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Related Concept Videos

Functionalism01:11

Functionalism

William James, John Dewey, and Charles Sanders Peirce were instrumental in founding functional psychology, which draws heavily from Darwin's theory of evolution by natural selection. This theory suggests that individual traits, including behaviors, are adapted to their environments through natural selection. At the heart of functionalism is the concept of adaptation, meaning that a trait enhances an individual's chances of survival and reproduction.
James envisioned psychology's role as...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

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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)...
Applications of Integration to Probability Density Functions01:27

Applications of Integration to Probability Density Functions

Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF), which...
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
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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...

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Density functional theory.

Maylis Orio1, Dimitrios A Pantazis, Frank Neese

  • 1Lehrstuhl für Theoretische Chemie, Institut für Physikalische und Theoretische Chemie, Universität Bonn, Wegelerstrasse 12, 53115 Bonn, Germany.

Photosynthesis Research
|February 25, 2009
PubMed
Summary
This summary is machine-generated.

Density functional theory (DFT) enables high-quality predictions for biological systems, complementing experiments and exploring new research areas. DFT calculates geometries, energies, reaction mechanisms, and various spectroscopic properties.

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Area of Science:

  • Computational chemistry
  • Biophysics
  • Quantum mechanics

Background:

  • Density functional theory (DFT) is increasingly applied to biological systems.
  • Methodological and implementation advancements allow for high-quality property predictions.

Purpose of the Study:

  • To provide an overview of calculable properties using DFT in biological contexts.
  • To highlight the capabilities and limitations of current DFT methods.

Main Methods:

  • Density functional theory (DFT) calculations.
  • Review of recent literature examples.

Main Results:

  • DFT can accurately predict molecular geometries, energies, and reaction mechanisms.
  • A wide array of spectroscopic properties are accessible, including IR, optical, X-ray absorption, Mössbauer, and electron paramagnetic resonance (EPR) parameters (excluding relaxation times).

Conclusions:

  • DFT is a valuable tool for studying biological systems, augmenting experimental data.
  • DFT can confidently investigate areas lacking experimental data, despite current method limitations.