# References

Here is the original reference for the COHP technique, and also for its projected (plane-wave based) extension. We kindly ask that if you use any of these in a scientific work, please give proper credit by citing as follows:

**Crystal Orbital Hamilton Populations (COHP). Energy-Resolved Visualization of Chemical Bonding in Solids based on Density-Functional Calculations.**

R. Dronskowski, P. E. Blöchl,

*J. Phys. Chem.*

**1993**,

*97*, 8617—8624.

The definitely first COHP paper. It goes back to the late 1980s and Richard Dronskowski's and Peter Blöchl's work at the Max-Planck-Institute for Solid-State Research in Stuttgart, Germany; please have a look at the History section. This is the theory upon which

*any*COHP analysis you find in the literature is built. If you use the plane-wave based pCOHP (e.g., within the LOBSTER package that you can get on this site), please

*additionally*make reference to the following three papers:

**Crystal Orbital Hamilton Population (COHP) Analysis as Projected from Plane-Wave Basis Sets.**

V. L. Deringer, A. L. Tchougreeff, R. Dronskowski,

*J. Phys. Chem. A*

**2011**,

*115*, 5461—5466.

The first time that COHP curves were reconstructed from popular plane-wave DFT workhorses such as VASP, based on Volker's diploma thesis. This paper introduced the term "projected COHP" and the underlying ideas, and applies them to classical textbook cases: diamond (of course), the semiconductor GaAs, sodium metal, and even ionic bonding in CsCl. The technical implementation of our own projection scheme (with some important further developments) was finally mastered two years later:

**Analytic Projection from Plane-Wave and PAW Wavefunctions and Application to Chemical-Bonding Analysis in Solids.**

S. Maintz, V. L. Deringer, A. L. Tchougreeff, R. Dronskowski,

*J. Comput. Chem.*

**2013**,

*34*, 2557—2567.

This paper expands upon the previous one: by exploiting an orthonormalization technique, we can now use any suitable local basis (e.g., Slater type orbitals), which is a central part of Stefan's PhD research. The new procedure also produces reasonable and quantitative

*projected DOS*as a side product! Finally, this paper provides the inevitable mathematical apparatus in a (we hope) comprehensive way, and the LOBSTER program is directly built on it.

**LOBSTER: A tool to extract chemical bonding from plane-wave based DFT.**

S. Maintz, V. L. Deringer, A. L. Tchougreeff, R. Dronskowski,

*J. Comput. Chem.*

**2016**,

*37*, 1030—1035.

This Software News and Updates article explains the new developments in LOBSTER 2.0.0, that is, improved (augmented) basis sets, new projection-quality measures, wave-function visualization, orthonormalization procedures, and digesting results from other quantum-mechanical codes (VASP and ABINIT). In addition, we briefly cover new third-party as well as our own LOBSTER applications.

**Efficient Rotation of Local Basis Functions Using Real Spherical Harmonics.**

S. Maintz, M. Esser, R. Dronskowski,

*Acta Phys. Pol. B*

**2016**,

*47*, 1165—1175.

This article describes the mathematics to align basis functions to the local chemical environment, as automatically performed in LOBSTER 2.1. We exemplify its use by applying an orbital-resolved pCOHP bonding analysis.

**LOBSTER: Local orbital projections, atomic charges, and chemical-bonding analysis from projector-augmented-wave-based density-functional theory**

R. Nelson, C. Ertural, J. George, V. L. Deringer, G. Hautier, R. Dronskowski,

*J Comput Chem.*

**2020**, 1–10.

The article describes how time-reversal (TR) symmetry is incorporated into LOBSTER, in addition to new features: charge/population analysis as well as k-dependent COHP. On average, TR symmetry saves 50% of computation time and memory. Furthermore, charge and population analysis is useful for examining ionic bonding in suchlike (or polar) compounds, whereas the k-dependent COHP provides detailed band-wise and k-point-wise chemical-bonding analysis which may be more convenient in some cases.

last modified: 2020-06-15