Related Experiment Video
Updated: May 5, 2026
12:11
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
9.2K
Communication: A reduced-space algorithm for the solution of the complex linear response equations used in coupled
Joanna Kauczor1, Patrick Norman, Ove Christiansen
1Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden.
The Journal of Chemical Physics
|December 11, 2013
Summary
A new reduced-space algorithm efficiently solves complex linear response equations for coupled cluster methods. This advancement is crucial for developing damped coupled cluster response methods, especially in resonant frequency regions.
Area of Science:
- Computational quantum chemistry
- Theoretical chemistry
Background:
- Accurate computation of molecular properties requires advanced quantum chemical methods.
- Linear response theory is essential for understanding molecular interactions with external fields.
Purpose of the Study:
- To develop a novel reduced-space algorithm for solving complex linear response equations.
- To enable the computation of the complex linear response function for various coupled cluster methods.
Main Methods:
- Implementation of a reduced-space algorithm.
- Application to coupled cluster singles (CCS), coupled cluster singles and iterative approximate doubles (CC2), and coupled cluster singles and doubles (CCSD) response calculations.
Main Results:
- The algorithm efficiently solves the complex (damped) linear response equations.
- The developed solver is a key component for damped coupled cluster response methods.
Conclusions:
- The reduced-space algorithm facilitates the study of linear and nonlinear effects in resonant frequency regions.
- This work advances the development of damped coupled cluster response theory.
Related Concept Videos
01:12Reduced Mass Coordinates: Isolated Two-body Problem
2.5K
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...
2.5K
01:27State Space Representation
785
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...
Consider an RLC circuit, a...
785
01:11Types of Responses of Series RLC Circuits
2.3K
A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.
2.3K
01:12Double Resonance Techniques: Overview
870
Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
Spin decoupling is usually achieved by...
870
01:30RLC Circuit as a Damped Oscillator
2.7K
An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
2.7K
01:21Linear Approximation in Time Domain
460
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,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
460