Draft:Single point energy

• Comment: There are too many technical problems with this topic.
  1. Single point calculations without structural relaxations are a subset of calculations, not just in quantum chemistry or molecules. For instance, often they are done with bulk CIF data.
  2. Much of this is already elsewhere, e,g. basis sets, methods.
  3. Fails WP:NOTEVERYTHING
  4. It is very incomplete, for instance why such a minute list of software, see List of quantum chemistry and solid-state physics software.
  I suggest looking at core DFT & QM methods pages and adding a paragraph. I don't see this as ever being a visible page by itself. Ldm1954 (talk) 12:33, 14 March 2025 (UTC)

• Comment: Please add in-text citations to help verify information. Significa liberdade (she/her) (talk) 21:33, 6 February 2025 (UTC)

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In computational quantum chemistry, a Single-Point Energy (SPE) calculation determines the total electronic energy of a molecular system at a fixed geometry, without performing structural optimization. Single point energies are the most straight forward properties one might aim to obtain. They are the lowest energy solution for the Schrödinger equation. These calculations are essential for various applications, including geometry optimizations, reaction energy assessments, and molecular dynamics simulations. Obtaining the SPE allows for a reference for comparison of other methods of other energy calculation methods and the prediction of chemical pathways and Reactivity (chemistry). This reference allows for researchers to determine the best quantum chemical method by using the SPE as a benchmark. It also allows for prediction of different potential reaction pathways by comparing the energy values relative to the SPE.

Theoretical background

Quantum chemical methods

SPE is computed using electronic structure theories, which solve the Schrödinger equation for a given molecular geometry. SPE calculations employ various electronic structure theories to approximate the electronic energy of molecules (Energy level). One of the theories is Hartree-Fock (HF) Method. This approach approximates the total energy by treating electron-electron interactions using mean-field approximation. The electronic wavefunction is represented as a Slater determinant of molecular orbitals. However, HF lacks electron correlation effects, which can lead to inaccuracies in SPE values. Another important theory is the Density Functional Theory (DFT). DFT replaces the complex many-body wavefunction with the electron density, solving the Kohn-Sham equations. DFT is widely used due to its balance between accuracy and computational cost . SPE can be calculated also using Møller–Plesset perturbation theory (MP2) , Coupled cluster (CC), Configuration interaction or Semiempirical Methods (SQM).

Basis sets in SPE calculations

A basis set in computational chemistry is a collection of mathematical functions used to approximate the electronic wave function of a system. These functions, typically centered on atoms, are combined linearly to model molecular orbitals. Basis sets simplify the complex equations of quantum chemistry into algebraic forms suitable for computational methods such as Hartree–Fock or density Functional Theory (DFT). Single Point Energy (SPE) calculations determine the energy of a molecular system at a fixed geometry using a specific electronic structure method and basis set. The choice of basis set is critical. The accuracy of SPE calculations depends heavily on the quality and size of the basis set. Larger and more comprehensive basis sets (e.g., augmented or polarized ones) provide better approximations of electron distributions, leading to more precise energy values. While larger basis sets improve accuracy, they also increase computational cost. A balance must be struck between accuracy and efficiency, especially for large systems.. For example, Gaussian-type basis sets are favored for their computational efficiency in post-Hartree–Fock methods. Moreover, Different basis sets are optimized for specific tasks. For instance, correlation-consistent basis sets are designed for electron correlation energies, while polarization-consistent sets are better suited for DFT and Hartree–Fock energies

Significance of SPE calculations in computational studies

Single-Point Energy calculations play a crucial role in computational chemistry by providing highly accurate energy evaluations of molecular structures at fixed geometries. These calculations are fundamental for various applications.

• Evaluation of Computational Methods

SPE calculations are widely used to compare and validate different computational methods, ensuring their accuracy and reliability.. SPE calculations allow researchers to assess the performance of various electronic structure methods by computing their deviations from high-accuracy reference data and select an optimal functional or basis Set. Also, SPE values can be compared to experimental enthalpies, ionization energies, or reaction barriers to determine the reliability of computational models

• Prediction of Molecular Properties:

SPE calculations provide insights into various molecular properties that are essential for studying chemical systems: reaction energies and activation barriers, energy ranking of isomers and conformers and intermolecular interactions.

Applications

• Thermochemistry and Reaction Energies:

SPE calculations are used to calculate enthalpy, entropy, and Gibbs free energy changes in chemical reactions.

• Potential energy surfaces (PES):

SPE calculations help generate PES for transition state searches and reaction pathways.

• SPE in Force Fields and Electronic Spectra:

Molecular Dynamics and Spectroscopy are important in force field development for molecular dynamics simulations and in calculating electronic spectra using methods like Time-Dependent DFT (TD-DFT).

Computational chemistry software for SPE calculations

Several computational chemistry software packages facilitate SPE calculations, including:

• Gaussian
• ORCA
• NWChem
• Q-Chem
• GAMESS