For the Hirshfeld-I atom-in-molecule model, associated single-atom energies and interaction energies at the Hartree-Fock level are determined efficiently in one-electron Hilbert space. In contrast to most other approaches, the energy terms are fully consistent with the partitioning of the underlying one-electron density matrix. Starting from the Hirshfeld-I atom-in-molecule model for the electron density, the molecular one-electron density matrix is partitioned with a previously introduced double-atom scheme [Vanfleteren D. et al., J Chem Phys 2010, 132, 164111]. Single-atom density matrices are constructed from the atomic and bond contributions of the double-atom scheme. Since the Hartree-Fock energy can be expressed solely in terms of the one-electron density matrix, the partitioning of the latter over the atoms in the molecule leads naturally to a corresponding partitioning of the Hartree-Fock energy. When the size of the molecule or the molecular basis set does not grow too large, the method shows considerable computational advantages compared to other approaches that require cumbersome numerical integration of the molecular energy integrals weighted by atomic weight functions.
A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method…
In this work, a method is described to extend the iterative Hirshfeld-I method, generally used for molecules, to periodic systems. The implementation makes use of precalculated pseudo-potential based charge density distributions, and it is shown that high quality results are obtained for both molecules and solids, such as ceria, diamond, and graphite. The use of such grids makes the implementation independent of the solid state or quantum chemical code used for studying the system. The extension described here allows for easy calculation of atomic charges and charge transfer in periodic and bu…
The issues raised in the comment by T.A. Manz are addressed through the presentation of calculated atomic charges for NaF, NaCl, MgO, SrTiO$_3$ and La$_2$Ce$_2$O$_7$, using our previously presented method for calculating Hirshfeld-I charges in Solids [J. Comput. Chem.. doi: 10.1002/jcc.23088]. It is shown that the use of pseudo-valence charges is sufficient to retrieve the full all-electron Hirshfeld-I charges to good accuracy. Furthermore, we present timing results of different systems, containing up to over $200$ atoms, underlining the relatively low cost for large systems. A number of theor…
An efficient computational algorithm to implement a local operator approach to partitioning electronic energy in general molecular systems is presented. This approach, which rigorously defines the electronic energy on any subsystem within a molecule, gives a precise meaning to the subsystem ground and excited electronic energies, which is crucial for investigating electronic energy transfer from first principles. We apply the technique to the $9-$(($1-$naphthyl)$-$methyl)-anthracene (A1N) molecule by partitioning A1N into anthracenyl and CH$_2-$naphthyl groups as subsystems, and examine their …
Using a Deep Neuronal Network model (DNN) trained on the large ANI-1 data set of small organic molecules, we propose a transferable density-free many-body dispersion model (DNN-MBD). The DNN strategy bypasses the explicit Hirshfeld partitioning of the Kohn-Sham electron density required by MBD models to obtain the atom-in-molecules volumes used by the Tkatchenko-Scheffler polarizability rescaling. The resulting DNN-MBD model is trained with minimal basis iterative Stockholder atomic volumes and, coupled to Density Functional Theory (DFT), exhibits comparable (if not greater) accuracy to other …
A double-index atomic partitioning of the molecular first-order density matrix is proposed. Contributions diagonal in the atomic indices correspond to atomic density matrices, whereas off-diagonal contributions carry information about the bonds. The resulting matrices have good localization properties, in contrast to single-index atomic partitioning schemes of the molecular density matrix. It is shown that the electron density assigned to individual atoms, when derived from the density matrix partitioning, can be made con- sistent with well-known partitions of the electron density over AIM bas…
Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using the distributed nature of the electron cloud and atomic multipoles. In this work, an electrostatic force field is defined through a concise approximation of the electron density, for which the Coulomb interaction is trivially evaluated. This approximate "pro-density" is expanded in a minimal basis of atom-centered s-type Slater density functions, whose paramet…
The formation, properties and lifetime of secondary organic aerosols in the atmosphere are largely determined by gas-particle partitioning coefficients of the participating organic vapours. Since these coefficients are often difficult to measure or compute, we developed a machine learning (ML) model to predict them given molecular structure as input. Our data-driven approach is based on the dataset by Wang et al. (Atmos. Chem. Phys., 17, 7529 (2017)), who computed the partitioning coefficients and saturation vapour pressures of 3414 atmospheric oxidation products from the master chemical mecha…
Accurate treatment of the long-range electron correlation energy, including van der Waals (vdW) or dispersion interactions, is essential for describing the structure, dynamics, and function of a wide variety of systems. Among the most accurate models for including dispersion into density functional theory (DFT) is the range-separated many-body dispersion (MBD) method [A. Ambrossetti et al., J. Chem. Phys. 140, 18A508 (2014)], in which the correlation energy is modeled at short-range by a semi-local density functional and at long-range by a model system of coupled quantum harmonic oscillators. …
The localized operator partitioning method [Y. Khan and P. Brumer, J. Chem. Phys. 137, 194112 (2012)] rigorously defines the electronic energy on any subsystem within a molecule and gives a precise meaning to the subsystem ground and excited electronic energies, which is crucial for investigating electronic energy transfer from first principles. However, an efficient implementation of this approach has been hindered by complicated one- and two-electron integrals arising in its formulation. Using a resolution of the identity in the definition of partitioning we reformulate the method in a compu…
Net atomic charges (NACs) are widely used in all chemical sciences to concisely summarize key information about the partitioning of electrons among atoms in materials. Although widely used, there is currently no atomic population analysis method suitable for being used as a default method in quantum chemistry programs. To address this challenge, we introduce a new atoms-in-materials method with the following nine properties: (1) exactly one electron distribution is assigned to each atom, (2) core electrons are assigned to the correct host atom, (3) NACs are formally independent of the basis se…
Background: Guanine quadruplexes (GQs) play vital roles in many cellular processes and are of much interest as drug targets. In contrast to the availability of many structural studies, there is still limited knowledge on GQ folding. Scope of review: We review recent molecular dynamics (MD) simulation studies of the folding of GQs, with an emphasis paid to the human telomeric DNA GQ. We explain the basic principles and limitations of all types of MD methods used to study unfolding and folding in a way accessible to non-specialists. We discuss the potential role of G-hairpin, G-triplex and alter…
We introduce a system-independent method to derive effective atomic C$_6$ coefficients and polarizabilities in molecules and materials purely from charge population analysis. This enables the use of dispersion-correction schemes in electronic structure calculations without recourse to electron-density partitioning schemes and expands their applicability to semi-empirical methods and tight-binding Hamiltonians. We show that the accuracy of our method is en par with established electron-density partitioning based approaches in describing intermolecular C$_6$ coefficients as well as dispersion en…
We discuss the partitioning of a quantum system by subsystem separation through unitary block-diagonalization (SSUB) applied to a Fock operator. Our separation can be formulated in a very general way. It can be applied to very different partitionings ranging from those driven by features in the molecular structure (such as a solute surrounded by solvent molecules) to those that aim at an orbital separation (such as core-valence separation). Our framework embraces recent developments of Manby and Miller as well as older ones of Huzinaga and Cantu. Projector-based embedding is simplified and acc…
Verstraelen et al. (J. Chem. Theory Comput. 12 (2016) 3894-3912) recently introduced a new method for partitioning the electron density of a material into constituent atoms. Their approach falls within the class of atomic population analysis methods called stockholder charge partitioning methods in which a material electron distribution is divided into overlapping atoms. The Minimal Basis Iterative Stockholder (MBIS) method proposed by Verstraelen et al. composes the pro-atom density as a sum of exponential functions, where the number of exponential functions equals that element's row in the P…
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an increase in the size of system treated comes an increase in complexity, making it challenging to analyze such large systems and determine the cause of emergent properties. To address this issue, in this paper we present a systematic complexity reduction methodology which can break down large systems into their constituent fragments, and quantify inter-fragment …
The quantum theory of atoms in molecules, QTAIM, is employed to identify AIM and quantify their interactions through the partitioning of molecule into atomic basins in the real space and it is confined only to the purely electronic systems composed of electrons as quantum particles and the nuclei as clamped point charges. The extended version of the QTAIM, called the multi-component QTAIM, MC-QTAIM, bypasses this border and makes it possible to identify AIM and quantify their interactions in systems composed of multiple quantum particles that electrons may or may not be one of their components…
Chemical bonding concepts emerge naturally from maximally entangled atomic orbitals
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）
The sensitivity of computed DFT (Density Functional Theory) molecular properties (including energetics, geometries, vibrational frequencies, and infrared intensities) to the radial and angular numerical integration grid meshes, as well as to the partitioning scheme, is discussed for a number of molecules using the Gaussian 98 program system. Problems with typical production grid sizes are particularly acute for third-row transition metal systems, but may still result in qualitatively incorrect results for a molecule as simple as CCH. Practical recommendations are made with respect to grid choi…
A procedure for calculation of rotation-vibration states of medium sized molecules is presented. It combines the advantages of variational calculations and perturbation theory. The vibrational problem is solved by diagonalizing a Hamiltonian matrix, which is partitioned into two sub-blocks. The first, smaller sub-block includes matrix elements with the largest contribution to the energy levels targeted in the calculations. The second, larger sub-block comprises those basis states which have little effect on these energy levels. Numerical perturbation theory, implemented as a Jacobi rotation, i…
By leveraging the fundamental doctrine of The Quantum Theory of Atoms in Molecules---the partitioning of the electron charge density ($ρ$) into regions bounded by surfaces of zero flux---we map the gradient field of $ρ$ onto a 2D space called the gradient bundle condensed charge density ($\cal{P}$). The topology of $\cal{P}$ appears to correlate with regions of chemical significance in $ρ$. The bond wedge is defined as the image in $ρ$ of the basin of attraction in $\cal{P}$, analogous to the Bader atom, which is the basin of attraction in $ρ$. A bond bundle is defined as the union of bond wed…
The eigenvectors of the electronic stress tensor have been identified as useful for the prediction of chemical reactivity because they determine the most preferred directions to move the bonds that correspond to a qualitative change in the molecular electronic structure. A new 3-D vector based interpretation of the chemical bond that we refer to as the bond-path framework set $\mathbb{B} = \{p,q,r\}$ provides a version of the quantum theory of atoms in molecules (QTAIM) beyond the minimum definition for bonding that is particularly suitable for understanding changes in molecular electronic str…
Quantum--Mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the Frozen Density Emb…
At room temperature, the quantum contribution to the kinetic energy of a water molecule exceeds the classical contribution by an order of magnitude. The quantum kinetic energy (QKE) of a water molecule is modulated by its local chemical environment and leads to uneven partitioning of isotopes between different phases in thermal equilibrium, which would not occur if the nuclei behaved classically. In this work, we use ab initio path integral simulations to show that QKEs of the water molecules and the equilibrium isotope fractionation ratios of the oxygen and hydrogen isotopes are sensitive pro…
A way to account for correlations between the chemically active (valence) and innermore (core) electrons in the framework of the generalized relativistic effective core potential (GRECP) method is suggested. The "correlated" GRECP's (CGRECP's) are generated for the Hg and Pb atoms. Only correlations for the external twelve and four electrons of them, correspondingly, should be treated explicitly in the subsequent calculations with these CGRECP's whereas the innermore electrons are excluded from the calculations. Results of atomic calculations with the correlated and earlier GRECP versions are …
We estimate polarizabilities of atoms in molecules without electron density, using a Voronoi tesselation approach instead of conventional density partitioning schemes. The resulting atomic dispersion coefficients are calculated, as well as many-body dispersion effects on intermolecular potential energies. We also estimate contributions from multipole electrostatics and compare them to dispersion. We assess the performance of the resulting intermolecular interaction model from dispersion and electrostatics for more than 1,300 neutral and charged, small organic molecular dimers. Applications to …
