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Band Theory

Band Theory

When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
The energy difference between these bands is known as the band gap.
Conductor, Semiconductor,...

Energy Bands in Solids

Energy Bands in Solids

Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
Band Formation:
When atoms are brought close together, as in a solid, these discrete energy levels begin to split due to the overlap of electron orbitals from adjacent atoms. This split occurs because of the Pauli exclusion principle, which states...

Semiconductors

Semiconductors

There is variation in the electrical conductivity of materials - metals, semiconductors, and insulators that are showcased with the help of the energy band diagrams.
Metals such as copper (Cu), zinc (Zn), or lead (Pb) have low resistivity and feature conduction bands that are either not fully occupied or overlap with the valence band, making a bandgap non-existent. This allows electrons in the highest energy levels of the valence band to easily transition to the conduction band upon gaining...

MO Theory and Covalent Bonding

MO Theory and Covalent Bonding

The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...

Valence Bond Theory

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

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Related Experiment Video

Updated: Dec 11, 2025

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Tight binding models accurately predict band structures for copolymer semiconductors.

Prithvi Tipirneni¹, Vishal Jindal, Michael J Janik

¹Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802, USA. stm9@psu.edu.

Physical Chemistry Chemical Physics : PCCP

|August 25, 2020

Summary

Researchers developed a faster method to predict organic photovoltaic copolymer properties. This approach uses homopolymer data to efficiently screen new materials for organic photovoltaics (OPVs).

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Last Updated: Dec 11, 2025

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

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Published on: October 12, 2019

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Area of Science:

Materials Science
Organic Electronics
Computational Chemistry

Background:

Conjugated polymers are promising for organic photovoltaics (OPVs) due to their tunable electronic and physical properties.
Push-pull copolymers offer enhanced optical absorption and charge transfer, but exploring combinations is computationally expensive.
Current methods for screening OPV copolymers using first-principles calculations are time-consuming.

Purpose of the Study:

To develop a computationally efficient method for predicting the band structures of organic photovoltaic copolymers.
To enable rapid screening of potential OPV materials by leveraging homopolymer data.
To reduce the computational cost associated with discovering new push-pull copolymers for OPVs.

Main Methods:

Constructed tight-binding models for copolymer band structures.
Parameters for tight-binding models were derived from density functional theory (DFT) calculations on homopolymers.
Predicted copolymer valence and conduction bands using the developed tight-binding models.

Main Results:

The tight-binding models successfully predicted copolymer band structures.
Predicted band structures showed good agreement with direct DFT calculations of copolymers.
The method offers a significant speed-up for material screening compared to direct DFT calculations.

Conclusions:

A computationally efficient approach using tight-binding models parameterized by DFT calculations on homopolymers is feasible.
This method allows for rapid prediction and screening of OPV copolymer properties.
The findings pave the way for accelerated discovery of novel materials for organic photovoltaics.