Ensemble DFT Approach to Excited States of Strongly Correlated Molecular Systems

2015 ◽  
pp. 97-124 ◽  
Author(s):  
Michael Filatov
Keyword(s):  
Excited States ◽  
Strongly Correlated ◽  
Molecular Systems

scholarly journals Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

Atoms ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 70 ◽  
Author(s):  
Jen-Hao Ou ◽  
Yew Kam Ho
Keyword(s):  
Excited States ◽  
Shannon Entropy ◽  
Electronic Structures ◽  
Tsallis Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Electron Delocalization ◽  
Information Theoretic ◽  
Molecular Systems ◽  
Information Energy

Knowledge of the electronic structures of atomic and molecular systems deepens our understanding of the desired system. In particular, several information-theoretic quantities, such as Shannon entropy, have been applied to quantify the extent of electron delocalization for the ground state of various systems. To explore excited states, we calculated Shannon entropy and two of its one-parameter generalizations, Rényi entropy of order α and Tsallis entropy of order α , and Onicescu Information Energy of order α for four low-lying singly excited states (1s2s 1 S e , 1s2s 3 S e , 1s3s 1 S e , and 1s3s 3 S e states) of helium. This paper compares the behavior of these three quantities of order 0.5 to 9 for the ground and four excited states. We found that, generally, a higher excited state had a larger Rényi entropy, larger Tsallis entropy, and smaller Onicescu information energy. However, this trend was not definite and the singlet–triplet reversal occurred for Rényi entropy, Tsallis entropy and Onicescu information energy at a certain range of order α .

RELATION BETWEEN QUANTUM AND GEOMETRIC DIMENSIONALITIES IN MOLECULAR NONLINEAR OPTICS: BEYOND THE TWO-LEVEL MODEL FOR ANISOTROPIC SYSTEMS

1996 ◽  
Vol 05 (04) ◽  
pp. 671-693 ◽  
Author(s):  
S. BRASSELET ◽  
J. ZYSS
Keyword(s):  
Excited States ◽  
Second Harmonic ◽  
Three Dimensional ◽  
Wavelength Dependence ◽  
Quantum Model ◽  
Substitution Pattern ◽  
Molecular Systems ◽  
Level Model ◽  
Anisotropic Systems ◽  
Two Level Model

The nonlinear optical susceptibilities of two- or three-dimensional molecular systems exhibit variable anisotropic features depending on their structure and substitution pattern. We show that appropriate geometric (e.g. tensorial) considerations combined with an n-level quantum model (n≥3) are able to account for such nonlinear anisotropy as rigorously defined in an invariant spherical formalism by extension of classical linear anisotropy. We call on two kinds of experiments to investigate these properties: firstly, variation of the incident polarization (VIP) in harmonic light scattering (HLS) experiments is being performed to sort out individual tensorial components of the quadratic hyperpolarizability β tensor; secondly, wavelength dependence studies in coherent second harmonic generation (SHG) from poled thin film media are shown at a preliminary stage to be able to designate those excited states responsible for the nonlinear anisotropy.

scholarly journals Fast electronic structure methods for strongly correlated molecular systems

2005 ◽  
Vol 16 ◽  
pp. 233-242 ◽  
Author(s):  
Martin Head-Gordon ◽  
Gregory J O Beran ◽  
Alex Sodt ◽  
Yousung Jung
Keyword(s):  
Electronic Structure ◽  
Strongly Correlated ◽  
Molecular Systems ◽  
Electronic Structure Methods ◽  
Fast Electronic

scholarly journals Equation-of-Motion Coupled-Cluster Cumulant Green’s Function for Excited States and X-Ray Spectra

2021 ◽  
Vol 9 ◽  
Author(s):  
F. D. Vila ◽  
J. J. Kas ◽  
J. J. Rehr ◽  
K. Kowalski ◽  
B. Peng
Keyword(s):  
Green’S Function ◽  
Spectral Function ◽  
Excited States ◽  
Green's Function ◽  
Coupled Cluster ◽  
X Ray ◽  
Molecular Systems ◽  
Self Energy ◽  
The Core ◽  
Non Linear

Green’s function methods provide a robust, general framework within many-body theory for treating electron correlation in both excited states and x-ray spectra. Conventional methods using the Dyson equation or the cumulant expansion are typically based on the GW self-energy approximation. In order to extend this approximation in molecular systems, a non-perturbative real-time coupled-cluster cumulant Green’s function approach has been introduced, where the cumulant is obtained as the solution to a system of coupled first order, non-linear differential equations. This approach naturally includes non-linear corrections to conventional cumulant Green’s function techniques where the cumulant is linear in the GW self-energy. The method yields the spectral function for the core Green’s function, which is directly related to the x-ray photoemission spectra (XPS) of molecular systems. The approach also yields very good results for binding energies and satellite excitations. The x-ray absorption spectrum (XAS) is then calculated using a convolution of the core spectral function and an effective, one-body XAS. Here this approach is extended to include the full coupled-cluster-singles (CCS) core Green’s function by including the complete form of the non-linear contributions to the cumulant as well as all single, double, and triple cluster excitations in the CC amplitude equations. This approach naturally builds in orthogonality and shake-up effects analogous to those in the Mahan-Noizeres-de Dominicis edge singularity corrections that enhance the XAS near the edge. The method is illustrated for the XPS and XAS of NH3.

scholarly journals Chebyshev matrix product states with canonical orthogonalization for spectral functions of strongly correlated systems

2021 ◽  
Author(s):  
Tong Jiang ◽  
Jiajun Ren ◽  
Zhigang Shuai
Keyword(s):  
Excited States ◽  
Strongly Correlated Systems ◽  
Time Dependent ◽  
Matrix Product ◽  
Strongly Correlated ◽  
Effective Hamiltonian ◽  
Spectral Functions ◽  
Correlated Systems ◽  
Matrix Product States ◽  
First Time

We propose a method to calculate the spectral functions of strongly correlated systems by Chebyshev expansion in the framework of matrix product states coupled with canonical orthogonalization (coCheMPS). The canonical orthogonalization can improve the accuracy and efficiency significantly because the orthogonalized Chebyshev vectors can provide an ideal basis for constructing the effective Hamiltonian in which the exact recurrence relation can be retained. In addition, not only the spectral function but also the excited states and eigen energies can be directly calculated, which is usually impossible for other MPS-based methods such as time-dependent formalism or correction vector. The remarkable accuracy and efficiency of coCheMPS over other methods are demonstrated by calculating the spectral functions of spin chain and ab initio hydrogen chain. We demonstrate for the first time that Chebyshev MPS can be used in quantum chemistry. We also caution the application for electron-phonon system with densed density of states.

Sign in / Sign up

Export Citation Format

Share Document