Kohn-Sham Density Matrix and the Kernel Energy MethodSCI北大核心CSCD

The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the purposes of calculation.The results from the kernels are summed according to an expression characteristic of KEM to obtain the full molecule energy.A generalization of the kernel expansion to density matrices provides the full molecule density matrix and orbitals.In this study,the kernel expansion for the density matrix is examined in the context of density functional theory(DFT) Kohn-Sham(KS) calculations.A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined,and is then converted into a normalizedprojector by using the Clinton algorithm.Such normalized projectors are factorizable into linear combination of atomic orbitals(LCAO) matrices that deliver full-molecule Kohn-Sham molecular orbitals in the atomic orbital basis.Both straightforward KEM energies and energies from a normalized,idempotent density matrix obtained from a density matrix kernel expansion to which the Clinton algorithm has been applied are compared to reference energies obtained from calculations on the full system without any kernel expansion.Calculations were performed both for a simple proof-of-concept system consisting of three atoms in a linear configuration and for a water cluster consisting of twelve water molecules.In the case of the proof-of-concept system,calculations were performed using the STO-3 G and6-31 G(d,p) bases over a range of atomic separations,some very far from equilibrium.The water cluster was calculated in the 6-31 G(d,p) basis at an equilibrium geometry.The normalized projector density energies are more accurate than the straightforward KEM energy results in nearly all cases.In the case of the water cluster,the energy of the normalized projector is approximately four times more accurate than the straightforward KEM energy result.The KS density matrices of this study are applicable to quantum crystallography.     

Quantum crystallography: A perspective

Extraction of the complete quantum mechanics from X‐ray scattering data is the ultimate goal of quantum crystallography. This article delivers a perspective for that possibility. It is desirable to have a method for the conversion of X‐ray diffraction data into an electron density that reflects the antisymmetry of an N‐electron wave function. A formalism for this was developed early on for the determination of a constrained idempotent one‐body density matrix. The formalism ensures pure‐state N‐representability in the single determinant sense. Applications to crystals show that quantum mechanical density matrices of large molecules can be extracted from X‐ray scattering data by implementing a fragmentation method termed the kernel energy method (KEM). It is shown how KEM can be used within the context of quantum crystallography to derive quantum mechanical properties of biological molecules (with low data‐to‐parameters ratio). © 2017 Wiley Periodicals, Inc.     

A generalized higher order kernel energy approximation method

We present a general mathematical model that can be used to improve almost all fragment‐based methods for ab initio calculation of total molecular energy. Fragment‐based methods of computing total molecular energy mathematically decompose a molecule into smaller fragments, quantum‐mechanically compute the energies of single and multiple fragments, and then combine the computed fragment energies in some particular way to compute the total molecular energy. Because the kernel energy method (KEM) is a fragment‐based method that has been used with much success on many biological molecules, our model is presented in the context of the KEM in particular. In this generalized model, the total energy is not based on sums of all possible double‐, triple‐, and quadruple‐kernel interactions, but on the interactions of precisely those combinations of kernels that are connected in the mathematical graph that represents the fragmented molecule. This makes it possible to estimate total molecular energy with high accuracy and no superfluous computation and greatly extends the utility of the KEM and other fragment‐based methods. We demonstrate the practicality and effectiveness of our model by presenting how it has been used on the yeast initiator tRNA molecule, ytRN (1YFG in the Protein Data Bank), with kernel computations using the Hartree‐Fock equations with a limited basis of Gaussian STO‐3G type. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Kernel energy method: Basis functions and quantum methods

The kernel energy method (KEM) has been illustrated with peptides and has been shown to reduce the computational difficulty associated with obtaining ab initio quality quantum chemistry results for large biological compounds. In a recent paper, the method was illustrated by application to 15 different peptides, ranging in size from 4 to 19 amino acid residues, and was found to deliver accurate Hartree–Fock (HF) molecular energies within the model, using Slater‐type orbital (STO)‐3G basis functions. A question arises concerning whether the results obtained from the use of KEM are wholly dependent on the STO‐3G basis functions that were employed, because of their relative simplicity, in the first applications. In the present work, it is shown that the accuracy of KEM does not depend on a particular choice of basis functions. This is done by calculating the ground‐state energy of a representative peptide, ADPGV7B, containing seven amino acid residues, using seven different commonly employed basis function sets, ranging in size from small to medium to large. It is shown that the accuracy of the KEM does not vary in any systematic way with the size or mathematical completeness of the basis set used, and good accuracy is maintained over the entire variety of basis sets that have been tested. Both approximate HF and density functional theory (DFT) calculations are made. We conclude that the accuracy inherent in the KEM is not dependent on a particular choice of basis functions. The first application, to 15 different peptides mentioned above, employed only HF calculations. A second question that arises is whether the results obtained with the use of KEM will be accurate only within the HF approximation. Therefore, in the present work we also study whether KEM is applicable across a variety of quantum computational methods, characterized by differing levels of accuracy. The peptide, Zaib4, containing 74 atoms, was used to calculate its energy at seven different levels of accuracy. These include the semi‐empirical methods, AM1 and PM5, a DFT B3LYP model, and ab initio HF, MP2, CID, and CCSD calculations. KEM was found to be widely applicable across the spectrum of quantum methods tested. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Fast quantum crystallography

Typical contemporary X-ray crystallography delivers the geometries and, at best, the electron densities of molecules or periodic systems in the crystalline phase. Energies, electron momentum densities, and information relating to the pair density such as electron delocalization measures—all crucial to chemistry—are simply missed. Quantum crystallography (QCr) is an emerging line of research aimed at filling this gap by solving the crystallographic problem under the constraints of quantum mechanics. In this way, not only geometries and electron densities become experimentally accessible but also the entire panoply of quantum mechanical properties that are in the output of any quantum chemical software package. However, QCr remains limited to smaller systems (small molecules or small unit cells) due to the exponential bottleneck that plagues quantum mechanical calculations. When combined with a fragmentation technique, termed the “kernel energy method (KEM)”, QCr's reach to larger molecules is extended considerably to almost “any size”, that is, systems of up to many hundreds of thousands of atoms. KEM has made this doable with any chemical model and is capable of providing the entire quantum mechanics of large molecular systems. The smallness of the R-factor adjudicates the accuracy of the quantum mechanics extracted from the crystallography.     

A benchmark quantum Monte Carlo study of the ground state chromium dimer

We report calculations of the ground state energy and binding curve of the chromium dimer using the variational and diffusion quantum Monte Carlo (VMC and DMC) methods. We examined various single‐determinant and multideterminant wavefunctions multiplied by a Jastrow factor as a trial/guiding wavefunction for VMC/DMC. The molecular orbitals in the single determinants were calculated using restricted or unrestricted Hartree–Fock or density functional theory (DFT) calculations where five commonly used local (SVWN5), semilocal (PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The multideterminant expansions were obtained from the generalized valence bond and (truncated) unrestricted configuration interaction with single and double excitations (UCISD) methods. We also examined a UCISD wavefunction in which UCISD expansions were added to the UB3LYP single‐determinant reference, and their coefficients were optimized at the VMC level. In addition to the wavefunction dependence, the effects of pseudopotentials and backflow transformation were also investigated. The UB3LYP single‐determinant and multideterminant wavefunctions were found to give the variationally best DMC energies within the framework of single‐determinant and multideterminants, respectively, though both the DMC energies were higher than twice the DMC atomic energy. Some of the VMC binding curves show a flat or quite shallow well bottom, which gets recovered deeper by DMC. All the DMC binding curves have a minimum indicating a bound state, but the unrestricted ones overestimate the equilibrium bond length. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Quantum chemistry beyond Born–Oppenheimer approximation on a quantum computer: A simulated phase estimation study

We present an efficient quantum algorithm for beyond‐Born–Oppenheimer molecular energy computations. Our approach combines the quantum full configuration interaction method with the nuclear orbital plus molecular orbital method. We give the details of the algorithm and demonstrate its performance by classical simulations. Two isotopomers of the hydrogen molecule (H₂, HT) were chosen as representative examples and calculations of the lowest rotationless vibrational transition energies were simulated. © 2016 Wiley Periodicals, Inc.     

Necessary conditions for the N‐representability of pair distribution functions

A necessary condition for the N‐representability of the electron pair density proposed by one of the authors (E. R. D.) is generalized. This shows a link between this necessary condition and other, more widely known, N‐representability conditions for the second‐order density matrix. The extension to spin‐resolved electron pair densities is considered, as is the extension to higher‐order distribution functions. Although quantum mechanical systems are our primary focus, the results are also applicable to classical systems, where they reduce to an inequality originally derived by Garrod and Percus. As a simple application, bounds to the average angle between an electron pair are derived. It is shown that computational methods based on variational minimization of the energy with respect to the electron pair density can give extremely poor results unless robust N‐representability constraints are considered. For reference, constraints for the N‐representability of the pair density are summarized. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Polymorphism of methyl 4‐amino‐3‐phenylisothiazole‐5‐carboxylate: an experimental and theoretical study

Being a close analogue of amflutizole, methyl 4‐amino‐3‐phenylisothiazole‐5‐carboxylate (C₁₁H₁₀N₂O₂S) was assumed to be capable of forming polymorphic structures. Noncentrosymmetric and centrosymmetric polymorphs have been obtained by crystallization from a series of more volatile solvents and from denser tetrachloromethane, respectively. Identical conformations of the molecule are found in both structures. The two polymorphs differ mainly in the intermolecular interactions formed by the amino group and in the type of stacking interactions between the π‐systems. The most effective method for revealing packing motifs in structures with intermolecular interactions of different types (hydrogen bonding, stacking, dispersion, etc.) is to study the pairwise interaction energies using quantum chemical calculations. Molecules form a column as the primary basic structural motif due to stacking interactions in both polymorphic structures under study. The character of a column (straight or zigzag) is determined by the orientations of the stacked molecules (in a `head‐to‐head' or `head‐to‐tail' manner). Columns bound by intermolecular N—H…O and N—H…N hydrogen bonds form a double column as the main structural motif in the noncentrosymmetric structure. Double columns in the noncentrosymmetric structure and columns in the centrosymmetric structure interact strongly within the ab crystallographic plane, forming a layer as a secondary basic structural motif. The noncentrosymmetric structure has a lower density and a lower (by 0.59 kJ mol^?1) lattice energy, calculated using periodic calculations, compared to the centrosymmetric structure.     

Quantum effects on the stability of the He5I2 van der Waals conformers

We present 15-dimensional quantum multiconfiguration time-dependent Hartree calculations of the vibrational levels of the He₅I₂ van der Waals (vdW) complex employing an ab initio-based potential energy surface (PES). The energies and spatial features of such bound structures are analyzed, providing predictions on the structures and relative stabilities of its three lowest isomers. We found that the most stable isomer corresponds to all five He atoms encircling the I₂ molecule, indicating that in this case the anharmonic quantum effects do not stabilize the isomers involving a He atom in a linear configuration as reported previously for the smaller He_NI₂ systems. Such finding provides information on the overall structuring of the finite-size-solvent systems, highlighting the intriguing interplay between weak intermolecular interactions and quantum effects. © 2019 Wiley Periodicals, Inc.     

Water Catalysis of the Reaction of Methanol with OH Radical in the Atmosphere is Negligible

Faced with the contradictory results of two recent experimental studies [Jara‐Toro et al., Angew. Chem. Int. Ed. 2017 , 56, 2166 and Chao et al., Angew. Chem. Int. Ed. 2019 , 58, 5013] of the possible catalytic effect of water vapor on CH₃OH + OH reaction, we report calculations that corroborate the conclusion made by Chao et al. and extend the rate constant evaluation down to 200 K. The rate constants of the CH₃OH + OH reaction catalyzed by a water molecule are computed as functions of temperature and relative humidity using high‐level electronic structure and kinetics calculations. The Wuhan–Minnesota Scaling (WMS) method is used to provide accurate energetics to benchmark a density functional for direct dynamics. Both high‐frequency and low‐frequency anharmonicities are included. Variational and tunneling effects are treated by canonical variational transition state theory with multidimensional small‐curvature tunneling. And, most significantly, we include multistructural effects in the rate constant calculations. Our calculations show that the catalytic effect of water vapor is not observable at 200–400 K.     

Density matrix approach to orbital relaxation dynamics in ionization

Dynamical response of electrons to a hole generated during ionization is formulated in time domain with the density matrix equations in the time‐dependent unrestricted Hartree–Fock approximation. Time evolutions of orbital energies and electron‐density distributions are computed for K‐shell and M‐shell ionizations of a Na atom by taking into account nonlinear coupling of density matrices beyond linear response. When the hole is generated so slowly that the adiabatic theorem is satisfied, the simulation eventually converges to the state of a fully relaxed Na⁺ ion. A rapid generation of a K‐shell hole (within about 1 fs) leads to a breakdown of the adiabatic theorem, triggering a collective oscillation of the electrons with the period of sub‐femtoseconds. The shake‐up effect associated with strong orbital relaxation in inner‐shell ionization is manifested as a mixing of occupied and unoccupied states in the density matrix.     

WKB and MAF quantization rules for spatially confined quantum mechanical systems

A formalism is developed to obtain the energy eigenvalues of spatially confined quantum mechanical systems in the framework of the usual Wentzel–Kramers–Brillouin (WKB) and modified airy function (MAF) methods. To illustrate the working rule, the techniques are applied to three different cases, viz. the confined one‐dimensional harmonic and quartic oscillators and a boxed‐in charged particle subject to an external electric field. The energies thus obtained are compared with those from shifted 1/N expansion, variational, and other methods, as well as the available exact numerical results. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 497–504, 1999     

Bound states of oscillators in infinite and finite domains: A semiclassical study

By involving the uncertainty product along with a semiclassical requirement for observables, a simple variational scheme is employed to extract major features of bound states of systems in (?∞,∞) and the same of systems confined in (?L,L). Special attention is paid to perturbative studies on the asymptotic behavior of energies for oscillators in infinite domains and dependence of energy spectra of oscillators in finite domains on various system parameters. A corrected form of the virial theorem is obtained in the latter case. The governing equations for quantum isothermal and adiabatic processes, derived recently, are also shown to be modified for general confined oscillator systems and closed‐form expressions are found. These results are useful in dealing with the quantum Carnot cycles. Advantages of the present route over other semiclassical strategies are stressed. Pilot calculations demonstrate nicely the efficacy of the endeavor under various situations. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Quantum Monte Carlo calculations of bond dissociation energies for some nitro and amino molecules

Bond dissociation energies (BDEs) for some nitro or amino contained prototypical molecules in energetic materials are computed by fixed‐node diffusion quantum Monte Carlo method. The nodes are determined from a Slater determinant calculated within density functional theory at the B3LYP/6‐311G** level. The possible errors, the nodal error, and the cancellation of nodal errors in calculating BDE are discussed, and the accuracy is compared with other available ab initio computations and experimental results. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Si‐Doped B12N12 Nanocage as an Adsorbent for Dissociation of N2O to N2 Molecule

Adsorption of N₂O molecule by using density functional theory calculations at the B3LYP/6–31G* level onto pristine and Si‐doped B₁₂N₁₂ nanocage in terms of energetic, geometric, and electronic properties was investigated. The results of calculations showed that the N₂O molecule is physically adsorbed on the pristine and Si‐doped B₁₂N₁₂ (Si_N) models, releasing energies in the range of –1.13 to –2.02 kcal mol⁻¹. It was found that the electronic properties of the models have not changed significantly upon the N₂O adsorption. On the other hand, the adsorption energy of N₂O on the Si‐doped B₁₂N₁₂ (Si_B model) was about –67.20 kcal mol⁻¹and the natural bond orbital charge of 0.58|e| is transferred from the nanocage to the N₂O molecule. In the configuration, the O atom of N₂O molecule is bonded to the Si atom of the nanocage, so that an N₂ molecule escapes from the wall of the nanocage. The results showed that the Si_B model can be an adsorbent for dissociation of the N₂O molecule.     

Laser effects in excitons in a quantum wire

We investigate the effects of laser field intensity over the ground state binding energy of light and heavy hole excitons confined in GaAs/Ga_1?xAl_x As cylindrical quantum wire. We have applied the variational method using 1s‐hydrogenic wave functions, in the framework of the single band effective mass approximation with the spatial dielectric function. The polaronic effects are included in the calculation to compute the exciton binding energy as a function of the wire radius for different field of laser intensity. The valence‐band anisotropy is included in our theoretical model by using different hole masses in different spatial directions. The dressed laser donor binding energies are calculated and compared with the results of binding energy of excitons. The results show that (i) the binding energy is found to increase with decrease with the wire radius, and decrease with increase with the value of laser field amplitude, (ii) the heavy‐hole exciton in a cylindrical quantum wire is more strongly bound than the light‐hole exciton, (iii) the values of ground state binding energy for the laser field amplitude α₀ = 10 Å resemble with the values of heavy hole exciton binding energy, and (iv) the binding energy of the impurity for the narrow well wire is more sensitive to the laser field amplitude. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical Approach Towards the Understanding of Asymmetric Additions of Dialkylzinc to Enals and Iminals Catalysed by [2.2]Paracyclophane‐Based N,O‐Ligands

The 1,2‐ and 1,4‐asymmetric additions of dialkylzinc reagents (ZnMe₂ and ZnEt₂) to cinnamaldehyde and N‐formylbenzylimine catalysed by [2.2]paracyclophane‐based N,O‐ligands were studied with quantum chemical methods. High level LPNO‐CEPA/1 (local pair natural orbital coupled electron pair approximation 1) calculations were performed to obtain reliable reaction barriers and binding energies. The calculations supported the experimentally observed selectivities. In the reaction, the alkyl transfer takes place on a binuclear zinc complex. Regioselectivity can be traced back to changes in π‐conjugation. Because the less conjugated N‐formylbenzylimine is more flexible, it is better suited for 1,4‐additions. Moreover, bulky ligands were shown to be important for stereoselectivity. The reason is that the tricyclic motif present in the transition states is sterically less hindered in the anti conformation. Based on the LPNO‐CEPA/1 data, a set of popular theoretical methods are validated. Although it was possible to set up a procedure to obtain the stereoselectivities with computationally less demanding methods, this was not possible for the regioselectivity of the reactions.