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Related Concept Videos

Mechanistic Models: Overview of Compartment Models01:21

Mechanistic Models: Overview of Compartment Models

Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
State Space Representation01:27

State Space Representation

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...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Control Volume and System Representations01:16

Control Volume and System Representations

Two key frameworks are employed to analyze mass, energy, and momentum transfer: the control volume approach and the system approach. These frameworks offer different perspectives, depending on whether the focus is on a specific region in space (control volume approach) or a defined mass of fluid (system approach).
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Compartment Models: Single-Compartment Model01:14

Compartment Models: Single-Compartment Model

The single-compartment model serves as a simplified representation of the human body. This model assumes that the body functions as a single, well-mixed open compartment. When a drug is administered intravenously, it enters the body and quickly distributes uniformly. The drug then undergoes biotransformation and elimination, ultimately leaving the body. The volume of this compartment is referred to as the apparent volume of distribution into which the drug can uniformly distribute. In this...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Energy partitioning scheme based on self-consistent method for subsystems: populational space approach.

Piotr De Silva1, Jacek Korchowiec

  • 1K. Guminski Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, R. Ingardena 3, Cracow 30-060, Poland.

Journal of Computational Chemistry
|March 10, 2011
PubMed
Summary

This study refines an energy partitioning scheme for molecular subsystems, improving accuracy by accounting for all interactions and ensuring wavefunction symmetry. Natural orbitals are used to analyze charge reorganization in chemical processes.

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Area of Science:

  • Quantum chemistry
  • Computational chemistry
  • Theoretical chemistry

Background:

  • Accurate calculation of molecular properties requires effective methods for partitioning complex systems into smaller, manageable subsystems.
  • Previous energy partitioning schemes, like the self-consistent charge and configuration method, have limitations in fully accounting for inter-subsystem interactions and symmetry.
  • Understanding charge reorganization is crucial for describing chemical phenomena such as polarization and charge transfer.

Purpose of the Study:

  • To present a refined energy partitioning scheme for molecular subsystems.
  • To rigorously incorporate all inter-subsystem interactions and ensure the symmetry of intermediate wavefunctions.
  • To introduce natural orbitals for chemical valence for detailed analysis of charge reorganization.

Main Methods:

  • Refinement of the self-consistent charge and configuration method for subsystems.
  • Implementation of a scheme that accounts for all inter-subsystem interactions.
  • Inclusion of natural orbitals for chemical valence analysis.
  • Application to model systems like the water dimer and ammonia borane.

Main Results:

  • The proposed refinement ensures proper symmetry of intermediate wavefunctions.
  • The new method rigorously accounts for all interactions between subsystems.
  • Natural orbitals effectively trace charge reorganization during polarization and charge transfer.
  • The formalism is demonstrated to be applicable to relevant chemical systems.

Conclusions:

  • The refined energy partitioning scheme offers improved accuracy and theoretical rigor.
  • The method provides valuable insights into charge dynamics in molecular systems.
  • This approach is a significant advancement for computational studies of molecular interactions and electronic properties.