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Register a new userOn The Inclusion of One Double Within CIS and TD-DFT
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We present an improved approach for generating a set of optimized frontier orbitals (HOMO and LUMO) that minimizes the energy of one double configuration. We further benchmark the effect of including such a double within a CIS or TD-DFT configuration interaction Hamiltonian for a set of test cases. We find that, although we cannot achieve quantitative accuracy, the algorithm is quite robust and routinely delivers an enormous qualitative improvement to standard single-reference electronic structure calculations.
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Using a set of oscillator strengths and excited-state dipole moments of near full configuration interaction (FCI) quality determined for small compounds, we benchmark the performances of several single-reference wave function methods (CC2, CCSD, CC3, CCSDT, ADC(2), and ADC(3/2)) and time-dependent density-functional theory (TD-DFT) with various functionals (B3LYP, PBE0, M06-2X, CAM-B3LYP, and $omega$B97X-D). We consider the impact of various gauges (length, velocity, and mixed) and formalisms: equation of motion (EOM) emph{vs} linear response (LR), relaxed emph{vs} unrelaxed orbitals, etc. Beyond the expected accuracy improvements and a neat decrease of formalism sensitivy when using higher-order wave function methods, the present contribution shows that, for both ADC(2) and CC2, the choice of gauge impacts more significantly the magnitude of the oscillator strengths than the choice of formalism, and that CCSD yields a notable improvement on this transition property as compared to CC2. For the excited-state dipole moments, switching on orbital relaxation appreciably improves the accuracy of both ADC(2) and CC2, but has a rather small effect at the CCSD level. Going from ground to excited states, the typical errors on dipole moments for a given method tend to roughly triple. Interestingly, the ADC(3/2) oscillator strengths and dipoles are significantly more accurate than their ADC(2) counterparts, whereas the two models do deliver rather similar absolute errors for transition energies. Concerning TD-DFT, one finds: i) a rather negligible impact of the gauge on oscillator strengths for all tested functionals (except for M06-2X); ii) deviations of ca.~0.10 D on ground-state dipoles for all functionals; iii) the better overall performance of CAM-B3LYP for the two considered excited-state properties.
This paper elaborates the integral transformation technique of [K. Pachucki, W. Cencek, and J. Komasa, J. Chem. Phys. 122, 184101 (2005)] and uses it for the case of the non-relativistic kinetic and Coulomb potential energy operators, as well as for the relativistic mass-velocity and Darwin terms. The techniques are tested for the ground electronic state of the helium atom and new results are reported for the ground electronic state of the H$_3^+$ molecular ion near its equilibrium structure.
Hamiltonian and Schrodinger evolution equations on finite-dimensional projective space are analyzed in detail. Hartree-Fock (HF) manifold is introduced as a submanifold of many electron projective space of states. Evolution equations, exact and linearized, on this manifold are studied. Comparison of matrices of linearized Schrodinger equations on many electron projective space and on the corresponding HF manifold reveals the appearance in the HF case a constraining matrix that involves matrix elements of many-electron Hamiltonian between HF state and double excited determinants. Character of dependence of transition energies on the matrix elements of constraining matrix is established by means of perturbation analysis. It is demonstrated that success of time-dependent HF theory in calculation of transition energies is mainly due to the wrong behavior of these energies as functions of matrix elements of constraining matrix as compared with the exact transition energies
In their famous paper Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of $N$ interacting electrons, albeit limited at the time by certain troubling representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays however the realization that Nature is not always so nearsighted has driven us up Perdews Jacobs ladder to find increasingly nonlocal density/wavefunction hybrid functionals. Time-dependent (TD-) DFT is a younger development which allows DFT concepts to be used to describe the temporal evolution of the density in the presence of a perturbing field. Linear response (LR) theory then allows spectra and other information about excited states to be extracted from TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in practical calculations and this has historically been done using the TD-DFT adiabatic approximation (AA) which is to TD-DFT very much like what the local density approximation (LDA) is to conventional ground-state DFT. While some of the recent advances in TD-DFT focus on what can be done within the AA, others explore ways around the AA. After giving an overview of DFT, TD-DFT, and LR-TD-DFT, this article will focus on many-body corrections to LR-TD-DFT as one way to building hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.
Defining and modeling the relation of inclusion between continuous belief function may be considered as an important operation in order to study their behaviors. Within this paper we will propose and present two forms of inclusion: The strict and the partial one. In order to develop this relation, we will study the case of consonant belief function. To do so, we will simulate normal distributions allowing us to model and analyze these relations. Based on that, we will determine the parameters influencing and characterizing the two forms of inclusion.
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