Visualizing molecular wavefunctions using Monte Carlo methods

Using explicitly correlated wavefunctions and variational Monte Carlo we calculate the electron density, the electron density difference, the intracule density, the extracule density, two forms of the kinetic energy density, the Laplacian of the electron density, the Laplacian of the intracule density, and the Laplacian of the extracule density on a dense grid of points for the ground state of the hydrogen molecule at three internuclear distances (0.6, 1.4, 8.0). With these values we construct a contour plot of each function and describe how it can be used to visualize the distribution of electrons in this molecule. We also examine the influence of electron correlation on each expectation value by calculating each function with a Hartree–Fock wavefunction and then comparing these values with our explicitly correlated values. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

A note on atomic density

In atomic systems, electron density has a simple finite expansion in spherical harmonics times radial factors. The difficulties in the calculation of some radial factors are illustrated in the low‐lying states of the carbon atom. Single‐particle methods such as Hartree–Fock and approximate density functional theory cannot ensure the correct expansion of the density in spherical harmonics. Wave‐function methods are appropriate but, as some expansion terms are entirely due to correlation, these methods only will give correct results for high‐quality variational functions. Using full‐configuration integration (CI), all the terms predicted by the theory appear and are not negligible but the convergence of the term due to correlation toward its correct value is uncertain even for very large CI spaces. © 2012 Wiley Periodicals, Inc.     

Sublattice Method in Chemical Bond Theory for Dolomite Crystals

The distribution of valence and difference densities in crystalline CaMg(CO₃)₂ was calculated within the framework of the local density functional theory. It is shown that the terminal maxima of difference density located beyond the oxygen atom nuclei have different values due to the polarizing influence of the cations.     

On the inner and outer radial density functions

Starting from the two-electron radial density D ₂(r ₁,r ₂), a generalized partitioning of the one-electron radial density function D(r) into two component densities D _a (r) and D _b (r) is discussed for many-electron systems. The literature partitioning (Koga and Matsuyama Theor Chem Acc 115:59, 2006) of D(r) into the inner D _<(r) and outer D _>(r) radial densities is shown to minimize the average variance of the two component density functions D _a (r) and D _b (r). It is also found that the average radial separation halved, , constitutes a lower bound to the standard deviation σ of D(r).     

INFLUENCE OF PLASMA DENSITY ON NUCLEATED DENSITY OF DIAMOND

The predeposition method for mereasing CH_4 concentration ininitial stage of diamond synthesis by plasma chemical vapor deposition.isused to enhance nucleated density of diamond films.The plasma parametersare diagnosed in situ using the Langmuir double probe.The relation betweenplasma ion density and nucleated densitv of diamond is revealed Increasingplasma ion density results in enhancement of nucleated density of diamondobviously     

LiPN<Subscript>2</Subscript> and NaPN<Subscript>2</Subscript> crystals: Structural features and chemical bonding

The band structure spectra, densities of states, and valence and difference densities of LiPN₂ and NaPN₂ crystals were obtained by DFT self-consistent calculations using the nonlocal pseudopotentials and the localized pseudoorbital basis. Crystal-chemical analysis of these compounds shows that they occupy an intermediate position between the ideal structures of β-cristobalite and chalcopyrite, which manifests itself in the peculiarities of the electronic structure and chemical bonding. The valence band consists of three allowed subbands and differs radically from the typical valence band of chalcopyrite crystals in both subband structure and contributions of the s, p, and d atomic orbitals to the crystal orbitals.     

Density matrices from position and momentum densities

Summary One-electron density matrices, which are representable in single-centers-orbital basis sets, have been investigated with respect to their reconstruction from densities. The maximum allowed dimension for reconstruction from a combination of position & momentum density dependent properties is only slightly bigger than the dimension in the case of position (or momentum) densities only. Since for a given one-particle basis of dimensionM, the number of one-matrix elements which can be determined is also of orderM only, while the total number of one-matrix elements is of orderM ², it is in general necessary to introduce severe constraints and restrictions. The accuracy demands on the data and algorithms increase exponentially for linearly increasing size of basis set.     

An open‐source framework for analyzing N‐electron dynamics. II. Hybrid density functional theory/configuration interaction methodology

In this contribution, we extend our framework for analyzing and visualizing correlated many‐electron dynamics to non‐variational, highly scalable electronic structure method. Specifically, an explicitly time‐dependent electronic wave packet is written as a linear combination of N‐electron wave functions at the configuration interaction singles (CIS) level, which are obtained from a reference time‐dependent density functional theory (TDDFT) calculation. The procedure is implemented in the open‐source Python program det CI@ORBKIT, which extends the capabilities of our recently published post‐processing toolbox (Hermann et al., J. Comput. Chem. 2016, 37, 1511). From the output of standard quantum chemistry packages using atom‐centered Gaussian‐type basis functions, the framework exploits the multideterminental structure of the hybrid TDDFT/CIS wave packet to compute fundamental one‐electron quantities such as difference electronic densities, transient electronic flux densities, and transition dipole moments. The hybrid scheme is benchmarked against wave function data for the laser‐driven state selective excitation in LiH. It is shown that all features of the electron dynamics are in good quantitative agreement with the higher‐level method provided a judicious choice of functional is made. Broadband excitation of a medium‐sized organic chromophore further demonstrates the scalability of the method. In addition, the time‐dependent flux densities unravel the mechanistic details of the simulated charge migration process at a glance. © 2017 Wiley Periodicals, Inc.     

Moment expansion of the linear density‐density response function

We present a low rank moment expansion of the linear density‐density response function. The general interacting (fully nonlocal) density‐density response function is calculated by means of its spectral decomposition via an iterative Lanczos diagonalization technique within linear density functional perturbation theory. We derive a unitary transformation in the space of the eigenfunctions yielding subspaces with well‐defined moments. This transformation generates the irreducible representations of the density‐density response function with respect to rotations within SO(3). This allows to separate the contributions to the electronic response density from different multipole moments of the perturbation. Our representation maximally condenses the physically relevant information of the density‐density response function required for intermolecular interactions, yielding a considerable reduction in dimensionality. We illustrate the performance and accuracy of our scheme by computing the electronic response density of a water molecule to a complex interaction potential. © 2015 Wiley Periodicals, Inc.     

Exact and exclusive electron localization indices within QTAIM atomic basins

Novel measures of electron (de)localization within the Quantum Theory of Atoms in Molecules (QTAIM) atomic basins are presented which, unlike orthodox localization indices (LIs), are fully exclusive and can be easily visualized. This work shows that QTAIM‐defined LIs describe a portion of interatomic delocalized electrons; hence, the chemical/physical interpretation of orthodox LIs is misleading. Using the recently introduced Fragment, Atomic, Localized, Delocalized, and Interatomic (FALDI) density decomposition technique we derive two novel sets of LIs and delocalization indices (DIs), by accounting for the overlap between localized and delocalized density functions. The FALDI‐based LIs and DIs perfectly recover chemically expected core and bonded electron count. Usefulness of new (de)localization indices and their 3D representations were demonstrated on a number of examples, including formamide and benzene. We therefore expect that the scheme reported in this work will provide a valuable stepping stone between classical conceptual chemistry and quantum chemical topology. © 2018 Wiley Periodicals, Inc.     

Analytical formulas for the magnetic field produced by a spin or a paramagnetic current density in the case of Gaussian basis functions

We present a derivation of simple formulas for the evaluation at any point of space of the magnetic field produced by a spin or a paramagnetic orbital current when Cartesian Gaussian basis functions are used, as is often the case in quantum chemistry. These formulas can be useful to plot the magnetic field vector density obtained from ab initio calculations or from a density operator fitted on experimental data. The magnetic field density is the observable probed in polarized neutron diffraction (PND) experiment, for it is, in fact, with this quantity that the neutron spins interact and not with the spin or magnetization density. The formulas make extensive use of the confluent hypergeometric function. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 11–15, 2001     

密度泛函理论方法研究双核铜化合物的磁性和自旋密度分布

Magnetic coupling constants J between Cu ions and spin density map for a binuclear complex Cu₂(2,2′-bpy)₂(4,4′-bpy)₂L₂ have been calculated by the combination of the broken symmetry approach with the spin project method under the DFT framework and the effect of nonorthogonality between magnetic α and β orbitals in the broken symmetry solution. The result indicates that using SV/SVP basis sets in the calculation of Gaussian 98 is much better than using LanL2DZ pseudo-potential function in above system. It is interesting that calculated J value is quite near to the experimental value in the studies of magnetic susceptibility.     

Theoretical study of atoms by the electronic kinetic energy density and stress tensor density

The electronic structure of atoms in the first, second, and third periods were analyzed using the electronic kinetic energy density and stress tensor density, which are local quantities motivated by quantum field theoretic consideration, specifically the rigged quantum electrodynamics. The zero surfaces of the electronic kinetic energy density, which are called as the electronic interfaces, of the atoms were computed. It was found that their sizes exhibited clear periodicity and were comparable to the conventional atomic and ionic radii. The electronic stress tensor density and its divergence, tension density, of the atoms, were also computed and how their electronic structures were characterized by them was discussed. © 2016 Wiley Periodicals, Inc.     

石墨烯条带的电子结构与性质:电场及长度效应

在密度泛函理论(DFT)和含时密度泛函理论(TDDFT)的基础上对宽度上含有8个zigzag链的石墨烯条带(8-ZGNR)的基态和激发态的性质进行了理论研究,着重考察了条带长度及电场的影响.B3LYP杂化泛函的计算结果显示:在基态上,8-ZGNR的最低能量态并不具有磁性,随着长度的增加,才会显示出反铁磁的性质.静电场的加入使8-ZGNR显示出反铁磁性和半金属性.在激发态上,诱导电子会随着外激光脉冲的变化而发生移动和变化,但是相比而言,α自旋电子更容易被激发而产生较明显的诱导电子密度,而β自旋电子则更容易脱离外激光场的控制而产生非绝热现象.     

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).     

Air microwave-induced plasma: Relation between ion density and atomic oxygen density

Electron temperature and ion density are measured in an air microwave-induced plasma (2450 MHz) by means of a floating double probe. A 'cinetic scheme for ion formation and decay is set up, and a relationship between atomic oxygen and ion densities is obtained. From this relationship an order-of-magnitude of atomic oxygen concentration in the discharge is derived and compared with results obtained by optical actinometry in another work.     

Constraint-based analysis of a physics-guided kinetic energy density expansion

An approach guided by physical consistency in determining the general forms of D-dimensional kinetic energy density functionals (KEDF) has been demonstrated previously, producing an expansion which contains the majority of the known one-point KEDF forms. It has also been shown that any noninteracting KEDF must necessarily have a homogeneity degree of 2 in coordinate scaling, and that the ratio of the collective KED to electron density must approach the ionization energy as $r\to \infty$. This article demonstrates that the scaling condition is already satisfied in the general expansion despite not being conceived with the scaling as a constraint, and that the second condition places a restriction on the expansion terms of the KED. The discussion is extended as well for some known KEDs for comparison.     

DFT in a nutshell

The purpose of this short essay is to introduce students and other newcomers to the basic ideas and uses of modern electronic density functional theory, including what kinds of approximations are in current use, and how well they work (or not). The complete newcomer should find it orients them well, while even longtime users and aficionados might find something new outside their area. Important questions varying in difficulty and effort are posed in the text, and are answered in the Supporting Information. © 2012 Wiley Periodicals, Inc.