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The propagation of general electronic quantum states provides information of the interaction of molecular systems with external driving fields. These can also offer understandings regarding non-adiabatic quantum phenomena. Well established methods focus mainly on propagating a quantum system that is initially described exclusively by the ground state wavefunction. In this work, we expand a previously developed size-extensive formalism within coupled cluster theory, called second response theory, so it propagates quantum systems that are initially described by a general linear combination of different states, which can include the ground state, and show how with a special set of time-dependent cluster operators such propagations are performed. Our theory shows strong consistency with numerically exact results for the determination of quantum mechanical observables, probabilities, and coherences. We discuss unperturbed non-stationary states within second response theory and their ability to predict matrix elements that agree with those found in linear and quadratic response theories. This work also discusses an approximate regularized methodology to treat systems with potential instabilities in their ground-state cluster amplitudes, and compares such approximations with respect to reference results from standard unitary theory., Comment: 27 pages, 7 figures

Two-dimensional (2D) materials are being explored as a novel multiferroic platform. One of the most studied magnetoelectric multiferroic 2D materials are antiferromagnetically-coupled (AFM) CrI$_3$ bilayers. Neglecting magnetism, those bilayers possess a crystalline point of inversion, which is only removed by the antiparallel spin configuration among its two constituent monolayers. The resultant intrinsic electric dipole on those bilayers has a magnitude no larger than 0.04 pC/m, it points out-of-plane, and it reverts direction when the--Ising-like--cromium spins are flipped (toward opposite layers {\em versus} away from opposite layers). The combined presence of antiferromagnetism and a weak intrinsic electric dipole makes this material a two-dimensional magnetoelectric multiferroic. Here, we remove the crystalline center of inversion of the bilayer by a relative $60^{\circ}$ rotation of its constituent monolayers. This process {\em enhances} the out-of-plane intrinsic electric dipole tenfold with respect to its magnitude in the non-rotated AFM bilayer and also creates an even stronger and switchable in-plane intrinsic electric dipole. The ability to create a three-dimensional electric dipole is important, because it enhances the magnetoelectric coupling on this experimentally accessible 2D material, which is explicitly calculated here as well., Comment: Accepted at PRB on May 1, 2023

Quantum information science is driving progress in a vast number of scientific and technological areas that cover molecular spectroscopy and matter-light interactions in general. In these fields, the ability to generate quantum mechanically-entangled photons is opening avenues to explore the interaction of molecules with quantum light. This work considers an alternative way of correlating photons by including energy superpositions. We study how the multichromatic quantum superposition, or color superposition of photon-pair states, influences the optical properties of organic chromophores. This work uses electronic structure calculations based on time-dependent density functional theory, and a simple modification of the standard entangled two-photon absorption theory. Our calculations show that it is possible to substantially modify the optical absorption cross section of molecules, where constructive and destructive interferences are computed. The quantum interference effects are more pronounced than the constructive ones. These quantum effects, or related ones, could be observed in quantum spectroscopic experiments where qudit photon states are generated., Comment: 6 Figures

Density functional theory (DFT) provides convenient electronic structure methods for the study of molecular systems and materials. Regular Kohn-Sham DFT calculations rely on unitary transformations to determine the ground-state electronic density, ground state energy, and related properties. However, for dissociation of molecular systems into open-shell fragments, due to the self-interaction error present in a large number of density functional approximations, the self-consistent procedure based on the this type of transformation gives rise to the well-known charge delocalization problem. To avoid this issue, we showed previously that the cluster operator of coupled-cluster theory can be utilized within the context of DFT to solve in an alternative and approximate fashion the ground-state self-consistent problem. This work further examines the application of the singles cluster operator to molecular ground state calculations. Two approximations are derived and explored: i), A linearized scheme of the quadratic equation used to determine the cluster amplitudes, and, ii), the effect of carrying the calculations in a non-self-consistent field fashion. These approaches are found to be capable of improving the energy and density of the system and are quite stable in either case. The theoretical framework discussed in this work could be used to describe, with an added flexibility, quantum systems that display challenging features and require expanded theoretical methods., Comment: 17 pages, 5 figures, 1 table, submitted to ChemPhysChem

Traditional ferroelectrics undergo thermally-induced phase transitions whereby their structural symmetry increases. The associated higher-symmetry structure is dubbed {\em paraelectric}. Ferroelectric transition metal dichalcogenide bilayers have been recently shown to become paraelectric, but not much has been said of the atomistic configuration of such a phase. As discovered through numerical calculations that include molecular dynamics here, their paraelectricity can only be ascribed to a time average of ferroelectric phases with opposing intrinsic polarizations, whose switching requires macroscopically large areas to slip in unison., Comment: Accepted in Nano Letters as of 9/28/2022

Time-dependent response theories are foundational to the development of algorithms that determine quantum properties of electronic excited states of molecules and periodic systems. They are employed in wave-function, density-functional, and semiempirical methods, and are applied in an incremental order: linear, quadratic, cubic, etc. Linear response theory is known to produce electronic transitions from ground to excited state, and vice versa. In this work, a linear-response approach, within the context of the coupled cluster formalism, is developed to offer transition elements between different excited states (including permanent elements), and related properties. Our formalism, second linear response theory, is consistent with quadratic response theory, and can serve as an alternative to develop and study excited-state theoretical methods, including pathways for algorithmic acceleration. This work also formulates an extension of our theory for general propagations under non-linear external perturbations, where the observables are given by linked expressions which can predict their time-evolution under arbitrary initial states and could serve as a means of constructing general state propagators. A connection with the physics of wavefunction theory is developed as well, in which dynamical cluster operator amplitudes are related to wavefunction linear superposition coefficients., Comment: 44 pages, 6 figures, submitted to Physical Review A

X-ray standing wave (XSW) excited photoelectron emission was used to measure the site-specific valence band (VB) for 1/2 monolayer (ML) Pt grown on a SrTiO3 (001) surface. The XSW induced modulations in the core level (CL) and VB photoemission from the surface and substrate atoms were monitored for three hkl substrate Bragg reflections. The XSW CL analysis shows the Pt to have an fcc-like cube-on-cube epitaxy with the substrate. The XSW VB information compares well to a density functional theory calculated projected density of states from the surface and substrate atoms. Overall, this work represents a novel method for determining the contribution to the density of states by valence electrons from specific atomic surface sites.

The accuracy of charge-transfer excitation energies, solvatochromic shifts and other environmental effects calculated via various density embedding techniques depend critically on the approximations employed for the non-additive non-interacting kinetic energy functional, $T_{\scriptscriptstyle\rm s}^{\scriptscriptstyle\rm nad}[n]$. Approximating this functional remains an important challenge in electronic structure theory. To assist in the development and testing of approximations for $T_{\scriptscriptstyle\rm s}^{\scriptscriptstyle\rm nad}[n]$, we derive two virial relations for fragments in molecules. These establish separate connections between the non-additive kinetic energies of the non-interacting and interacting systems of electrons, and quantities such as the electron-nuclear attraction forces, the partition (or embedding) energy and potential, and the Kohn-Sham potentials of the system and its parts. We numerically verify both relations on diatomic molecules.

Conceiving a molecule as composed of smaller molecular fragments, or subunits, is one of the pillars of the chemical and physical sciences, and leads to productive methods in quantum chemistry. Using a fragmentation scheme, efficient algorithms can be proposed to address problems in the description of chemical bond formation and breaking. We present a formally exact time-dependent density-functional theory for the electronic dynamics of molecular fragments with variable number of electrons. This new formalism is an extension of previous work [Phys. Rev. Lett. {\bf 111}, 023001 (2013)]. We also introduce a stable density-inversion method that is applicable to time-dependent and ground-state density-functional theory, and their extensions, including those discussed in this work., Comment: 9 pages, 3 figures

Density functional approximations to the exchange-correlation energy of Kohn-Sham theory, such as the local density approximation and generalized gradient approximations, lack the well-known integer discontinuity, a feature that is critical to describe molecular dissociation correctly. Moreover, standard approximations to the exchange-correlation energy also fail to yield the correct linear dependence of the ground-state energy on the number of electrons when this is a non-integer number obtained from the grand canonical ensemble statistics. We present a formal framework to restore the integer discontinuity of any density functional approximation. Our formalism derives from a formula for the exact energy functional and a new constrained search functional that recovers the linear dependence of the energy on the number of electrons., Comment: 5 pages, 2 figures

Using the Runge-Gross theorem that establishes the foundation of Time-dependent Density Functional Theory (TDDFT) we prove that for a given electronic Hamiltonian, choice of initial state, and choice of fragmentation, there is a unique single-particle potential (dubbed time-dependent partition potential) which, when added to each of the pre-selected fragment potentials, forces the fragment densities to evolve in such a way that their sum equals the exact molecular density at all times. This uniqueness theorem suggests new ways of computing time-dependent properties of electronic systems via fragment-TDDFT calculations. We derive a formally exact relationship between the partition potential and the total density, and illustrate our approach on a simple model system for binary fragmentation in a laser field., Comment: 5 pages, 2 figures

The Runge-Gross [E. Runge, and E. K. U. Gross, Phys. Rev. Lett., 52, 997 (1984)] action functional of time-dependent density-functional theory leads to a well-known causality paradox, i.e., a perturbation of the electronic density in the future affects the response of the system in the present. This paradox is known to be caused by an inconsistent application of the Dirac-Frenkel variational principle. In view of the recent solutions to this problem, the action functional employed by Runge and Gross in their formulation of time-dependent density functional theory is analyzed in the context of the Keldysh contour technique. The time-dependent electronic density, as well as the concept of causality, are extended to the contour. We derive a variational equation that obeys causality and relates the exchange-correlation potential with its kernel, and the functional derivative of the exchange-correlation action functional with respect to the density. It is shown that the adiabatic local-density approximation is a consistent solution of this equation and that the time-dependent optimized potential method can also be derived from it. The formalism presented here can be used to find new approximations methods to the exchange-correlation potential and avoid the causality dilemma., Comment: 12 pages

In this work, analytical solutions were derived (for any methanol oxidation reaction order) for the profiles of methanol concentration and proton current density by assuming diffusion mass transport mechanism, Tafel kinetics, and fast proton transport in the anodic catalyst layer of a direct methanol fuel cell. An expression for the Thiele modulus that allows to express the anodic overpotential as a function of the cell current, and kinetic and mass transfer parameters was obtained. For high cell current densities, it was found that the Thiele modulus ($\phi^2$) varies quadratically with cell current density; yielding a simple correlation between anodic overpotential and cell current density. Analytical solutions were derived for the profiles of both local methanol concentration in the catalyst layer and local anodic current density in the catalyst layer. Under the assumptions of the model presented here, in general, the local methanol concentration in the catalyst layer cannot be expressed as an explicit function of the position in the layer. In spite of this, the equations presented here for the anodic overpotential allow the derivation of new semi-empirical equations., Comment: 18 pages, 6 figures, submitted to Electrochimica Acta

A simple model to fit experimental data of adsorption of gases and vapours on microporous adsorbents (type I isotherms) is proposed. The main assumption is that the adsorbate phase can be divided into identical and non-interacting effective subsystems. This gives rise to a simple multiparametric isotherm based on the grand canonical ensemble statistics, whose functional form is a ratio of two polynomial functions. The parameters are interpreted as effective equilibrium constants. A simplified isotherm that reduces the number of adjustable parameters with respect to the general isotherm is also proposed. We show how to use these isotherms to fit the adsorption data in such way that the parameters have statistical significance. Due to their high accuracy, both isotherms can be used to estimate thermodynamic properties like isosteric and differential heats of adsorption. A simple method is presented for systems that show an apparent variation in the coverage limit with temperature. This method avoids overparametrization and improves fitting deviations. Finally, several applications to fitting data, taken from literature, of adsorption of some gases on activated carbon, molecular sieving carbon, silica gel, and pillared clays are presented., Comment: 21 pages, 6 figures, 2 tables. Submitted to Fluid Phase Equilibria