Investigation of intermolecular interactions based on the atomic statistical model

Possibilities of improving individual contributions to the statistical interaction energy (kinetic and exchange) are examined. A new method of calculating statistical interaction energies is proposed. The exchange term is calculated using a suitably modified second-order gradient correction. For the kinetic contribution the accurate formula corresponding to the first-order perturbation theory is applied. The calculations have been carried out for several pairs of noble gas atoms.     

Link between the kinetic‐ and exchange‐energy functionals in the generalized gradient approximation

An approximate kinetic‐energy functional of the generalized gradient approximation form was derived following the “conjointness conjecture” of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange‐energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed‐shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic‐energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Hierarchy of equations in the generalized density functional theory

Functional relations and equations of hierarchy in the generalized density functional theory (DFT) are derived from coordinate scaling and adiabatic connection. Local and nonlocal solutions for the noninteracting kinetic energy, exchange energy, correlation energy, and the kinetic energy correction functionals are presented. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

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.     

几种密度泛函理论公式用于镧系硫属化合物计算的比较

以镧系元素La、Gd、Lu的硫属化合物为对象,系统考察几种密度泛函理论公式对镧系化合物计算的适用情况,考虑了相对论效应的影响. 计算结果显示,相对论效应引起的键长变化在十2Pm到-3Pm之间,引起的键能减小为0. 4～0. 6eV,与采用的密度泛函公式关系不明显. 不同的密度泛函公式对键长的计算结果影响也不太大,但对键能有显著影响,其中LDA(VWN)＋PW86X公式给出最好结果. 交换能梯度校正明显改善键能计算结果,而相关能梯度校正反而使之变差. 简单的X_α公式给出相当好的键能计算结果. 在考虑相对论效应和梯度校正以后,密度泛函理论方法给出比较可靠的键长数值,键能则仍然偏高,但不超过20％.     

The main beam correction term in kinetic energy release from metastable peaks

The correction term for the precursor ion signal width in determination of kinetic energy release is reviewed, and the correction term is formally derived. The derived correction term differs from the traditionally applied term. An experimental finding substantiates the inaccuracy in the latter. The application of the “T ‐value” to study kinetic energy release is found preferable to kinetic energy release distributions when the metastable peaks are slim and simple Gaussians. For electronically predissociated systems, a “borderline zero” kinetic energy release can be directly interpreted in reaction dynamics with strong curvature in the reaction coordinate.     

The Influence of the Exchange-Correlation Functional on the Non-Interacting Kinetic Energy and Its Implications for Orbital-Free Density Functional ApproximationsSCI北大核心CSCD

In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.     

Proton affinities of molecules containing nitrogen and oxygen: Comparing density functional results to experiment

Summary Proton affinities were calculated using density functional theory for 11 small molecules whose primary protonation site is on nitrogen, and eight small molecules that protonate on oxygen. Calculations were performed using both the local spin density approximation and nonlocal gradient corrections to the exchange correlation functional. The results were not sensitive to whether the nonlocal gradient correction was implemented on the final local spin density optimized geometry or whether the correction was included in the self-consistent calculation of the energy at each optimization step. Although negligible basis set dependence was found using the analytic Gaussian basis sets, numerical basis sets required augmentation by a double set of polarization functions to achieve reasonable agreement with experiment. All calculations systematically underestimated oxygen proton affinities.     

The weizsacker term in density functional theory

A general expression for the first-order reduced density matrix suggested by its form in terms of the natural spin orbitals is used to show that the Weizsacker term is a natural component of the exact kinetic energy density functional.     

Functional derivative of the kinetic energy functional for spherically symmetric systems

Ensemble non-interacting kinetic energy functional is constructed for spherically symmetric systems. The differential virial theorem is derived for the ensemble. A first-order differential equation for the functional derivative of the ensemble non-interacting kinetic energy functional and the ensemble Pauli potential is presented. This equation can be solved and a special case of the solution provides the original non-interacting kinetic energy of the density functional theory.     

Method for evaluation of density functional integrals in molecular calculations

Numerical methods for computing variationally optimized molecular orbitals within the Hartree–Fock approximation are augmented to include correlation functionals of the density in the energy and the numerical methods for carrying this out are described. The approach is applied explicitly to the Colle–Salvetti correlation energy functional. It is found that the gradient terms in the Colle–Salvetti functional present numerical problems associated with the low-density behavior, but also that they make a relatively small contribution to the correlation energy. In the three cases considered, HF, H₂O and N₂, it is found that the Colle–Salvetti correction considerably underestimates the correlation energies obtained in coupled-cluster theory.     

Electron correlations in Kohn–Sham exchange‐only theory

We provide an interpretation for the “exchange” energy and potential of Kohn–Sham exchange‐only theory, or equivalently that of the optimized potential method (OPM), which shows that in addition to contribution due to the Pauli exclusion principle, there is a kinetic component to these properties. The interpretation is in terms of a conservative field R ^OPM( r ), which is a sum of two fields, one representative of Pauli electron correlations and the other of kinetic effects. The OPM exchange potential is derived via the differential virial theorem to be the work done to move an electron in the field R ^OPM( r ). The OPM exchange energy is then expressed via the integral virial theorem in terms of this field. A similar interpretation for the energy and potential may also be derived directly from the OPM integral equation. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71:473–480, 1999     

Does the gradient-regulated connection improve the description of correlated metal bond properties?

Gradient-regulated connection (GRAC) is a generalized gradient approximation exchange density functional designed by combining the revPBE and PW91 exchange functionals to impose their behaviors in the slowly- and fast-varying density regions, respectively. Such a construction allows one single density functional to accurately estimate both covalent and weak interactions occurring in main-group-based molecular systems. For the first time, the assessment of the performance of the GRAC exchange functional is extended to the modeling of various metal bond energy and structure properties. This assessment shows that when GRAC is coupled with the Perdew, Burke, Ernzerhof (PBE) correlation, the resulting exchange-correlation density functional is an excellent alternative to global hybrids to model bond dissociation energy, atomic electronic excitation energy, and bond length structure properties of single-reference metal bonds. It also shows that coupling with the Tognetti, Cortona, Adamo (TCA) correlation constitutes a robust approach to tackle energy bond properties of organometallic complexes with multi-reference character.     

香豆素衍生物的荧光发射能计算及XC泛函的合理选择

采用含时密度泛函理论(TDDFT)与单激发组态相互作用(CIS)处理相结合的计算方案对香豆素系列15种已知荧光化合物的发射能进行了系统考察. 结果表明, 发射能与吸收能一样, 其计算值主要取决于交换-相关(XC)泛函的选择. 只要泛函选用得当, 在使用较小基组的TDDFT/6-31G(d)//CIS/3-21G(d)理论水平上即可使绝大部分化合物的实验发射能在精度达0.16 eV以内得以重现. 与吸收能计算不同的是, 无法选用单一的一种泛函来对全系列化合物的发射能作出满意的理论预测. 激发态无明显电荷转移的、7位上有氨(或胺)基取代或有氮原子相连的化合物, 其适用泛函为不含Hartree-Fock(HF)交换能的纯泛函OLYP和BLYP. 而激发态发生较大程度电荷转移的、3 位上有共轭取代基的衍生物, 其适用泛函则为含20%的HF交换成分的混合泛函B3LYP. 因此, 发射能计算中的XC泛函选择, 应同时考虑取代基团效应以及激发态的电子结构特征. 其中, 发射能计算值受XC泛函中HF交换能比例的影响十分敏感. 文中还对激发能计算中的溶剂效应校正方案和激发态几何优化精度的影响进行了讨论.     

Proper Choice of XC Functionals and Calculations of Fluorescence-Emitting Energies for Coumarin Derivatives

A scheme of time-dependent density functional theory (TDDFT) combined with single-excitation configuration interaction (CIS) approach was employed to make a detailed investigation of the emitting energy for fifteen well-known coumarin derivatives. The results showed that the predicted emitting energies as well as the absorption ones were dominated mainly by the exchange-correlation (XC) functional to be used. So long as a functional is properly chosen, the experimental emitting energy of most derivatives can be accurately reproduced within 0.16 eV by a calculation at the TDDFT/6-31G(d)//CIS/3-21G(d) theoretical level. It was found that, nevertheless, the hybrid functional, B3LYP, well predicted the absorption energies for all the fifteen coumarin derivatives but none of the functionals could work equally well for the emitting energy calculations. Two pure functionals, OLYP and BLYP, yield good emitting energies for the 7-aminocoumarins or derivatives with a N atom connected to 7-position, which exhibit inconspicuous charge transfer (CT) in their excited states, whereas the B3LYP hybrid functional, with 20% Hartree-Fock (HF) exchange energy, performs significantly better than OLYP and BLYP for those 3-substituted coumarins with larger CT in excited states. Thus, in comparison with the absorption energies, the selection of proper functionals for the emitting energy calculations becomes more complex. In all probability, it is effective and doable to choose an XC-functional with alterable fraction of HF exchange energy according to the composition and structure characteristics of molecule.     

Hartree–Fock exchange energy of an inhomogeneous electron gas

We examine the short-range behavior of the spherically averaged Hartree–Fock exchange charge density by performing a simple Taylor expansion. On the basis of this expansion, a theoretical model is constructed that generates gradient correction terms to the local density approximation for the exchange energy of an inhomogeneous electron gas. In particular, we derive the Xαβ exchange energy functional and a theoretical value for the parameter β. Our value for β agrees well with previous empirical estimates, and with empirical calculations in the present work.     

Variation of parameters in Becke‐3 hybrid exchange‐correlation functional

We have investigated the consequences of varying the three parameters in Becke's hybrid exchange‐correlation functional, which includes five contributions: Hartree–Fock exchange, local exchange, Becke's gradient exchange correction, local correlation, and some form of gradient correlation correction. Our primary focus was upon obtaining orbital energies with magnitudes that are reasonable approximations to the electronic ionization potentials; however, we also looked at the effects on molecular geometries and atomization enthalpies. A total of 12 parameter combinations was considered for each of three different gradient correlation corrections: the Lee–Yang–Parr, the Perdew‐86, and the Perdew–Wang 91. Five molecules were included in the study: HCN, N₂, N₂O, F₂O, and H₂O. For comparison, a Hartree–Fock calculation was also carried out for each of these. The 6‐31+G** basis set was used throughout this work. We found that the ionization potential estimates can be greatly improved (to much better than Hartree–Fock levels) by increasing the Hartree–Fock exchange contribution at the expense of local exchange. In itself, this also introduces major errors in the atomization enthalpies. However, this can be largely or even completely counteracted by reducing or eliminating the role of the gradient exchange correction. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 227–238, 2000     

镱硫属化合物的密度泛函理论研究

用密度泛函理论(DFT)研究镱硫属化合物的电子结构和性质,通过与实验比较考察了现有的几种近似密度泛函公式对镧系元素化合物的适用程度和相对论效应的影响.结果表明,用DFT计算的YbO键长对实验值的偏差约为0.002nm;但得到的键能即使在考虑梯度校正和相对论效应之后,仍比实验值高,在定域密度近似基础上引入交换梯度校正使键能计算值减小,其中PW86x使键能计算值减小稍多些,结果更接近实验值;相关梯度校正使键能计算值升高.相对论效应使键长缩短0.004～0.006nm,键能减小约0.5eV.计算结果的分析表明,Yb的5d轨道和配体的np轨道间形成σ键和π键.在所研究的分子体系中,配体原子从O到Te、Yb原子的5d轨道布后数依次减少,同键能减弱的顺序一致.相对论效应使键能减小的主要原因是在成键过程中发生了Yb的6s电子向5d轨道的转移,而相对论效应使该过程能量增加.偶极矩和电荷分布的计算表明,Yb-L键以共价性为主,相对论效应使共价性成份增加.     

Vibrational frequency scale factors for density functional theory and the polarization consistent basis sets

Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a scale factor. Scale factors for: (i) harmonic vibrational frequencies [categorized into low (<1000 cm^?1) and high (>1000 cm^?1)], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero‐point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc‐n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree‐Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05‐2X, M06‐2X), a double hybrid functional with Møller‐Plesset correlation (B2GP‐PLYP), and a dispersion corrected functional (B97‐D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the scale factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested scale factor for each density functional when employing polarization consistent basis sets (pc‐n, n = 1,2,3,4). A separate scale factor is recommended when the un‐polarized basis set, pc‐0, is used in combination with the density functionals. © 2012 Wiley Periodicals, Inc.