Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...

Thermodynamic Potentials

Thermodynamic Potentials

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...

Theory of Metallic Conduction

Theory of Metallic Conduction

The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the results of quantum mechanics. It is called the theory of metallic conduction.
In this theory, Newton's second law of motion is used to determine the acceleration of an electron in the presence of an applied electric field. Then, its velocity is expressed via this acceleration.
An electron moves through the crystal, containing positive ions,...

Gauss's Law

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Crystal Field Theory - Tetrahedral and Square Planar Complexes

Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...

Maxwell's Thermodynamic Relations

Maxwell's Thermodynamic Relations

Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Beyond electronic stabilization: towards a multicomponent conceptual density-functional theory for positron-driven bonding.

Physical chemistry chemical physics : PCCP·2026

Same author

A New Family of Seniority-Restricted Coupled Cluster Methods.

The journal of physical chemistry. A·2026

Same author

Systematic Testing of the Maximum Hardness and Minimum Electrophilicity Principles.

The journal of physical chemistry. A·2026

Same author

Ubiquitous Negative Electron Densities Discredit Smooth Energy Interpolation in Density Functional Theory.

The journal of physical chemistry letters·2026

Same author

Revisiting the Maximum Hardness Principle: A Quantitative Analysis on Reaction Datasets.

Journal of computational chemistry·2026

Same author

The Scaled Hirshfeld Partitioning: Mathematical Development and Information-Theoretic Foundation.

Entropy (Basel, Switzerland)·2026

Same journal

Enhanced and selective oxygen reduction by iron porphyrin with a biguanide residue in the second coordination sphere.

Chemical science·2026

Same journal

Excited-state orbital angular momentum enables all-optical molecular spin coherence.

Chemical science·2026

Same journal

Polyvinyl-based hole-transporting materials processed with non-destructive and green solvents for tin-lead perovskite solar cells and all-perovskite tandems.

Chemical science·2026

Same journal

Pd-catalyzed regio- and enantioselective allylation of cyclic allylboronates.

Chemical science·2026

Same journal

Covalent polyoxometalate-polyimide hybridization: multi-scale molecular engineering toward high-performance sodium-ion battery anodes.

Chemical science·2026

Same journal

Catalytic visible light-driven alkane dehydrogenation by a di-uranyl germanotungstate.

Chemical science·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 7, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Temperature and external fields in conceptual density functional theory.

Marco Franco-Pérez¹, Farnaz Heidar-Zadeh², Paul W Ayers³

¹Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma, de México, Cd Universitaria Ciudad de México Mexico.

Chemical Science

|November 21, 2024

Summary

This summary is machine-generated.

Conceptual DFT (CDFT) now incorporates temperature and external fields, enhancing chemical reactivity descriptors. This extension addresses the N-differentiability problem and introduces new thermodynamic reactivity concepts for better molecular synthesis and analysis.

More Related Videos

Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry

Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry

Published on: August 1, 2017

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Related Experiment Videos

Last Updated: Jun 7, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry

Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry

Published on: August 1, 2017

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Area of Science:

Theoretical Chemistry
Computational Chemistry
Quantum Chemistry

Background:

Conceptual Density Functional Theory (CDFT) traditionally relies on energy functionals dependent on electron number (N) and external potential (v).
CDFT's strength lies in its adaptability to incorporate additional state variables.
Recent advancements necessitate extensions to CDFT to address complex chemical systems and reactions.

Purpose of the Study:

To incorporate temperature and external fields (electric, magnetic, mechanical, pressure) as fundamental variables in CDFT.
To develop new, well-behaved chemical reactivity descriptors, including thermodynamic concepts and local analogs of global descriptors.
To explore the impact of these new variables on chemical selectivity and properties.

Main Methods:

Utilized the Grand Canonical Ensemble to introduce finite temperature, mitigating the N-differentiability problem.
Extended the energy functional to include external fields (X), defining response functions analogous to classical thermodynamics.
Analyzed the behavior of electronegativity and hardness under various external fields and mechanical forces.

Main Results:

Finite temperature introduces novel thermodynamic reactivity descriptors, such as heat capacity, and aids in defining local hardness.
External fields, like electric fields, induce selectivity in reaction channels (e.g., Fukui function).
Atomic electronegativity and hardness exhibit piecewise behavior in magnetic fields and change under mechanical force and pressure, correlating with structural and volume evolution.

Conclusions:

Extending CDFT with temperature and external fields provides a more comprehensive framework for understanding chemical reactivity.
The developed descriptors offer new insights into molecular behavior under diverse experimental conditions.
These advancements are crucial for designing and synthesizing novel molecules with tailored properties.