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Related Concept Videos

State Space Representation01:27

State Space Representation

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
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Reduced Mass Coordinates: Isolated Two-body Problem01:12

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In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
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Linear Approximation in Time Domain01:21

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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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Transfer Function to State Space01:23

Transfer Function to State Space

839
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
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Molecular Orbital Theory II03:51

Molecular Orbital Theory II

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Molecular Orbital Energy Diagrams
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Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Multistate Complete-Active-Space Second-Order Perturbation Theory Based on Density Matrix Renormalization Group

Takeshi Yanai1,2, Masaaki Saitow2, Xiao-Gen Xiong3

  • 1Department of Theoretical and Computational Molecular Science, Institute for Molecular Science , Okazaki, 444-8585 Aichi Japan.

Journal of Chemical Theory and Computation
|September 8, 2017
PubMed
Summary

We developed a new computational method, DMRG-cu(4)-XMS-CASPT2, combining density matrix renormalization group (DMRG) with multireference second-order perturbation theory (CASPT2) for large active spaces. This approach accurately models complex chemical reactions like photoisomerization.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Accurate modeling of electronic structure is crucial for understanding chemical reactions.
  • Large active spaces in molecules pose significant computational challenges for traditional quantum chemistry methods.
  • Multireference methods are necessary for systems with static and dynamic electron correlation.

Purpose of the Study:

  • To develop a computationally efficient and accurate method for multistate calculations involving large active spaces.
  • To extend the capabilities of coupled-cluster and perturbation theory methods to handle complex electronic structures.
  • To enable the study of photochemical processes like isomerization in organic molecules.

Main Methods:

  • Development of multistate multireference second-order perturbation theory (CASPT2) utilizing density matrix renormalization group (DMRG) for multiroot references.
  • Expansion of first-order wave functions into an internally contracted (IC) basis within the single-state single-reference (SS-SR) scheme.
  • Incorporation of extended multistate (XMS) treatment and approximate elimination of fourth-order reduced density matrices (RDMs) via cumulant reconstruction.

Main Results:

  • The proposed DMRG-cu(4)-XMS-CASPT2 method efficiently handles large active spaces by using DMRG references.
  • The SS-SR scheme proves feasible for DMRG references, avoiding the need for fourth-order transition RDMs and exhibiting linear scaling with the number of states.
  • The method successfully computed multistate potential energy curves for the photoisomerization of diarylethene derivatives.

Conclusions:

  • The developed DMRG-cu(4)-XMS-CASPT2 method offers a powerful and feasible approach for studying complex photochemical reactions.
  • This theoretical advancement provides a more accurate and computationally tractable way to investigate systems with large active spaces.
  • The study demonstrates the broad applicability of the method in computational chemistry and materials science.