The strengths of eQE reside in a hierarchical parallelization scheme that allows for an efficient and fully self‐consistent treatment of the electronic structure (via the addition of an additional DIIS extrapolation layer) while simultaneously exploiting the inherent symmetries and periodicities in the system (via sampling of subsystem‐specific first Brillouin zones and utilization of subsystem‐specific basis sets). While bulk liquids and molecular crystals are two classes of systems that exemplify the utility of the FDE approach (as these systems can be partitioned into weakly interacting subunits), we show that eQE has significantly extended this regime of applicability by outperforming standard semilocal Kohn–Sham DFT (KS‐DFT) for large‐scale heterogeneous catalysts with quite different layer‐specific electronic structure and intrinsic periodicities. eQE features very favorable strong parallel scaling for a model system of bulk liquid water composed of 256 water molecules, which allows for a significant decrease in the overall time to solution when compared to KS‐DFT. We show that eQE achieves speedups greater than one order of magnitude ( ) when performing AIMD simulations of such large‐scale condensed‐phase systems as: (1) molecular liquids via bulk liquid water represented by 1024 independent water molecules (3072 atoms with a 25.3× speedup over KS‐DFT), (2) polypeptide/biomolecule solvation via (gly )₆ solvated in (H₂O)₃₉₅ (1230 atoms with a 38.6× speedup over KS‐DFT), and (3) molecular crystals via a 3 × 3 × 3 periodic supercell of pentacene (1940 atoms with a 12.0× speedup over KS‐DFT). These results represent a significant improvement over the current state‐of‐the‐art and now enable subsystem DFT‐based AIMD simulations of realistically sized condensed‐phase systems of interest throughout chemistry, physics, and materials science.     

Study of the formamide–methanol dimer with ab initio and density functional theory methods

For the first time, the structures and energies for the hydrogen bonding of a 1:1 complex formed between formamide and methanol molecules have been computed with various pure and hybrid density functional theory (DFT) and ab initio methods at varied basis set levels from 6‐31g to 6‐31+g(d,p). Five reasonable geometries on the potential energy surface of methanol and formamide system are considered and their relative stability is discussed. The infrared (IR) spectrum frequencies, IR intensities, and vibrational frequency shifts are reported. From the systematic studies, it is found that all the DFT methods selected here correctly compute the dimerization energies and geometries, with the B3P86 method predicting the hydrogen bond lengths relatively shorter and BPW91 yielding the interaction energies relatively lower. Finally, the solvent effects on the geometries of the formamide–methanol complexes have also been investigated using self‐consistent reaction field (SCRF) calculations with five different DFT methods at the 6‐31+g(d,p) basis set level. The results indicate that the polarity of the solvent has played an important role on the structures and relative stabilities of different isomers. Moreover, the basis set superposition error correction is critical to the interaction energies in the polar solvents. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Tight-binding density functional theory: an approximate Kohn-Sham DFT scheme

The DFTB method is an approximate KS-DFT scheme with an LCAO representation of the KS orbitals, which can be derived within a variational treatment of an approximate KS energy functional. But it may also be related to cellular Wigner-Seitz methods and to the Harris functional. It is an approximate method, but it avoids any empirical parametrization by calculating the Hamiltonian and overlap matrices out of DFT-derived local orbitals (atomic orbitals, AO's). The method includes ab initio concepts in relating the Kohn-Sham orbitals of the atomic configuration to a minimal basis of the localized atomic valence orbitals of the atoms. Consistent with this approximation, the Hamiltonian matrix elements can strictly be restricted to a two-center representation. Taking advantage of the compensation of the so-called "double counting terms" and the nuclear repulsion energy in the DFT total energy expression, the energy may be approximated as a sum of the occupied KS single-particle energies and a repulsive energy, which can be obtained from DFT calculations in properly chosen reference systems. This relates the method to common standard "tight-binding" (TB) schemes, as they are well-known in solid-state physics. This approach defines the density-functional tight-binding (DFTB) method in its original (non-self-consistent) version.     

Generalized hybrid-orbital method for combining density functional theory with molecular mechanicals.

The generalized hybrid orbital (GHO) method has previously been formulated for combining molecular mechanics with various levels of quantum mechanics, in particular semiempirical neglect of diatomic differential overlap theory, ab initio Hartree-Fock theory, and self-consistent charge density functional tight-binding theory. To include electron-correlation effects accurately and efficiently in GHO calculations, we extend the GHO method to density functional theory in the generalized-gradient approximation and hybrid density functional theory (denoted by GHO-DFT and GHO-HDFT, respectively) using Gaussian-type orbitals as basis functions. In the proposed GHO-(H)DFT formalism, charge densities in auxiliary hybrid orbitals are included to calculate the total electron density. The orthonormality constraints involving the auxiliary Kohn-Sham orbitals are satisfied by carrying out the hybridization in terms of a set of L?wdin symmetrically orthogonalized atomic basis functions. Analytical gradients are formulated for GHO-(H)DFT by incorporating additional forces associated with GHO basis transformations. Scaling parameters are introduced for some of the one-electron integrals and are optimized to obtain the correct charges and geometry near the QM/MM boundary region. The GHO-(H)DFT method based on the generalized gradient approach (GGA) (BLYP and mPWPW91) and HDFT methods (B3 LYP, mPW1PW91, and MPW1 K) is tested-for geometries and atomic charges-against a set of small molecules. The following quantities are tested: 1) the C--C stretch potential in ethane, 2) the torsional barrier for internal rotation around the central C--C bond in n-butane, 3) proton affinities for a set of alcohols, amines, thiols, and acids, 4) the conformational energies of alanine dipeptide, and 5) the barrier height of the hydrogen-atom transfer between n-C4H10 and n-C4H9, where the reaction center is described at the MPW1 K/6-31G(d) level of theory.     

四唑互变异构反应的密度泛函理论(DFT)研究

运用11种密度泛函理论方法对四唑互变异构反应进行了计算研究。结果表明,B3LYP-DFT法与从头算的优化几何和能量最为吻合;在6-31^*基组下B3LYP计算的IR频率与MP2/6-311G^*^*计算结果相差很小;用未经校正的B3LYP计算频率求得的产物(2H-四唑)的热力学性质与实测结果也完全一致;由此推荐B3LYP-DFT法适合于对四唑化合物作系统研究。     

密度泛函理论与Hartree-Fock方法混合处理中的稳态相关能校正

本文分析了通常的Hartree-Fock(HF)相关能定义和密度泛函理论(DFT)中的相关能定义的等价性条件。认为在参考电子密度与真实密度相差很大时两种定义是不等价的, 严格的DFT相关能比HF相关能(绝对值)要大。而在DFT与HF混合处理中得到的相关能比HF相关能(绝对值)要小, 两者之差相当于稳态相关能。实际计算表明, 通过合理地选择组态, 采用有限CI可以求得这一差值。本文描绘了双原子分子H2(X^1∑g^+), HF(X^1∑^+), N2(X^1∑g^+)的势能曲线, 结果比完全CISD和MP4的曲线还要好。H2的离解能是0.17a.u., 逼近实验值0.1747a.u..。     

Molecular analysis of water clusters: Calculation of the cluster structures and vibrational spectrum using density functional theory

Density functional theory (DFT) is applied to obtain absorption spectra at THz frequencies for molecular clusters of H₂O. The vibrational modes of the clusters are calculated. Coupling among molecular vibrational modes explains their spectral features associated with THz excitation. THz excitation is associated with vibrational frequencies which are here calculated within the DFT approximation of electronic states. This is done for both isolated molecules and collections of molecules in a cluster. The principal result of the paper is that a crystal-like cluster of 38 water molecules together with a continuum solvent background is sufficient to replicate well the experimental vibrational frequencies.     

Computational study of water and ammonia dimers with density functional theory methods

The structures and energies for the dimerization of water and ammonia molecules were computed with density functional theory (DFT) and ab initio methods. For all studies the same 6-311+G(2d,2p) basis set was used. Two linear hydrogen-bonded and cyclic ammonia dimer structures were computed and their relative stability is discussed. From the systematic studies, hybrid DFT methods were selected as reliable for computing the parameters of these types of van der Waals' complex.     

Exact-exchange density functional theory for hyperpolarizabilities

Time-dependent density functional theory (TDDFT) employing the exact-exchange functional (TDDFTx) has been formulated using the optimized effective potential method for the beta static hyperpolarizabilities, where it reduces to coupled-perturbed Kohn-Sham theory. A diagrammatic technique is used to take the functional derivatives for the derivation of the adiabatic second kernel, which is required for the analytical calculation of the beta static hyperpolarizabilities with DFT. The derived formulas have been implemented using Gaussian basis sets. The structure of the adiabatic exact-exchange second kernel is described and numerical examples are presented. It is shown that no current DFT functional satisfies the correct properties of the second kernel. Not surprisingly, TDDFTx, which corrects the self-interaction error in standard DFT methods and has the correct long-range behavior, provides results close to those of time-dependent Hartree-Fock in the static limit.     

Solvent effects on the S(N)2 reaction: Application of the density functional theory-based effective fragment potential method

The performance of the density functional theory (DFT)-based effective fragment potential (EFP) method is assessed using the S(N)2 reaction: Cl- + nH2O + CH3Br = CH3Cl + Br- + nH2O. The effect of the systematic addition of water molecules on the structures and relative energies of all species involved in the reaction has been studied. The EFP1 method is compared with second-order perturbation theory (MP2) and DFT results for n = 1, 2, and 3, and EFP1 results are also presented for four water molecules. The incremental hydration effects on the barrier height are the same for all methods. However, only full MP2 or MP2 with EFP1 solvent molecules are able to provide an accurate treatment of the transition state (TS) and hence the central barriers. Full DFT and DFT with EFP1 solvent molecules both predict central barriers that are too small. The results illustrate that the EFP1-based DFT method gives reliable results when combined with an accurate quantum mechanical (QM) method, so it may be used as an efficient alternative to fully QM methods in the treatment of larger microsolvated systems.     

Orbital-dependent correlation energy in density-functional theory based on a second-order perturbation approach: success and failure

We have developed a second-order perturbation theory (PT) energy functional within density-functional theory (DFT). Based on PT with the Kohn-Sham (KS) determinant as a reference, this new ab initio exchange-correlation functional includes an exact exchange (EXX) energy in the first order and a correlation energy including all single and double excitations from the KS reference in the second order. The explicit dependence of the exchange and correlation energy on the KS orbitals in the functional fits well into our direct minimization approach for the optimized effective potential, which is a very efficient method to perform fully self-consistent calculations for any orbital-dependent functionals. To investigate the quality of the correlation functional, we have applied the method to selected atoms and molecules. For two-electron atoms and small molecules described with small basis sets, this new method provides excellent results, improving both second-order Moller-Plesset expression and any conventional DFT results significantly. For larger systems, however, it performs poorly, converging to very low unphysical total energies. The failure of PT based energy functionals is analyzed, and its origin is traced back to near degeneracy problems due to the orbital- and eigenvalue-dependent algebraic structure of the correlation functional. The failure emerges in the self-consistent approach but not in perturbative post-EXX calculations, emphasizing the crucial importance of self-consistency in testing new orbital-dependent energy functionals.     

Real-time time-dependent density functional theory using density fitting and the continuous fast multipole method

An implementation of real-time time-dependent density functional theory (RT-TDDFT) within the TURBOMOLE program package is reported using Gaussian-type orbitals as basis functions, second and fourth order Magnus propagator, and the self-consistent field as well as the predictor–corrector time integration schemes. The Coulomb contribution to the Kohn–Sham matrix is calculated combining density fitting approximation and the continuous fast multipole method. Performance of the implementation is benchmarked for molecular systems with different sizes and dimensionalities. For linear alkane chains, the wall time for density matrix time propagation step is comparable to the Kohn-Sham (KS) matrix construction. However, for larger two- and three-dimensional molecules, with up to about 5,000 basis functions, the computational effort of RT-TDDFT calculations is dominated by the KS matrix evaluation. In addition, the maximum time step is evaluated using a set of small molecules of different polarities. The photoabsorption spectra of several molecular systems calculated using RT-TDDFT are compared to those obtained using linear response time-dependent density functional theory and coupled cluster methods.     

Hybrid density functional theory band structure engineering in hematite

We present a hybrid density functional theory (DFT) study of doping effects in α-Fe(2)O(3), hematite. Standard DFT underestimates the band gap by roughly 75% and incorrectly identifies hematite as a Mott-Hubbard insulator. Hybrid DFT accurately predicts the proper structural, magnetic, and electronic properties of hematite and, unlike the DFT+U method, does not contain d-electron specific empirical parameters. We find that using a screened functional that smoothly transitions from 12% exact exchange at short ranges to standard DFT at long range accurately reproduces the experimental band gap and other material properties. We then show that the antiferromagnetic symmetry in the pure α-Fe(2)O(3) crystal is broken by all dopants and that the ligand field theory correctly predicts local magnetic moments on the dopants. We characterize the resulting band gaps for hematite doped by transition metals and the p-block post-transition metals. The specific case of Pd doping is investigated in order to correlate calculated doping energies and optical properties with experimentally observed photocatalytic behavior.     

Scaling dynamical correlation energy from density functional theory correlation functionals

The scaling of dynamical correlation energy in molecules obtained by the correlation functionals of density functional theory (DFT) is examined. The approach taken is very similar to the scaled external correlation method of Brown and Truhlar but is based on the observation that DFT correlation functionals, especially the LYP, appear to represent the dynamical portion of the correlation energy in molecules. We examine whether higher accuracy in atomization energies can be gained by scaling without significant deterioration of the structural and spectroscopic properties of the molecules using four DFT functionals (BLYP, OLYP, B3LYP, and O3LYP) on 19 molecules including the six molecule AE6 database, the latter being representative of a much larger, 109 molecule training set. We show that, with molecule specific scale factors, nearly perfect agreement with experiment can be achieved in atomization energies without increasing the average errors in other molecular properties relative to the DFT calculation. We further show that it is possible to find optimal scale factors which reduce the mean unsigned error per bond to levels comparable to those of some multilevel multicoefficient methods.     

Calculation of bond dissociation energies for oxygen containing molecules by ab initio and density functional theory methods

Two ab initio (ROHF and MP2), one local (SVWN), four hybrid (BHandH, BHandHLYP, Becke3LYP, and Becke3P86), and two nonlocal (BLYP and BP86) density functional theory (DFT) methods are used for calculating the dissociation energies of molecules that contain H(SINGLE BOND)O, O(SINGLE BOND)O and O(SINGLE BOND)C bonds. The sensitivity to the basis set of the prediction of bond dissociation energies with DFT methods was tested with Becke3LYP on the H(SINGLE BOND)O dissociation energy of water. The 6–31 + G(d) methods are chosen as the smallest basis set which produces reasonable results. The calculated values for all other ab initio and DFT methods were performed with these basis sets and then compared with the experimental data. The suitability of DFT methods for computing reliable bond dissociation energies of oxygen containing molecules is discussed. © 1996 John Wiley & Sons, Inc.     

Electronic structures of one-dimensional metal-molecule hybrid chains studied using scanning tunneling microscopy and density functional theory

The electronic structures of self-assembled hybrid chains comprising Ag atoms and organic molecules were studied using scanning tunneling microscopy (STM) and spectroscopy (STS) in parallel with density functional theory (DFT). Hybrid chains were prepared by catalytic breaking of Br-C bonds in 4,4″-dibromo-p-terphenyl molecules, followed by spontaneous formation of Ag-C bonds on Ag(111). An atomic model was proposed for the observed hybrid chain structures. Four electronic states were resolved using STS measurements, and strong energy dependence was observed in STM images. These results were explained using first-principles calculations based on DFT.     

A hybrid method for predicting the microstructure of polymers with complex architecture: combination of single-chain simulation with density functional theory

A hybrid method is proposed to investigate the microstructure of various polymeric fluids confined between two parallel surfaces. The hybrid method combines a single-chain Monte Carlo (MC) simulation for the ideal-gas part of the Helmholtz energy and a density functional theory (DFT) for the excess part that arises from nonbonded intersegment interactions. The latter consists of a modified fundamental measure theory for excluded-volume effect, the first-order thermodynamics perturbation theory for chain connectivity, and a mean-field approximation for the van der Waals attraction. In comparison with a conventional DFT, the hybrid method avoids calculation of the time-consuming recursive functions and is directly applicable to polymers with arbitrary molecular architecture. Its numerical performance has been validated by extensive comparisons with MC data for the density distributions of totally flexible, semiflexible, or rigid polymers and those with starlike architecture. Special attention is also given to the formation of a nematic monolayer by rigid molecules laying perpendicular to a planar surface. The hybrid method predicts the surface pressure versus surface coverage in good agreement with experiment.