Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree-Fock and density functional theory

An efficient and accurate analytic gradient method is presented for Hartree-Fock and density functional calculations using multiresolution analysis in multiwavelet bases. The derivative is efficiently computed as an inner product between compressed forms of the density and the differentiated nuclear potential through the Hellmann-Feynman theorem. A smoothed nuclear potential is directly differentiated, and the smoothing parameter required for a given accuracy is empirically determined from calculations on six homonuclear diatomic molecules. The derivatives of N2 molecule are shown using multiresolution calculation for various accuracies with comparison to correlation consistent Gaussian-type basis sets. The optimized geometries of several molecules are presented using Hartree-Fock and density functional theory. A highly precise Hartree-Fock optimization for the H2O molecule produced six digits for the geometric parameters.     

Multiresolution quantum chemistry: basic theory and initial applications

We describe a multiresolution solver for the all-electron local density approximation Kohn-Sham equations for general polyatomic molecules. The resulting solutions are obtained to a user-specified precision and the computational cost of applying all operators scales linearly with the number of parameters. The construction and use of separated forms for operators (here, the Green's functions for the Poisson and bound-state Helmholtz equations) enable practical computation in three and higher dimensions. Initial applications include the alkali-earth atoms down to strontium and the water and benzene molecules.     

On geminals and symplectic bases in quantum chemistry

The construction of a symplectic basis set with >N electrons is exhibited by means of three kinds of units, the first kind geminal, the second kind geminal and the one‐particle operators. The optimization procedure of the variation method is extended to the coefficients in the linear sum of the symplectic bases, the parameters in the geminals, and the orbitals. For practical use, these bases are expanded explicitly as a linear sum of the Slater determinants. For illustration, the LiH molecule, which is taken as an example, is calculated by using some symplectic bases. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the role of the nonlocal Hartree-Fock exchange in ab initio quantum transport: H2 in Pt nanocontacts revisited

We propose a practical way to overcome the ubiquitous problem of the overestimation of the zero-bias and zero-temperature conductance, which is associated with the use of local approximations to the exchange-correlation functional in density-functional theory when applied to quantum transport. This is done through partial substitution of the local exchange term in the functional by the nonlocal Hartree-Fock exchange. As a nontrivial example of this effect we revisit the smallest molecular bridge studied so far: a H(2) molecule placed in between Pt nanocontacts. When applied to this system the value of the conductance diminishes as compared to the local-exchange-only value, which is in close agreement with the results predicted from time-dependent current-density-functional theory. Our results issue a warning message on recent claims of perfect transparency of a H(2) molecule in Pt nanocontacts.     

Basis set limit Hartree-Fock and density functional theory response property evaluation by multiresolution multiwavelet basis

We describe the evaluation of response properties using multiresolution multiwavelet (MRMW) basis sets. The algorithm uses direct projection of the perturbed density operator onto the zeroth order density operator on the real space spanned by the MRMW basis set and is applied for evaluating the polarizability of small molecules using Hartree-Fock and Kohn-Sham density functional theory. The computed polarizabilities can be considered to be converged to effectively complete space within the requested precision. The efficiency of the method against the ordinary Gaussian basis computation is discussed.     

主成分分析方法在核酸碱基量子化学计算数据处理中的应用

由于碱基在核酸中的重要性 ,多年来一直有关于碱基的理论计算报道[1～ 7] 。本文将化学计量学中的主成分分析方法[8] 用来分析五种碱基 :腺嘌呤 (Ａ)、鸟嘌呤 (Ｇ)、胞嘧啶 (Ｃ)、尿嘧啶 (Ｕ)和胸腺嘧啶 (Ｔ)计算结果的几何参数 ,以期取得有用的结构信息。1　方法通过ＡＣＤ ＣｈｅｍＳｋｅｔｃｈ 3 .5 [9] 的三维优化 (分子力学方法ＣＨＡＲＭＭ力场 )获得碱基的起始几何结构 ,其原子编号见图 1。所有的计算均采用Ｇａｕｓｓｉａｎ 94程序[10 ] 在ＩＢＭ ＰＣ兼容机上完成。首先 ,对 5种碱基作了 6种半经验方法 (ＡＭ1、ＰＭ3、ＭＮＤＯ、…     

Implementation of divide-and-conquer method including Hartree-Fock exchange interaction

The divide-and-conquer (DC) method, which is one of the linear-scaling methods avoiding explicit diagonalization of the Fock matrix, has been applied mainly to pure density functional theory (DFT) or semiempirical molecular orbital calculations so far. The present study applies the DC method to such calculations including the Hartree-Fock (HF) exchange terms as the HF and hybrid HF/DFT. Reliability of the DC-HF and DC-hybrid HF/DFT is found to be strongly dependent on the cut-off radius, which defines the localization region in the DC formalism. This dependence on the cut-off radius is assessed from various points of view: that is, total energy, energy components, local energies, and density of states. Additionally, to accelerate the self-consistent field convergence in DC calculations, a new convergence technique is proposed.     

Haptic quantum chemistry

We present an implementation designed to physically experience quantum mechanical forces between reactants in chemical reactions. This allows one to screen the profile of potential energy surfaces for the study of reaction mechanisms. For this, we have developed a interface between the user and a virtual laboratory by means of a force‐feedback haptic device. Potential energy surfaces of chemical reactions can be explored efficiently by rendering in the haptic device the gradients calculated with first‐principles methods. The underlying potential energy surface is accurately fitted on the fly by the interpolating moving least‐squares (IMLS) scheme to a grid of quantum chemical electronic energies (and geometric gradients). In addition, we introduce a new IMLS‐based method to locate minimum‐energy paths between two points on a potential energy surface. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

Lie algebras in quantum chemistry: Symmetrized orbitals

The application of Lie algebras in quantum chemistry is considered. Particular attention is devoted to their application to high symmetry problems especially where icosahedral symmetry prevails. A general programme for implementing the theory of Lie algebras in the analysis of symmetry problems is outlined.     

A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

The Heisenberg exchange coupling parameter J (H = −2JS_i · S_j) characterises the isotropic magnetic interaction between unpaired electrons, and it is one of the most important spin Hamiltonian parameters of multi-spin open shell systems. The J value is related to the energy difference between high-spin and low-spin states, and thus computing the energies of individual spin states are necessary to obtain the J values from quantum chemical calculations. Here, we propose a quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing the J value directly, without calculating the energies of individual spin states. The BxB algorithm is composed of the quantum simulations of the time evolution of a broken-symmetry wave function under the Hamiltonian with an additional term jS², the wave function overlap estimation with the SWAP test, and Bayesian optimisation of the parameter j. Numerical quantum circuit simulations for H₂ under a covalent bond dissociation, C, O, Si, NH, OH⁺, CH₂, NF, O₂, and triple bond dissociated N₂ molecule revealed that the BxB can compute the J value within 1 kcal mol⁻¹ of errors with less computational costs than conventional quantum phase estimation-based approaches.

A quantum algorithm “Bayesian exchange coupling parameter calculator with broken-symmetry wave function (BxB)” enables us to calculate Heisenberg exchange coupling parameter J without inspecting total energies of individual spin states, within 1 kcal mol⁻¹ of energy tolerance.     

Central moments in quantum chemistry

We define central moments of operators on finite‐dimensional vector spaces and study some of their basic aspects. Central moments may be viewed as generalizations of the dispersion of a Hermitian operator. We show how eigenvalues may be represented by central moments, and how central moments may be used to obtain Krylov subspace approximations for operators on inner product spaces. We show that central‐moments approximations are compatible with the concepts of size‐consistency in quantum chemistry, and we use this to suggest a foundation for central‐moments approximations in Coupled Cluster theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Hartree-Fock exchange fitting basis sets for H to Rn

For elements H to Rn (except Lanthanides), a series of auxiliary basis sets fitting exchange and also Coulomb potentials in Hartree–Fock treatments (RI-JK-HF) is presented. A large set of small molecules representing nearly each element in all its common oxidation states was used to assess the quality of these auxiliary bases. For orbital basis sets of triple zeta valence and quadruple zeta valence quality, errors in total energies arising from the RI-JK approximation are below ∼1 meV per atom in molecular compounds. Accuracy of RI-JK-approximated HF wave functions is sufficient for being used for post-HF treatments like Møller–Plesset perturbation theory, MP2. Compared to nonapproximated treatments, RI-JK-HF leads to large computational savings for quadruple zeta valence orbital bases and, in case of small to midsize systems, to significant savings for triple zeta valence bases. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008     

4-(二乙氨基)水杨醛席夫碱的合成、光谱性质和热稳定性及量化计算

合成了两种酰腙类席夫碱4-(二乙氨基)水杨醛噻吩-2-甲酰腙(H_2L~1)和4-(二乙氨基)水杨醛异烟酰腙一水合物(H_2L~2·H_2O),利用元素分析、IR光谱、UV光谱和FL光谱及热重分析对其进行了表征.实验结果表明,两种化合物在可见光区均可产生荧光,最大发射峰波长分别为504和525nm.热分解温度分别为254和278℃.用Gaussian 09程序包对H_2L~1进行了量化计算,结果表明,该化合物的水杨基和酰腙基是金属离子很好的配位点.     

The multiconfiguration time-dependent Hartree-Fock method for quantum chemical calculations

We apply the multiconfiguration time-dependent Hartree-Fock method to electronic structure calculations and show that quantum chemical information can be obtained with this explicitly time-dependent approach. Different equations of motion are discussed, as well as the numerical cost. The two-electron integrals are calculated using a natural potential expansion, of which we describe the convergence behavior in detail.     

Spin-unrestricted calculations in quantum chemistry

The unrestricted complete active space self-consistent field (UCASSCF ) function is defined, and a proof that a UCASSCF eigenfunction of the spin operator S ² is a CASSCF function is given. The spin-contamination for an unrestricted Hartree–Fock (UHF ) function is evaluated by using Araki angle operators, and the UHF function is then projected on the restricted open-shell Hartree–Fock (ROHF ) space. The present analysis has deep consequences since it implies that the only non-spin-contaminated UHF functions are the ROHF functions. This is illustrated in a calculation of the spin density of He. © 1993 John Wiley & Sons, Inc.