Time-dependent quantum fluid density functional theory of hydrogen molecule under intense laser fields

A time-dependent generalized non-linear Schr?dinger equation (GNLSE) of motion was earlier derived in our laboratory by combining density functional theory and quantum fluid dynamics in three-dimensional space. In continuation of the work reported previously, the GNLSE is applied to provide additional knowledge on the femtosecond dynamics of the electron density in the hydrogen molecule interacting with high-intensity laser fields. For this purpose, the GNLSE is solved numerically for many time-steps over a total interaction time of 100 fs, by employing a finite-difference scheme. Various time-dependent (TD) quantities, namely, electron density, ground-state survival probability and dipole moment have been obtained for two laser wavelengths and four different intensities. The high-order harmonics generation (HHG) is also examined. The present approach goes beyond the linear response formalism and, in principle, calculates the TD electron density to all orders of change. Dedicated to Prof. D Mukherjee on his 60th birthday     

Rapidly convergent procedure to solve the density profile equation in the classical density functional theory

An efficient recursive procedure to solve the density profile equation in the classical density functional theory (DFT) using an inverse Broyden method is described. The present iterative procedure is free of calculation of the Jacobian matrix, and its inversion unavoidable for the well-known Newton-Raphson (NR) method and its variants. Numerical calculation indicates that only the approximate solution and iterative matrix of the lower bulk density case are employed as the corresponding initial guesses of the higher bulk density case, the present recursive procedure can converge quickly to the physical solution with an accuracy of epsilon = 10(-14); therefore, the procedure provides an efficient numerical algorithm for the theory in which acquirement of a density profile of high accuracy is a key step. Extensive numerical calculation shows the advantage of the present inverse Broyden method over Broyles' mixing procedure and a modified Powell hybrid algorithm (a variation of the NR method).     

Exploring odd-even effects of simple oligomer-like DRCNnT series: a study based on density functional theory/time-dependent density functional theory calculations

Odd-even effects of short-circuit current density and power conversion efficiency (PCE) are an interesting phenomenon in some organic solar cells. Although some explanations have been given, why they behave in such a way is still an open question. In the present work, we investigate a set of acceptor-donor-acceptor simple oligomer-like small molecules, named the DRCNnT (n = 5-9) series, to give an insight into this phenomenon because the solar cells based on them have high PCE (up to 10.08%) and show strong odd-even effects in experiments. By modeling the DRCNnT series and using density functional theory, we have studied the ground-state electronic structures of the DRCNnT (n = 5-9) series in condensed phase. The calculated results reproduce the experimental trends well. Furthermore, we find that the exciton-binding energies of the DRCNnT series may be one of the key parameters to explain this phenomenon because they also show odd-even effects. In addition, by studying the effects of alkyl branch and terminal group on odd-even effects of dipole moment, we find that eliminating one or two alkyl branches does not break the odd-even effects of dipole moments, but eliminating one or two terminal groups does. Finally, we conclude that removing one alkyl branch close to the terminal group of DRCN5T can decrease highest occupied molecular orbital (HOMO) energy (thus increasing open circuit voltage) and increase dipole moment (thus enhancing charge separation and short-circuit current). This could be a new and simple method to increase the PCE of DRCN5T-based solar cells.     

Exchange and correlation energy in density functional theory

Several different versions of density functional theory (DFT) that satisfy Hohenberg–Kohn theorems are characterized by different definitions of a reference or model state determined by an N‐electron ground state. A common formalism is developed in which exact Kohn–Sham equations are derived for standard Kohn–Sham theory, for reference‐state density functional theory, and for unrestricted Hartree–Fock (UHF) theory considered as an exactly soluble model Hohenberg–Kohn theory. A natural definition of exchange and correlation energy functionals is shown to be valid for all such theories. An easily computed necessary condition for the locality of exchange and correlation potentials is derived. While it is shown that in the UHF model of DFT the optimized effective potential (OEP) exchange satisfies this condition by construction, the derivation shows that this condition is not, in general, sufficient to define an exact local exchange potential. It serves as a test to eliminate proposed local potentials that are not exact for ground states. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 521–525, 2000     

Designing new donor materials based on functionalized DCCnT with different electron-donating groups: A density functional theory (DFT) and time dependent density functional theory (TDDFT)-based study

Finding a promising donor/acceptor material of organic solar cells is one of the most important ways to improve their power conversion efficiency. Extensive studies have focused on designing and synthesizing new and suitable materials. Small organic molecule materials, different from polymers, have many merits, such as easy synthesis and modification, less by-products, and crystallinity. In the present work, we theoretically design a series of new donor materials based on 1-(1,1-dicyanomethylene)-cyclohex-2-ene-substituted oligothiophenes, that is, DCCnT (n = 1-4) series. Furthermore, we model and predict photoelectric properties of functionalized DCCnT with different electron-donating groups (─CH₃/─CHCH₂/─OCH₃/─NH₂/─OH). The calculated results, based on density functional theory and time-dependent functional theory, show that DCCnT-X (X = OH, NH₂, and OCH₃) series show odd-even effect of dipole moments when n varies from 1 to 4, whereas DCCnT-CH₃ and DCCnT-CHCH₂ do not. Finally, we find that DCC3T-X (X = OH, OCH₃, and NH₂) may be better candidates of donor materials because of their larger dipole moments, stronger electron donating ability, and smaller exciton binding energy with respect to prototype DCCnT molecules.     

Time-dependent bond-current functional theory for lattice Hamiltonians: Fundamental theorem and application to electron transport

The cornerstone of time-dependent (TD) density functional theory (DFT), the Runge-Gross theorem, proves a one-to-one correspondence between TD potentials and TD densities of continuum Hamiltonians. In all practical implementations, however, the basis set is discrete and the system is effectively described by a lattice Hamiltonian. We point out the difficulties of generalizing the Runge-Gross proof to the discrete case and thereby endorse the recently proposed TD bond-current functional theory (BCFT) as a viable alternative. TDBCFT is based on a one-to-one correspondence between TD Peierl’s phases and TD bond-currents of lattice systems. We apply the TDBCFT formalism to electronic transport through a simple interacting device weakly coupled to two biased non-interacting leads. We employ Kohn-Sham Peierl’s phases which are discontinuous functions of the density, a crucial property to describe Coulomb blockade. As shown by explicit time propagations, the discontinuity may prevent the biased system from ever reaching a steady state.     

Differentiability of Lieb functional in electronic density functional theory

A solid understanding of the Lieb functional F_L is important because of its centrality in the foundations of electronic density functional theory. A basic question is whether directional derivatives of F_L at an ensemble‐V‐representable density are given by (minus) the potential. A widely accepted purported proof that F_L is Gâteaux differentiable at EV‐representable densities would say, “yes.” But that proof is fallacious, as shown here. F_L is not Gâteaux differentiable in the normal sense, nor is it continuous. By means of a constructive approach, however, we are able to show that the derivative of F_L at an EV‐representable density ρ₀ in the direction of ρ₁ is given by the potential if ρ₀ and ρ₁ are everywhere strictly greater than zero, and they and the ground state wave function have square integrable derivatives through second order. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Time-dependent density functional theory calculations of the photoabsorption of fluorinated alkanes

Time-dependent density functional theory (TD-DFT) calculations of the transition energies and oscillator strengths of fluorinated alkanes have been performed. The TD-DFT method with the non-local B3LYP potential yields transition energies for the methanes, which are smaller by about 10% as compared to the experimental values. An empirical linear correlation was found between the calculated and experimental transition energies both at the B3LYP/DZ+Ryd(C, F) and B3LYP/cc-pVTZ+Ryd(C, F, H) levels for a total of 19 transitions of the fluorinated methanes with linear correlation coefficients of 0.987 for the former and 0.988 for the latter. This empirical correlation for fluorinated methane molecules is found to agree well with the previously obtained empirical correlations between calculated and experimental values for non-fluorinated molecules. The results show that a single empirical-correlation relationship can be used for both non-fluorinated and fluorinated molecules to predict transition energies. This linear relationship is then used to predict the photoabsorption spectra of ethane, propane, butane, and partially and fully fluorinated derivatives. A key result of these calculations is the dominance of Rydberg transitions in the spectral region of interest.     

Theoretical study of metal‐free organic dyes based on different configurations for efficient dye‐sensitized solar cells

Considering different solar dyes configuration, four novel metal‐free organic dyes based on phenoxazine as electron donor, thiophene and cyanovinylene linkers as the ‐conjugation bridge and cyanoacrylic acid as electron acceptor were designed to optimize open circuit voltage and short circuit current parameters and theoretically inspected. Density functional theory and time‐dependent density functional theory calculations were used to study frontier molecular orbital energy states of the dyes and their optical absorption spectra. The results indicated that D2‐4 dyes can be suitable candidates as sensitizers for application in dye sensitized solar cells and among these three dyes, D3 showed a broader and more bathochromically shifted absorption band compared to the others. The dye also showed the highest molar extinction coefficient. This work suggests optimizing the configuration of metal‐free organic dyes based on simple D‐ ‐A configuration containing alkyl chain as substitution, starburst conformation, and symmetric double D‐ ‐A chains would produce good photovoltaic properties.     

Regional self-interaction correction of density functional theory

We propose a new simple scheme for self-interaction correction (SIC) of exchange functionals in the density functional theory. In the new scheme, exchange energies are corrected by substituting exchange self-interactions for exchange functionals in regions of self-interaction. To classify the regions of self-interaction, we take advantage of the property of the total kinetic energy density approaching the Weizs?cker density in the case of electrons in isolated orbitals. The scheme differs from conventional SIC methods in that it produces optimized molecular structures. Applying the scheme to the calculation of reaction energy barriers showed that it provides a clear improvement in cases where the barriers are underestimated by conventional "pure" functionals. In particular, we found that this scheme even reproduces a transition state that is not given by pure functionals.     

左旋葡聚糖热解机理的密度泛函理论研究

采用密度泛函理论B3LYP/6-31++G(d,p)方法,对纤维素热解的主要产物左旋葡聚糖的热解反应机理进行了理论计算分析,设计了四种可能的热解反应途径, 对各种反应的反应物、产物和过渡态的结构进行了能量梯度全优化。计算结果表明,左旋葡聚糖开环成链状中间体时,首先,左旋葡聚糖中的两个半缩醛键C(1)-O(7)和C(6)-O(8)断裂,经过渡态TS₁形成中间体IM₁,同时,C(6)-O(7)结合成键使C(5)-C(6)-O(7)形成环状结构,该反应的能垒较高,为296.53 kJ/mol,然后IM₁经过渡态TS₂转变为中间体IM₂,该反应的能垒为234.09 kJ/mol;对IM₂设计了四条可能的反应路径,反应路径2和3能垒较低,是IM₂最可能的热解反应途径;在反应路径1和4中都包含了脱羰基反应,其反应能垒较高,不易发生。     

Relative information in excited-state orbital-free density functional theory

Euler equations of the orbital-free excited-state density functional theory of Coulomb systems are derived for specific relative information. Derivation via variational extremization of the relative Fisher information is also presented. Relationships between the Fisher and Shannon information, the local wave vector, and the relative information are displayed.     

Implementation of empirical dispersion corrections to density functional theory for periodic systems

A recently developed empirical dispersion correction (Grimme et al., J. Chem. Phys. 2010, 132, 154104) to standard density functional theory (DFT‐D3) is implemented in the plane‐wave program package VASP. The DFT‐D3 implementation is compared with an implementation of the earlier DFT‐D2 version (Grimme, J. Comput. Chem. 2004, 25, 1463; Grimme, J. Comput. Chem. 2006, 27, 1787). Summation of empirical pair potential terms is performed over all atom pairs in the reference cell and over atoms in shells of neighboring cells until convergence of the dispersion energy is obtained. For DFT‐D3, the definition of coordination numbers has to be modified with respect to the molecular version to ensure convergence. The effect of three‐center terms as implemented in the original molecular DFT‐D3 version is investigated. The empirical parameters are taken from the original DFT‐D3 version where they had been optimized for a reference set of small molecules. As the coordination numbers of atoms in bulk and surfaces are much larger than in the reference compounds, this effect has to be discussed. The results of test calculations for bulk properties of metals, metal oxides, benzene, and graphite indicate that the original parameters are also suitable for solid‐state systems. In particular, the interlayer distance in bulk graphite and lattice constants of molecular crystals is considerably improved over standard functionals. With the molecular standard parameters (Grimme et al., J. Chem. Phys. 2010, 132, 154104; Grimme, J. Comput. Chem. 2006, 27, 1787) a slight overbinding is observed for ionic oxides where dispersion should not contribute to the bond. For simple adsorbate systems, such as Xe atoms and benzene on Ag(111), the DFT‐D implementations reproduce experimental results with a similar accuracy as more sophisticated approaches based on perturbation theory (Rohlfing and Bredow, Phys. Rev. Lett. 2008, 101, 266106). © 2012 Wiley Periodicals, Inc.     

Yb、YbO电子激发态的相对论含时密度泛函理论研究

本文用基于精确二分量哈密顿（exact two—component Hamiltonian）的相对论含时密度泛函理论（time-dependent relativistic density functional theory）计算了Yb和YbO的电子激发态,并利用对称性、自然原子轨道对激发态性质和归属进行了详细分析,所得结果支持实验对YbO基态与激发态的指认．     

Evaluation of density functional theory in the bond rupture of octane

Density functional methods at the 6-31G* level are applied to the rupture of n-octane into methyl–heptyl, ethyl–hexyl, propyl–pentyl, and butyl–butyl radical fragments. The energetics of the radicals at UMP3, UMP2/6-31G*//UHF/6-31G* (hereafter referred to as UMP), are compared to UB3LYP/6-31G* results (referred to as UB). Although the UMP approach matches additivity energies to within 5 kcal/mol, it fails to mimic the overall energetic trend. The UB energies agree with additivity estimates and trends to within 1–2 kcal/mol and radical entropies deviate by only 2 e.u. from available experimental data. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 154–167, 1998     

氢化可的松和表氢化可的松的密度泛函理论研究

采用密度泛函理论B3LYP/6-31G和B3LYP/6-311G*方法优化了氢化可的松和表氢化可的松的几何结构,利用优化的结构得到了氢化可的松和表氢化可的松的原子净电荷、总能量及前沿分子轨道组成.基于简谐振动分析求得了氢化可的松和表氢化可的松的红外光谱频率和强度,由统计热力学分析得到了热力学函数;进而确定了氢化可的松和...     

The exact Fermi potential yielding the Hartree–Fock electron density from orbital‐free density functional theory

The exact expression for the Fermi potential yielding the Hartree–Fock electron density within an orbital‐free density functional formalism is derived. The Fermi potential, which is defined as that part of the potential that depends on the particles’ nature, is in this context given as the sum of the Pauli potential and the exchange potential. The exact exchange potential for an orbital‐free density functional formalism is shown to be the Slater potential.     

Density functional theory study on electron and hole transport properties of organic pentacene derivatives with electron-withdrawing substituent

Attaching electron-withdrawing substituent to organic conjugated molecules is considered as an effective method to produce n-type and ambipolar transport materials. In this work, we use density functional theory calculations to investigate the electron and hole transport properties of pentacene (PENT) derivatives after substituent and simulate the angular resolution anisotropic mobility for both electron and hole transport. Our results show that adding electron-withdrawing substituents can lower the energy level of lowest unoccupied molecular orbital (LUMO) and increase electron affinity, which are beneficial to the electron injection and ambient stability of the material. Also the LUMO electronic couplings for electron transport in these pentacene derivatives can achieve up to a hundred meV which promises good electron transport mobility, although adding electron-withdrawing groups will introduce the increase of electron transfer reorganization energy. The final results of our angular resolution anisotropic mobility simulations show that the electron mobility of these pentacene derivatives can get to several cm(2) V(-1) s(-1), but it is important to control the orientation of the organic material relative to the device channel to obtain the highest electron mobility. Our investigation provide detailed information to assist in the design of n-type and ambipolar organic electronic materials with high mobility performance.