First-order relativistic corrections to MP2 energy from standard gradient codes: Comparison with results from density functional theory

The evaluation of the first-order scalar relativistic corrections to MP2 energy based on either direct perturbation theory or the mass–velocity and Darwin terms is discussed. In a basis set of Lévy-Leblond spinors the one- and two-electron matrix elements of the relativistic Hamiltonian can be decomposed into a nonrelativistic part and a relativistic perturbation. Thus, a program capable of calculating nonrelativistic energy gradients can be used to calculate the cross-term between relativity and correlation. The method has been applied to selected closed-shell atoms (He, Be, Ne, and Ar) and molecules (CuH, AgH, and AuH). The calculated equilibrium distances and harmonic frequencies were compared with results from first-order relativistic density functional calculations. It was found that the cross-term is not the origin of the nonadditivity of relativistic and correlation effects. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1596–1603, 1998     

Analytical energy gradient evaluation in relativistic and nonrelativistic density functional calculations

The expressions of analytical energy gradients in density functional theory and their implementation in programs are reported. The evaluation of analytical energy gradients can be carried out in the fully 4-component relativistic, approximate relativistic, and nonrelativistic density functional calculations under local density approximation or general gradient approximation with or without frozen core approximation using different basis sets in our programs. The translational invariance condition and the fact that the one-center terms do not contribute to the energy gradients are utilized to improve the calculation accuracy and to reduce the computational effort. The calculated results of energy gradients and optimized geometry as well as atomization energies of some molecules by the analytical gradient method are in very good agreement with results obtained by the numerical derivative method.     

密度泛函理论模拟外电场对铁氧体电子结构的影响

通过密度泛函理论(DFT)模拟了3种典型的铁氧体(Fe₂O₃、Fe₃O₄和α-FeOOH)受外电场作用下的电子结构,研究了外电场对不同铁氧体电子结构的影响。DFT模拟结果显示：外电场的存在能够有效提高Fe₂O₃、Fe₃O₄和α-FeOOH晶体结构的价带位置,从而导致3种铁氧体的带隙出现明显的降低;当外电场强度为0.01 V·nm^-1时,Fe₂O₃、Fe₃O₄和α-FeOOH的带隙分别降低了0.36、0.12和0.34 eV;当电场增大至0.1 V·nm^-1时,Fe₂O₃晶体出现击穿现象,Fe—O化学键断裂导致Fe原子的电子沿外电场方向高度离域至相邻Fe原子,而Fe₃O₄和α-FeOOH则仅出现不同价带能级电子局域性增强且能量同质化,因而显示出相对稳定的物理化学结构。此外,外电场的存在可导致3种铁氧体价带电子均出现简并现象,且随电场强度增大而增强。3种铁氧体中,外电场的存在导致Fe₂O₃晶体中Fe原子的电荷密度增大而降低O原子的电荷密度; Fe₃O₄晶体结构中不同配位结构的Fe原子以及配位O原子的Hirshfeld电荷几乎不受外电场的影响; α-FeOOH晶体中共边FeO₆配位结构的Hirshfeld电荷受外电场影响较小,而共角FeO₆配位结构的Hirshfeld电荷受外电场影响较大,且H原子的电荷在强外电场作用下发生歧化响应。随着外电场强度逐渐增大,Fe₃O₄晶体的电子自旋态密度逐渐增大,而α-FeOOH晶体的电子自旋态密度则显示出降低的规律。     

密度泛函理论模拟外电场对铁氧体电子结构的影响

通过密度泛函理论(DFT)模拟了3种典型的铁氧体(Fe₂O₃、Fe₃O₄和α-FeOOH)受外电场作用下的电子结构,研究了外电场对不同铁氧体电子结构的影响。DFT模拟结果显示:外电场的存在能够有效提高Fe₂O₃、Fe₃O₄和α-FeOOH晶体结构的价带位置,从而导致3种铁氧体的带隙出现明显的降低;当外电场强度为0.01 V·nm^-1时,Fe₂O₃、Fe₃O₄和α-FeOOH的带隙分别降低了0.36、0.12和0.34 eV;当电场增大至0.1 V·nm^-1时,Fe₂O₃晶体出现击穿现象,Fe—O化学键断裂导致Fe原子的电子沿外电场方向高度离域至相邻Fe原子,而Fe₃O₄和α-FeOOH则仅出现不同...     

Convergence of electric field and electric field gradient versus atomic basis sets in all-siliceous and Mg substituted phillipsites

Electrostatic potential (EP), electric field (EF), and electric field gradient (EFG) values are calculated in periodic models of magnesium substituted phillipsite (MgPHI) zeolite forms using periodic DFT (PDFT) hybrid B3LYP level with fourteen different basis sets. Relative root mean square differences between the EP, EF, or EFG values estimated between different basis sets are evaluated in several spatial domains available for adsorbate molecules in the zeolite. In these areas, the EF increase in MgPHI is evaluated relative to all-siliceous PHI types. The EP is interpreted in terms of framework ionicity for MgPHI and all-siliceous PHI models. Angular Si-O-Si dependence of the EFG asymmetry at (17)O atoms in all-siliceous zeolites is discussed.     

基于密度泛函理论的外电场下c-C4F8的结构及其特性

采用密度泛函理论CAM-B3LYP/DGDZVP2对c-C4F8进行优化计算,得到基态分子结构.在该结构基础上施加线性外电场(0~10.284 V·pm^-1),获得了c-C4F8的几何特性、能量、前线轨道能级、键能和红外光谱数据.结果表明:当电场沿x轴变大时,c-C4F8的点群从D2d变为C1,偶极矩和极化率不断增大,结构稳定性降低;分子总能量和能隙不断减小,且C(4)-F(10)键的键能降低速度最快,最有可能率先在外电场作用下断裂,导致c-C4F8结构和对称性被破坏.同时c-C4F8的绝热电子亲和能单调上升,分子吸收自由电子的能力增强;红外光谱中,吸收峰的个数增加,4个主要吸收峰发生了红移.     

Self-consistent field calculations using two-body density functionals for correlation energy component: II. Small molecules

In part I of this series, self-consistent calculations using two-body density functionals for correlation energy were done and applied to atomic systems, giving very good results. We now apply the same scheme to small molecules. The examples studied include diatomic (H₂, Li₂, B₂, C₂, N₂, O₂, F₂, HLi, HBe, HB, HF, and HCl) as well as polyatomic (H₂O, NH₃, H₂O₂, and O₃) molecules at their ground states. The values reported for equilibrium geometries, atomization energies, vibrational frequencies, and dipole moments are compared with experimental and other theoretical calculations, with good agreement in most cases. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1899–1908, 1998     

A CASSCF/icMRCI study of the electric field gradient in low-lying electronic states of N2/N2

The electric field gradients (EFG’s) at the nucleus are calculated as a function of internuclear separation in the X²Σ_g⁺ and B²Σ_u⁺ electronic states of the nitrogen molecule cation using the internally contracted multireference configuration interaction (icMRCI) method. The EFG’s and potential energy functions (PEF’s) are used to estimate the ¹⁴N nuclear quadrupole coupling constants (NQCC’s) in the two electronic states as functions of vibrational and end-over-end rotational quantum numbers. The dependences of the computed constants on the basis set and reference configuration space are investigated. Since no counterpart for comparison of the calculated NQCC’s exists, the N₂⁺ results are supported by analogous calculations on the X¹Σ_g⁺ and A³Σ_u⁺ states of N₂, for which established data are available. The overall good quality of the icMRCI wave functions is further corroborated by a favorable agreement of spectroscopic constants derived from the corresponding PEF’s and experimental data. Variations of the EFG with internuclear separation are explained in terms of wave function composition, and used for gaining specific insight into the chemical bonding in N₂⁺ and N₂.     

Applicability of density functional theory in reproducing accurate vibrational spectra of surface bound species

The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized‐gradient approximation (GGA), nonlocal correlation, meta‐GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised‐RPBE, vdW‐DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW‐DF and meta‐GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of ?2.62 and ?1.1% for the N? N stretching and Rh? H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh? H and N? N stretching modes from the bulk phonons and by solving one‐ and two‐dimensional Schrödinger equation associated with the Rh? H, Rh? N, and N? N potential energy we calculated the anharmonic correction for N? N and Rh? H stretching modes as ?31 cm^?1 and ?77 cm^?1 at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments. © 2014 Wiley Periodicals, Inc.     

Density functional computations of 99Ru chemical shifts: relativistic effects, influence of the density functional, and study of solvent effects on fac-[Ru(CO)3I3]-

Solvent effects on the 99Ru NMR chemical shift of the complex fac-[Ru(CO)3I3]- are investigated computationally using density functional theory. Further, benchmark calculations of the 99Ru shift for a set of ten Ru complexes have been performed in order to calibrate the computational model and to determine the importance of relativistic effects on the 99Ru nuclear magnetic shielding and on the chemical shift. A computational model for fac-[Ru(CO)3I3]- that includes both explicit solvent molecules and a continuum model is shown to yield the best agreement with experiment. Relativistic corrections are shown to be of minor importance for determining 99Ru chemical shifts. On the other hand, the nature of the density functional is of importance. In agreement with literature data for ligand trends of 99Ru chemical shifts, the chemical shift range for different solvents is also best reproduced by a hybrid functional.     

Effect of charge density gradient on characteristics of electric double layer for salt melts

The equilibrium conditions are analyzed for a spatially inhomogeneous ionic liquid using the density functional theory with allowance made for the second order gradient corrections. Solutions for the distribution of potential and charge density in the electric double layer at the ionic liquid/vapor interface are obtained using a parameterized total density profile normal to the surface. It is shown that taking into account the effects of the charge density gradient in the theory results in the appearance of damped oscillations of the charge density near the surface, while the double layer localized on the surface is reduced.     

Temperature-dependence of time-dependent friction and electric field fluctuations

Molecular-dynamics simulations of a model dipolar system containing two ions have been carried out to study the effect of temperature on the time-dependent friction (ζ(t)) on the solute ions as well as the electric fields in the vicinity of the ions. It is found that with an increase in temperature, (i) the magnitude of ζ (0) increases and (ii) the electric field time correlation functions decay more rapidly at higher temperatures due to faster reorientations and translational diffusion of the molecules. The effects of the size of the system on these properties have also been investigated.     

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange‐correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM‐B3LYP, LC‐BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all‐trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller–Plesset second‐order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM‐B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity‐dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro‐optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field‐induced second harmonic generation all of them, as well as the Hartree–Fock approximation, yield the wrong sign. We have also found that the Pople 6–31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc.     

Determination of the electric field gradient asymmetry from Berry’s phase in NQR of powder samples

An effect of Berry’s phase on the NQR spectrum of the rotating powder sample is described and applied for the determination of the electric field gradient asymmetry. The proposed method involves the analysis of the frequency singularities in the NQR powder patterns of the rotating samples. The Berry’s phases for the eigenstates, associated with an adiabatically changing quadrupole hamiltonian, are calculated for nuclei with a spin I = 3/2 and I = 1 as a function of the asymmetry parameter.     

Effects of an electric field on interaction of aromatic systems

The effect of uniform external electric field on the interactions between small aromatic compounds and an argon atom is investigated using post‐HF (MP2, SCS‐MP2, and CCSD(T)) and density functional (PBE0‐D3, PBE0‐TS, and vdW‐DF2) methods. The electric field effect is quantified by the difference of interaction energy calculated in the presence and absence of the electric field. All the post‐HF methods describe electric field effects accurately although the interaction energy itself is overestimated by MP2. The electric field effect is explained by classical electrostatic models, where the permanent dipole moment from mutual polarization mainly determines its sign. The size of π‐conjugated system does not have significant effect on the electric field dependence. We found out that PBE0‐based methods give reasonable interaction energies and electric field response in every case, while vdW‐DF2 sometimes shows spurious artifact owing to its sensitivity toward the real space electron density. © 2015 Wiley Periodicals, Inc.     

Calculation of multicenter electronic attraction,electric field and electric field gradient integrals of Coulomb potential over integer and noninteger <Emphasis Type="Italic">n</Emphasis> Slater orbitals

With the help of complete orthonormal sets of - ETOs, where = 1,0, – 1, – 2, ... a large number of series expansion formulas for the multicenter electronic attraction (EA), electric field (EF) and electric field gradient (EFG) integrals of integer and noninteger n Slater type orbitals (ISTOs and NISTOs) is established through the overlap integrals with the same screening constants and the new central and noncentral interaction potentials depending on the coordinates of the nuclei of a molecule are introduced. The convergence of the series is tested by calculating concrete cases for arbitrary quantum numbers, screening constants and location of ISTOs and NISTOs.     

Computational studies on aluminum nitride and aluminum phosphide nanotubes: density functional calculations of 27Al electric field gradient tensors

Abstract  

Nuclear quadrupole resonance (NQR) parameters including the nuclear quadrupole coupling constant (C _Q) and asymmetry parameter (η _Q) at the sites of various ²⁷Al nuclei on (6,0) zigzag and (4,4) armchair AlN and AlP nanotubes (NTs) were calculated by using the density functional theory (DFT) method to study the properties of the electronic structures of the nanotubes. Geometry optimizations were carried out at the B3LYP/6-31G* level of theory using the Gaussian 03 suite of programs. The calculated electric field gradient tensors were converted to the nuclear quadrupole resonance parameters, C _Q constant, and η _Q parameter. The quadrupole resonance parameters in each of the structures were divided into four layers with equivalent electric field gradient tensor eigenvalues in each layer. The results show that, in AlN and AlP nanotubes, the Al atoms at the edges of the nanotubes play dominant roles in determining the electronic behavior of the nanotubes and important roles in growth and synthesis processes of the nanotubes. Also the average values of C _Q(²⁷Al) for the AlNNT models were higher in comparison with the AlPNT models, while variations of C _Q(²⁷Al) in AlPNTs were greater in comparison with in AlNNTs.     

外电场对甲醛分子的结构与电子光谱的影响

采用密度泛函理论(DFT)在B3LYP/6-311++G(d,p)基组水平上,计算了不同外加电场(-8.22×10~9~8.22×10~9 V/m)下甲醛分子基态稳定构型、分子键长、电荷分布、能级分布、能隙、红外光谱、拉曼光谱和分子的总能量.在此基础上利用TDDFT/B3LYP/6-311++G(d,p)方法研究了甲醛分子由基态跃迁到前25个激发态的激发能E、谐振强度f、吸收波长λ受外电场的影响.结果表明:随着C=O连线方向外电场的增加,C=O键键长、氢原子电荷、偶极矩和能隙递增;C—H键键长、C,O原子电荷递减,总能量降低.振动频率与红外强度及拉曼强度由于不同振动有不同变化.甲醛分子UV-Vis光谱随外电场的增加,不同的吸收峰发生了不同程度的蓝移或者红移;外电场对甲醛分子的激发能、谐振强度和吸收波长的强度有一定影响,但随电场变化比较复杂.