refs.bib

@Article{Huber2021,
author={Huber, Sebastiaan P.
and Bosoni, Emanuele
and Bercx, Marnik
and Br{\"o}der, Jens
and Degomme, Augustin
and Dikan, Vladimir
and Eimre, Kristjan
and Flage-Larsen, Espen
and Garcia, Alberto
and Genovese, Luigi
and Gresch, Dominik
and Johnston, Conrad
and Petretto, Guido
and Ponc{\'e}, Samuel
and Rignanese, Gian-Marco
and Sewell, Christopher J.
and Smit, Berend
and Tseplyaev, Vasily
and Uhrin, Martin
and Wortmann, Daniel
and Yakutovich, Aliaksandr V.
and Zadoks, Austin
and Zarabadi-Poor, Pezhman
and Zhu, Bonan
and Marzari, Nicola
and Pizzi, Giovanni},
title={Common workflows for computing material properties using different quantum engines},
journal={npj Computational Materials},
year={2021},
month={Aug},
day={19},
volume={7},
number={1},
pages={136},
abstract={The prediction of material properties based on density-functional theory has become routinely common, thanks, in part, to the steady increase in the number and robustness of available simulation packages. This plurality of codes and methods is both a boon and a burden. While providing great opportunities for cross-verification, these packages adopt different methods, algorithms, and paradigms, making it challenging to choose, master, and efficiently use them. We demonstrate how developing common interfaces for workflows that automatically compute material properties greatly simplifies interoperability and cross-verification. We introduce design rules for reusable, code-agnostic, workflow interfaces to compute well-defined material properties, which we implement for eleven quantum engines and use to compute various material properties. Each implementation encodes carefully selected simulation parameters and workflow logic, making the implementer's expertise of the quantum engine directly available to non-experts. All workflows are made available as open-source and full reproducibility of the workflows is guaranteed through the use of the AiiDA infrastructure.},
issn={2057-3960},
doi={10.1038/s41524-021-00594-6},
url={https://doi.org/10.1038/s41524-021-00594-6}
}


@article{
delta2016,
author = {Kurt Lejaeghere  and Gustav Bihlmayer  and Torbjörn Björkman  and Peter Blaha  and Stefan Blügel  and Volker Blum  and Damien Caliste  and Ivano E. Castelli  and Stewart J. Clark  and Andrea Dal Corso  and Stefano de Gironcoli  and Thierry Deutsch  and John Kay Dewhurst  and Igor Di Marco  and Claudia Draxl  and Marcin Dułak  and Olle Eriksson  and José A. Flores-Livas  and Kevin F. Garrity  and Luigi Genovese  and Paolo Giannozzi  and Matteo Giantomassi  and Stefan Goedecker  and Xavier Gonze  and Oscar Grånäs  and E. K. U. Gross  and Andris Gulans  and François Gygi  and D. R. Hamann  and Phil J. Hasnip  and N. A. W. Holzwarth  and Diana Iuşan  and Dominik B. Jochym  and François Jollet  and Daniel Jones  and Georg Kresse  and Klaus Koepernik  and Emine Küçükbenli  and Yaroslav O. Kvashnin  and Inka L. M. Locht  and Sven Lubeck  and Martijn Marsman  and Nicola Marzari  and Ulrike Nitzsche  and Lars Nordström  and Taisuke Ozaki  and Lorenzo Paulatto  and Chris J. Pickard  and Ward Poelmans  and Matt I. J. Probert  and Keith Refson  and Manuel Richter  and Gian-Marco Rignanese  and Santanu Saha  and Matthias Scheffler  and Martin Schlipf  and Karlheinz Schwarz  and Sangeeta Sharma  and Francesca Tavazza  and Patrik Thunström  and Alexandre Tkatchenko  and Marc Torrent  and David Vanderbilt  and Michiel J. van Setten  and Veronique Van Speybroeck  and John M. Wills  and Jonathan R. Yates  and Guo-Xu Zhang  and Stefaan Cottenier },
title = {Reproducibility in density functional theory calculations of solids},
journal = {Science},
volume = {351},
number = {6280},
pages = {aad3000},
year = {2016},
doi = {10.1126/science.aad3000},
URL = {https://www.science.org/doi/abs/10.1126/science.aad3000},
eprint = {https://www.science.org/doi/pdf/10.1126/science.aad3000},
abstract = {Density functional theory (DFT) is now routinely used for simulating material properties. Many software packages are available, which makes it challenging to know which are the best to use for a specific calculation. Lejaeghere et al. compared the calculated values for the equation of states for 71 elemental crystals from 15 different widely used DFT codes employing 40 different potentials (see the Perspective by Skylaris). Although there were variations in the calculated values, most recent codes and methods converged toward a single value, with errors comparable to those of experiment. Science, this issue p. 10.1126/science.aad3000; see also p. 1394 A survey of recent density functional theory methods shows a convergence to more accurate property calculations. [Also see Perspective by Skylaris] The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements.}}

@article{Mulliken1955pt1,
    author = {Mulliken, R. S.},
    title = "{Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I}",
    journal = {The Journal of Chemical Physics},
    volume = {23},
    number = {10},
    pages = {1833-1840},
    year = {1955},
    month = {10},
    abstract = "{With increasing availability of good all‐electron LCAO MO (LCAO molecular orbital) wave functions for molecules, a systematic procedure for obtaining maximum insight from such data has become desirable. An analysis in quantitative form is given here in terms of breakdowns of the electronic population into partial and total ``gross atomic populations,'' or into partial and total ``net atomic populations'' together with ``overlap populations.'' ``Gross atomic populations'' distribute the electrons almost perfectly among the various AOs (atomic orbitals) of the various atoms in the molecule. From these numbers, a definite figure is obtained for the amount of promotion (e.g., from 2s to 2p) in each atom; and also for the gross charge Q on each atom if the bonds are polar. The total overlap population for any pair of atoms in a molecule is in general made up of positive and negative contributions. If the total overlap population between two atoms is positive, they are bonded; if negative, they are antibonded.Tables of gross atomic populations and overlap populations, also gross atomic charges Q, computed from SCF (self‐consistent field) LCAO‐MO data on CO and H2O, are given. The amount of s‐p promotion is found to be nearly the same for the O atom in CO and in H2O (0.14 electron in CO and 0.15e in H2O). For the C atom in CO it is 0.50e. For the N atom in N2 it is 0.26e according to calculations by Scherr. In spite of very strong polarity in the π bonds in CO, the σ and π overlap populations are very similar to those in N2. In CO the total overlap population for the π electrons is about twice that for the σ electrons. The most easily ionized electrons of CO are in an MO such that its gross atomic population is 94\\% localized on the carbon atom; these electrons account for the (weak) electron donor properties of CO. A comparison between changes of bond lengths observed on removal of an electron from one or another MO of CO and H2, and corresponding changes in computed overlap populations, shows good correlation. Several other points of interest are discussed.}",
    issn = {0021-9606},
    doi = {10.1063/1.1740588},
}

@article{Mulliken1955pt2,
    author = {Mulliken, R. S.},
    title = "{Electronic Population Analysis on LCAO–MO Molecular Wave Functions. II. Overlap Populations, Bond Orders, and Covalent Bond Energies}",
    journal = {The Journal of Chemical Physics},
    volume = {23},
    number = {10},
    pages = {1841-1846},
    year = {1955},
    month = {10},
    abstract = "{LCAO molecular orbital overlap populations give in general much more flexible and widely useful measures of the non‐Coulombic parts of covalent bond energies than do LCAO bond orders. They are immediately applicable to both π and σ bonds, including bonds involving hybrid AOs of all kinds, and they take account directly of the effects of variations in bond length on bond strength. In the last section of this paper, a number of ways of defining LCAO bond orders are reviewed, and their advantages and disadvantages discussed.If all LCAO parameters β are assumed proportional to corresponding overlap integrals S times suitable mean atomic ionization energies Ī, a simple general approximate formula for covalent resonance energies is obtained in terms of partial overlap populations and Ī's, including one or two empirical coefficients. This formula indicates that forced hybridization (see III of this series) due to inner shells should make important negative contributions to bond energies. The application of the formula to H2, CO, and H2O is discussed.The assumption of proportionality of β values to SĪ values may be useful also in estimating unknown β values.}",
    issn = {0021-9606},
    doi = {10.1063/1.1740589},
}

@article{Mulliken1955pt3,
    author = {Mulliken, R. S.},
    title = "{Electronic Population Analysis on LCAO‐MO Molecular Wave Functions. III. Effects of Hybridization on Overlap and Gross AO Populations}",
    journal = {The Journal of Chemical Physics},
    volume = {23},
    number = {12},
    pages = {2338-2342},
    year = {1955},
    month = {12},
    abstract = "{The effects of AO hybridization on gross AO and overlap populations for LCAO‐MO electron configurations are discussed in terms of some simple examples, using equations and graphs. The validity of ``gross AO populations'' as true measures of the population in various AOs is critically discussed. It is shown that the degree of hybridization in the AOs of an LCAO MO does not in general give the true amount of s or p character in the MO; this is given instead by the gross s or p population in the MO. Nevertheless, ``forced hybridization'' among the AOs, although not contributing to gross AO populations, leads to important negative contributions to overlap populations, hence to bond energies. For example, forced 2s—2p hybridization has the result that the total overlap population for two pairs of electrons occupying bonding σ LCAO MOs built from 2s and 2pσ AOs in a homopolar diatomic molecule is actually less than the sum of the overlap populations which one would have if one pair could be in an MO built from pure 2s AOs and the other in an MO built from pure 2pσ AOs. This sort of forced hybridization with resultant loss of bond strength may explain why double bonds seldom if ever consist of two σ bonds.}",
    issn = {0021-9606},
    doi = {10.1063/1.1741876},
}

@article{Mulliken1955pt4,
    author = {Mulliken, R. S.},
    title = "{Electronic Population Analysis on LCAO‐MO Molecular Wave Functions. IV. Bonding and Antibonding in LCAO and Valence‐Bond Theories}",
    journal = {The Journal of Chemical Physics},
    volume = {23},
    number = {12},
    pages = {2343-2346},
    year = {1955},
    month = {12},
    abstract = "{It is shown that there is a practically one‐to‐one correspondence between the occurrence, on the one hand, of positive (bonding) and negative (antibonding) overlap populations in LCAO theory and, on the other hand, of bonded attractions and nonbonded repulsions in VB (valence‐bond) theory. This correspondence is discussed in terms of examples, and is traced for the N2 molecule both for the assumed case of no s–p hybridization, and for the actual case with hybridization. It is pointed out that repulsions between nonbonded atoms in VB theory (including those which give rise to steric hindrance) have their counterpart in negative overlap populations between the same atoms in LCAO theory. The π overlap populations for the various links in 1,3‐butadiene are computed by LCAO theory. It is shown how they are affected by conjugation (see Table I) and the results are compared with those of VB theory.}",
    issn = {0021-9606},
    doi = {10.1063/1.1741877},
}

@article{Hirshfeld1977,
author={Hirshfeld, F. L.},
title={Bonded-atom fragments for describing molecular charge densities},
journal={Theoretica chimica acta},
year={1977},
month={Jun},
day={01},
volume={44},
number={2},
pages={129-138},
abstract={For quantitative description of a molecular charge distribution it is convenient to dissect the molecule into well-defined atomic fragments. A general and natural choice is to share the charge density at each point among the several atoms in proportion to their free-atom densities at the corresponding distances from the nuclei. This prescription yields well-localized bonded-atom distributions each of which closely resembles the molecular density in its vicinity. Integration of the atomic deformation densities --- bonded minus free atoms --- defines net atomic charges and multipole moments which concisely summarize the molecular charge reorganization. They permit calculation of the external electrostatic potential and of the interaction energy between molecules or between parts of the same molecule. Sample results for several molecules indicate a high transferability of net atomic charges and moments.},
issn={1432-2234},
doi={10.1007/BF00549096},
}

@article{Grimme2016,
author = {Grimme, Stefan and Hansen, Andreas and Brandenburg, Jan Gerit and Bannwarth, Christoph},
title = {Dispersion-Corrected Mean-Field Electronic Structure Methods},
journal = {Chemical Reviews},
volume = {116},
number = {9},
pages = {5105-5154},
year = {2016},
doi = {10.1021/acs.chemrev.5b00533},
note ={PMID: 27077966},
}

@article{GrimmeD2,
author = {Grimme, Stefan},
title = {Semiempirical {GGA}-type density functional constructed with a long-range dispersion correction},
journal = {Journal of Computational Chemistry},
volume = {27},
number = {15},
pages = {1787-1799},
keywords = {density functional theory, generalized gradient approximation, van der Waals interactions, thermochemistry},
doi = {https://doi.org/10.1002/jcc.20495},
abstract = {Abstract A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C6 · R−6. A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol−1. The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C6 · R−6 terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance. © 2006 Wiley Periodicals, Inc. J Comput Chem 2006},
year = {2006}
}

@article{GrimmeD3,
    author = {Grimme, Stefan and Antony, Jens and Ehrlich, Stephan and Krieg, Helge},
    title = "{A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu}",
    journal = {The Journal of Chemical Physics},
    volume = {132},
    number = {15},
    pages = {154104},
    year = {2010},
    month = {04},
    abstract = "{The method of dispersion correction as an add-on to standard Kohn–Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15\\%–40\\% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10\\%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.}",
    issn = {0021-9606},
    doi = {10.1063/1.3382344},
}

@article{GrimmeD3-BJ,
author = {Grimme, Stefan and Ehrlich, Stephan and Goerigk, Lars},
title = {Effect of the damping function in dispersion corrected density functional theory},
journal = {Journal of Computational Chemistry},
volume = {32},
number = {7},
pages = {1456-1465},
keywords = {dispersion energy, density functional theory, noncovalent interactions, van der Waals complexes},
doi = {https://doi.org/10.1002/jcc.21759},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.21759},
abstract = {Abstract It is shown by an extensive benchmark on molecular energy data that the mathematical form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a standard “zero-damping” formula and rational damping to finite values for small interatomic distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coefficients is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interatomic forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramolecular dispersion in four representative molecular structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermolecular distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of corrected GGAs for non-covalent interactions. According to the thermodynamic benchmarks BJ-damping is more accurate especially for medium-range electron correlation problems and only small and practically insignificant double-counting effects are observed. It seems to provide a physically correct short-range behavior of correlation/dispersion even with unmodified standard functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying density functional. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011},
year = {2011}
}

@article{vdW-DF2,
  title = {Higher-accuracy van der {W}aals density functional},
  author = {Lee, Kyuho and Murray, \'Eamonn D. and Kong, Lingzhu and Lundqvist, Bengt I. and Langreth, David C.},
  journal = {Phys. Rev. B},
  volume = {82},
  issue = {8},
  pages = {081101},
  numpages = {4},
  year = {2010},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.82.081101},
}

@article{vdW-DF-cx,
  title = {Exchange functional that tests the robustness of the plasmon description of the van der {W}aals density functional},
  author = {Berland, Kristian and Hyldgaard, Per},
  journal = {Phys. Rev. B},
  volume = {89},
  issue = {3},
  pages = {035412},
  numpages = {8},
  year = {2014},
  month = {Jan},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.89.035412},
}

@article{VV10,
    author = {Vydrov, Oleg A. and Van Voorhis, Troy},
    title = "{Nonlocal van der Waals density functional: The simpler the better}",
    journal = {The Journal of Chemical Physics},
    volume = {133},
    number = {24},
    pages = {244103},
    year = {2010},
    month = {12},
    abstract = "We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron density as input. The new functional is considerably simpler than its predecessors of a similar type. The functional has a tractable and robust analytic form that lends itself to efficient self-consistent implementation. When paired with an appropriate exchange functional, our nonlocal correlation model yields accurate interaction energies of weakly-bound complexes, not only near the energy minima but also far from equilibrium. Our model exhibits an outstanding precision at predicting equilibrium intermonomer separations in van der Waals complexes. It also gives accurate covalent bond lengths and atomization energies. Hence the functional proposed in this work is a computationally inexpensive electronic structure tool of broad applicability.",
    issn = {0021-9606},
    doi = {10.1063/1.3521275},
}

@article{vanSanten2015,
author = {van Santen, Jeffrey A. and DiLabio, Gino A.},
title = {Dispersion Corrections Improve the Accuracy of Both Noncovalent and Covalent Interactions Energies Predicted by a Density-Functional Theory Approximation},
journal = {The Journal of Physical Chemistry A},
volume = {119},
number = {25},
pages = {6703-6713},
year = {2015},
doi = {10.1021/acs.jpca.5b02809},
note ={PMID: 26030132},
}

@article{Zhao2008,
author={Zhao, Yan
and Truhlar, Donald G.},
title={The {M06} suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four {M06}-class functionals and 12 other functionals},
journal={Theoretical Chemistry Accounts},
year={2008},
month={May},
day={01},
volume={120},
number={1},
pages={215-241},
abstract={We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree--Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree--Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.},
issn={1432-2234},
doi={10.1007/s00214-007-0310-x},
}

@article{Klimes2011,
  title = {Van der {W}aals density functionals applied to solids},
  author = {Klime\v{s}, Ji\v{r}\'{i} and Bowler, David R. and Michaelides, Angelos},
  journal = {Phys. Rev. B},
  volume = {83},
  issue = {19},
  pages = {195131},
  numpages = {13},
  year = {2011},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.83.195131},
}

@Article{Dolgonos2019,
author = "Dolgonos, Grygoriy A. and Hoja, Johannes and Boese, A. Daniel",
title = "Revised values for the X23 benchmark set of molecular crystals",
journal = "Phys. Chem. Chem. Phys.",
year = "2019",
volume = "21",
issue = "44",
pages = "24333-24344",
publisher  ="The Royal Society of Chemistry",
doi = "10.1039/C9CP04488D",
abstract = "We present revised reference values for cell volumes and lattice energies for the widely used X23 benchmark set of molecular crystals by including the effect of thermal expansion. For this purpose{,} thermally-expanded structures were calculated via the quasi-harmonic approximation utilizing three dispersion-inclusive density-functional approximations. Experimental unit-cell volumes were back-corrected for thermal and zero-point energy effects{,} allowing now a direct comparison with lattice relaxations based on electronic energies. For the derivation of reference lattice energies{,} we utilized harmonic vibrational contributions averaged over four density-functional approximations. In addition{,} the new reference values also take the change in electronic and vibrational energy due to thermal expansion into account. This is accomplished by either utilizing experimentally determined cell volumes and heat capacities{,} or by relying on the quasi-harmonic approximation. The new X23b reference values obtained this way will enable a more accurate benchmark for the performance of computational methods for molecular crystals."
}

@article{Tkatchenko2009,
  title = {Accurate Molecular Van Der {W}aals Interactions from Ground-State Electron Density and Free-Atom Reference Data},
  author = {Tkatchenko, Alexandre and Scheffler, Matthias},
  journal = {Phys. Rev. Lett.},
  volume = {102},
  issue = {7},
  pages = {073005},
  numpages = {4},
  year = {2009},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.102.073005},
}

@article{Tkatchenko2012,
  title = {Accurate and Efficient Method for Many-Body van der {W}aals Interactions},
  author = {Tkatchenko, Alexandre and DiStasio, Robert A. and Car, Roberto and Scheffler, Matthias},
  journal = {Phys. Rev. Lett.},
  volume = {108},
  issue = {23},
  pages = {236402},
  numpages = {5},
  year = {2012},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.108.236402},
}

@article{Ruiz2012,
  title = {Density-Functional Theory with Screened van der {W}aals Interactions for the Modeling of Hybrid Inorganic-Organic Systems},
  author = {Ruiz, Victor G. and Liu, Wei and Zojer, Egbert and Scheffler, Matthias and Tkatchenko, Alexandre},
  journal = {Phys. Rev. Lett.},
  volume = {108},
  issue = {14},
  pages = {146103},
  numpages = {5},
  year = {2012},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.108.146103},
}

@article{Ambrosetti2014,
    author = {Ambrosetti, Alberto and Reilly, Anthony M. and {DiStasio, Jr.}, Robert A. and Tkatchenko, Alexandre},
    title = "{Long-range correlation energy calculated from coupled atomic response functions}",
    journal = {The Journal of Chemical Physics},
    volume = {140},
    number = {18},
    pages = {18A508},
    year = {2014},
    month = {02},
    abstract = "{An accurate determination of the electron correlation energy is an essential prerequisite for describing the structure, stability, and function in a wide variety of systems. Therefore, the development of efficient approaches for the calculation of the correlation energy (and hence the dispersion energy as well) is essential and such methods can be coupled with many density-functional approximations, local methods for the electron correlation energy, and even interatomic force fields. In this work, we build upon the previously developed many-body dispersion (MBD) framework, which is intimately linked to the random-phase approximation for the correlation energy. We separate the correlation energy into short-range contributions that are modeled by semi-local functionals and long-range contributions that are calculated by mapping the complex all-electron problem onto a set of atomic response functions coupled in the dipole approximation. We propose an effective range-separation of the coupling between the atomic response functions that extends the already broad applicability of the MBD method to non-metallic materials with highly anisotropic responses, such as layered nanostructures. Application to a variety of high-quality benchmark datasets illustrates the accuracy and applicability of the improved MBD approach, which offers the prospect of first-principles modeling of large structurally complex systems with an accurate description of the long-range correlation energy.}",
    issn = {0021-9606},
    doi = {10.1063/1.4865104},
}

@article{Smith2016,
author = {Smith, Daniel G. A. and Burns, Lori A. and Patkowski, Konrad and Sherrill, C. David},
title = {Revised Damping Parameters for the D3 Dispersion Correction to Density Functional Theory},
journal = {The Journal of Physical Chemistry Letters},
volume = {7},
number = {12},
pages = {2197-2203},
year = {2016},
doi = {10.1021/acs.jpclett.6b00780},
note ={PMID: 27203625},
}

@article{Jurecka2007,
author = {Jure\v{c}ka, Petr and \v{C}ern\'{y}, Ji\v{r}\'{i} and Hobza, Pavel and Salahub, Dennis R.},
title = {Density functional theory augmented with an empirical dispersion term. {I}nteraction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations},
journal = {Journal of Computational Chemistry},
volume = {28},
number = {2},
pages = {555-569},
keywords = {dispersion interaction, density functional theory, empirical corrections, van der Waals complexes},
doi = {10.1002/jcc.20570},
abstract = {Abstract Standard density functional theory (DFT) is augmented with a damped empirical dispersion term. The damping function is optimized on a small, well balanced set of 22 van der Waals (vdW) complexes and verified on a validation set of 58 vdW complexes. Both sets contain biologically relevant molecules such as nucleic acid bases. Results are in remarkable agreement with reference high-level wave function data based on the CCSD(T) method. The geometries obtained by full gradient optimization are in very good agreement with the best available theoretical reference. In terms of the standard deviation and average errors, results including the empirical dispersion term are clearly superior to all pure density functionals investigated—B-LYP, B3-LYP, PBE, TPSS, TPSSh, and BH-LYP—and even surpass the MP2/cc-pVTZ method. The combination of empirical dispersion with the TPSS functional performs remarkably well. The most critical part of the empirical dispersion approach is the damping function. The damping parameters should be optimized for each density functional/basis set combination separately. To keep the method simple, we optimized mainly a single factor, sR, scaling globally the vdW radii. For good results, a basis set of at least triple-ζ quality is required and diffuse functions are recommended, since the basis set superposition error seriously deteriorates the results. On average, the dispersion contribution to the interaction energy missing in the DFT functionals examined here is about 15 and 100\% for the hydrogen-bonded and stacked complexes considered, respectively. © 2006 Wiley Periodicals, Inc. J Comput Chem 28: 555–569, 2007},
year = {2007}
}

@article{Ortmann2006,
  title = {Semiempirical van der {W}aals correction to the density functional description of solids and molecular structures},
  author = {Ortmann, F. and Bechstedt, F. and Schmidt, W. G.},
  journal = {Phys. Rev. B},
  volume = {73},
  issue = {20},
  pages = {205101},
  numpages = {10},
  year = {2006},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.73.205101},
}

@article{Becke2007,
    author = {Becke, Axel D. and Johnson, Erin R.},
    title = "{A unified density-functional treatment of dynamical, nondynamical, and dispersion correlations}",
    journal = {The Journal of Chemical Physics},
    volume = {127},
    number = {12},
    pages = {124108},
    year = {2007},
    month = {09},
    abstract = "{In previous work we have introduced exact-exchange-based density-functional models of dynamical, nondynamical, and dispersion correlations. We have not yet, however, been able to combine these models into a single energy functional. The problem is that interaction curves in van der Waals complexes are too repulsive. A simple solution is proposed in the present work resulting in an exact-exchange-based energy functional for all chemical interactions, from the weakest (dispersion) to the strongest (molecular bonds).}",
    issn = {0021-9606},
    doi = {10.1063/1.2768530},
}

@article{Maillet2000,
  title = {Uniaxial Hugoniostat: A method for atomistic simulations of shocked materials},
  author = {Maillet, J.-B. and Mareschal, M. and Soulard, L. and Ravelo, R. and Lomdahl, P. S. and Germann, T. C. and Holian, B. L.},
  journal = {Phys. Rev. E},
  volume = {63},
  issue = {1},
  pages = {016121},
  numpages = {8},
  year = {2000},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevE.63.016121},
}

@article{Ravelo2004,
  title = {Constant-stress Hugoniostat method for following the dynamical evolution of shocked matter},
  author = {Ravelo, R. and Holian, B. L. and Germann, T. C. and Lomdahl, P. S.},
  journal = {Phys. Rev. B},
  volume = {70},
  issue = {1},
  pages = {014103},
  numpages = {9},
  year = {2004},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.70.014103},
}

@PhdThesis{Wilkins2019,
          author = {Jacob Wilkins},
           title = {Exploration of approaches to shock-wave simulations},
          school = {University of York},
           month = {July},
            year = {2019},
             url = {https://etheses.whiterose.ac.uk/24444/},
}

@article{Hoover1985,
  title = {Canonical dynamics: Equilibrium phase-space distributions},
  author = {Hoover, William G.},
  journal = {Phys. Rev. A},
  volume = {31},
  issue = {3},
  pages = {1695--1697},
  numpages = {0},
  year = {1985},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.31.1695},
}

@article{Hoover1986,
  title = {Constant-pressure equations of motion},
  author = {Hoover, William G.},
  journal = {Phys. Rev. A},
  volume = {34},
  issue = {3},
  pages = {2499--2500},
  numpages = {0},
  year = {1986},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.34.2499},
}

@article{Martyna1992,
    author = {Martyna, Glenn J. and Klein, Michael L. and Tuckerman, Mark},
    title = "{Nosé–Hoover chains: The canonical ensemble via continuous dynamics}",
    journal = {The Journal of Chemical Physics},
    volume = {97},
    number = {4},
    pages = {2635-2643},
    year = {1992},
    month = {08},
    abstract = "{Nosé has derived a set of dynamical equations that can be shown to give canonically distributed positions and momenta provided the phase space average can be taken into the trajectory average, i.e., the system is ergodic [S. Nosé, J. Chem. Phys. 81, 511 (1984), W. G. Hoover, Phys. Rev. A 31, 1695 (1985)]. Unfortunately, the Nosé–Hoover dynamics is not ergodic for small or stiff systems. Here a modification of the dynamics is proposed which includes not a single thermostat variable but a chain of variables, Nosé–Hoover chains. The ‘‘new’’ dynamics gives the canonical distribution where the simple formalism fails. In addition, the new method is easier to use than an extension [D. Kusnezov, A. Bulgac, and W. Bauer, Ann. Phys. 204, 155 (1990)] which also gives the canonical distribution for stiff cases.}",
    issn = {0021-9606},
    doi = {10.1063/1.463940},
}

@article{Andersen1980,
    author = {Andersen, Hans C.},
    title = "{Molecular dynamics simulations at constant pressure and/or temperature}",
    journal = {The Journal of Chemical Physics},
    volume = {72},
    number = {4},
    pages = {2384-2393},
    year = {1980},
    month = {02},
    abstract = "{In the molecular dynamics simulation method for fluids, the equations of motion for a collection of particles in a fixed volume are solved numerically. The energy, volume, and number of particles are constant for a particular simulation, and it is assumed that time averages of properties of the simulated fluid are equal to microcanonical ensemble averages of the same properties. In some situations, it is desirable to perform simulations of a fluid for particular values of temperature and/or pressure or under conditions in which the energy and volume of the fluid can fluctuate. This paper proposes and discusses three methods for performing molecular dynamics simulations under conditions of constant temperature and/or pressure, rather than constant energy and volume. For these three methods, it is shown that time averages of properties of the simulated fluid are equal to averages over the isoenthalpic–isobaric, canonical, and isothermal–isobaric ensembles. Each method is a way of describing the dynamics of a certain number of particles in a volume element of a fluid while taking into account the influence of surrounding particles in changing the energy and/or density of the simulated volume element. The influence of the surroundings is taken into account without introducing unwanted surface effects. Examples of situations where these methods may be useful are discussed.}",
    issn = {0021-9606},
    doi = {10.1063/1.439486},
}

@article{Martyna1994,
    author = {Martyna, Glenn J. and Tobias, Douglas J. and Klein, Michael L.},
    title = "{Constant pressure molecular dynamics algorithms}",
    journal = {The Journal of Chemical Physics},
    volume = {101},
    number = {5},
    pages = {4177-4189},
    year = {1994},
    month = {09},
    abstract = "{Modularly invariant equations of motion are derived that generate the isothermal–isobaric ensemble as their phase space averages. Isotropic volume fluctuations and fully flexible simulation cells as well as a hybrid scheme that naturally combines the two motions are considered. The resulting methods are tested on two problems, a particle in a one‐dimensional periodic potential and a spherical model of C60 in the solid/fluid phase.}",
    issn = {0021-9606},
    doi = {10.1063/1.467468},
}

@article{Parrinello1980,
  title = {Crystal Structure and Pair Potentials: A Molecular-Dynamics Study},
  author = {Parrinello, M. and Rahman, A.},
  journal = {Phys. Rev. Lett.},
  volume = {45},
  issue = {14},
  pages = {1196--1199},
  numpages = {0},
  year = {1980},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.45.1196},
}

@article{Parrinello1981,
    author = {Parrinello, M. and Rahman, A.},
    title = "{Polymorphic transitions in single crystals: A new molecular dynamics method}",
    journal = {Journal of Applied Physics},
    volume = {52},
    number = {12},
    pages = {7182-7190},
    year = {1981},
    month = {12},
    abstract = "{A new Lagrangian formulation is introduced. It can be used to make molecular dynamics (MD) calculations on systems under the most general, externally applied, conditions of stress. In this formulation the MD cell shape and size can change according to dynamical equations given by this Lagrangian. This new MD technique is well suited to the study of structural transformations in solids under external stress and at finite temperature. As an example of the use of this technique we show how a single crystal of Ni behaves under uniform uniaxial compressive and tensile loads. This work confirms some of the results of static (i.e., zero temperature) calculations reported in the literature. We also show that some results regarding the stress‐strain relation obtained by static calculations are invalid at finite temperature. We find that, under compressive loading, our model of Ni shows a bifurcation in its stress‐strain relation; this bifurcation provides a link in configuration space between cubic and hexagonal close packing. It is suggested that such a transformation could perhaps be observed experimentally under extreme conditions of shock.}",
    issn = {0021-8979},
    doi = {10.1063/1.328693},
}

@article{TPSS,
    author = {Barzilai, Jonathan and Borwein, Jonathan M.},
    title = "{Two-Point Step Size Gradient Methods}",
    journal = {IMA Journal of Numerical Analysis},
    volume = {8},
    number = {1},
    pages = {141-148},
    year = {1988},
    month = {01},
    abstract = "{We derive two-point step sizes for the steepest-descent method by approximating the secant equation. At the cost of storage of an extra iterate and gradient, these algorithms achieve better performance and cheaper computation than the classical steepest-descent method. We indicate a convergence analysis of the method in the two-dimensional quadratic case. The behaviour is highly remarkable and the analysis entirely nonstandard.}",
    issn = {0272-4979},
    doi = {10.1093/imanum/8.1.141},
}

@article{FIRE,
  title = {Structural Relaxation Made Simple},
  author = {Bitzek, Erik and Koskinen, Pekka and G\"ahler, Franz and Moseler, Michael and Gumbsch, Peter},
  journal = {Phys. Rev. Lett.},
  volume = {97},
  issue = {17},
  pages = {170201},
  numpages = {4},
  year = {2006},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.97.170201},
}

@article{ODE12R,
    author = {Makri, Stela and Ortner, Christoph and Kermode, James R.},
    title = "{A preconditioning scheme for minimum energy path finding methods}",
    journal = {The Journal of Chemical Physics},
    volume = {150},
    number = {9},
    pages = {094109},
    year = {2019},
    month = {03},
    abstract = "{Popular methods for identifying transition paths between energy minima, such as the nudged elastic band and string methods, typically do not incorporate potential energy curvature information, leading to slow relaxation to the minimum energy path for typical potential energy surfaces encountered in molecular simulation. We propose a preconditioning scheme which, combined with a new adaptive time step selection algorithm, substantially reduces the computational cost of transition path finding algorithms. We demonstrate the improved performance of our approach in a range of examples including vacancy and dislocation migration modeled with both interatomic potentials and density functional theory.}",
    issn = {0021-9606},
    doi = {10.1063/1.5064465},
}

@article{Helgaker2008,
title = {The quantum-chemical calculation of NMR indirect spin–spin coupling constants},
journal = {Progress in Nuclear Magnetic Resonance Spectroscopy},
volume = {53},
number = {4},
pages = {249-268},
year = {2008},
issn = {0079-6565},
doi = {10.1016/j.pnmrs.2008.02.002},
author = {Trygve Helgaker and Micha\l{} Jaszu\'{n}ski and Magdalena Pecul},
keywords = {Spin-spin coupling constants, Electronic-structure theory, Quantum chemistry, Ab initio calculations, Density-functional theory}
}

@article{Joyce2007,
    author = {Joyce, Si\^{a}n A. and Yates, Jonathan R. and Pickard, Chris J. and Mauri, Francesco},
    title = "{A first principles theory of nuclear magnetic resonance J-coupling in solid-state systems}",
    journal = {The Journal of Chemical Physics},
    volume = {127},
    number = {20},
    pages = {204107},
    year = {2007},
    month = {11},
    abstract = "{A method to calculate NMR J-coupling constants from first principles in extended systems is presented. It is based on density functional theory and is formulated within a planewave-pseudopotential framework. The all-electron properties are recovered using the projector augmented wave approach. The method is validated by comparison with existing quantum chemical calculations of solution-state systems and with experimental data. The approach has also been applied to the silicophosphate, Si5O(PO4)6, giving P31–Si29-couplings which are in excellent agreement with experiment.}",
    issn = {0021-9606},
    doi = {10.1063/1.2801984},
}

@article{Blaha1989,
author={Blaha, P.
and Sorantin, P.
and Ambrosch, C.
and Schwarz, K.},
title={Calculation of the electric field gradient tensor from energy band structures},
journal={Hyperfine Interactions},
year={1989},
month={Jun},
day={01},
volume={51},
number={1},
pages={917-923},
abstract={The electric field gradient tensor (EFG) can be measured accurately by various experimental techniques. The theoretical understanding, however, was restricted to point charge models, Sternheimer antishielding factors and model calculations for a restricted number of compounds. We have developed a method which obtains the EFG from a full potential linearized augmented plane wave (LAPW) energy band structure calculation. Starting from the total crystal charge density (including the core electrons) the EFG is obtained numerically without further approximations. We have applied our method successfully to all hep metals up to Cd, to semiconductors, and to insulators such as lithiumnitride or cuprite. Good agreement with experiment is found and we predict interesting changes in the sign of the EFG in the 3d and 4d transition metal series. The aspherical distribution of the valence electrons determines 80 or 90{\%} of the total EFG and the influence of the core electrons is small. Even for the 3d and 4d metals the asphericity of the valence p electrons dominates over the d contribution to the EFG due to the different radial behavior of p and d wave functions.},
issn={1572-9540},
doi={10.1007/BF02407802},
}

@article{Profeta2003,
author = {Profeta, Mickael and Mauri, Francesco and Pickard, Chris J.},
title = {Accurate First Principles Prediction of {17O NMR} Parameters in {SiO2}: Assignment of the Zeolite Ferrierite Spectrum},
journal = {Journal of the American Chemical Society},
volume = {125},
number = {2},
pages = {541-548},
year = {2003},
doi = {10.1021/ja027124r},
note ={PMID: 12517169},
}

@article{Blaha1990,
title = {Full-potential, linearized augmented plane wave programs for crystalline systems},
journal = {Computer Physics Communications},
volume = {59},
number = {2},
pages = {399-415},
year = {1990},
issn = {0010-4655},
doi = {10.1016/0010-4655(90)90187-6},
author = {P. Blaha and K. Schwarz and P. Sorantin and S.B. Trickey},
abstract = {In solids, linearized augmented plane waves (LAPW's) have proven to be an effective basis for the solution of the Kohn-Sham equations, the main calculational task in the local spin density approximation (LSDA) to density functional theory. The WIEN package uses LAPW's to calculate the LSDA total energy, spin densities, Kohn-Sham eigenvalues, and the electric field gradients at nuclear sites for a broad variety of space groups. Options include retention or omission of non-muffin-tin contributions (hence WIEN is a full-potential or F-LAPW code) and relativistic corrections (full treatment for core states, Scalar-relativistic for valence states).}
}

@book{Coppens1997,
  title={X-ray charge densities and chemical bonding},
  author={Coppens, Philip},
  volume={4},
  year={1997},
  publisher={International Union of Crystallography}
}

@book{Shmueli2001,
  author={},
  editor = {Shmueli, U. and Internationale Union f\"{u}r Kristallographie},
  title = {International Tables for Crystallography},
  publisher = {Kluwer Acad. Publ, Dordrecht},
  year = {2001},
  volume = {B: Reciprocal Space},
  edition = {2.},
}

@article{DeltaSCF1,
    author = {Maurer, Reinhard J. and Reuter, Karsten},
    title = "{Assessing computationally efficient isomerization dynamics: ΔSCF density-functional theory study of azobenzene molecular switching}",
    journal = {The Journal of Chemical Physics},
    volume = {135},
    number = {22},
    pages = {224303},
    year = {2011},
    month = {12},
    abstract = "{We present a detailed comparison of the S0, S1 (n → π*) and S2 (π → π*) potential energy surfaces (PESs) of the prototypical molecular switch azobenzene as obtained by Δ-self-consistent-field (ΔSCF) density-functional theory (DFT), time-dependent DFT (TD-DFT) and approximate coupled cluster singles and doubles (RI-CC2). All three methods unanimously agree in terms of the PES topologies, which are furthermore fully consistent with existing experimental data concerning the photo-isomerization mechanism. In particular, sum-method corrected ΔSCF and TD-DFT yield very similar results for S1 and S2, when based on the same ground-state exchange-correlation (xc) functional. While these techniques yield the correct PES topology already on the level of semi-local xc functionals, reliable absolute excitation energies as compared to RI-CC2 or experiment require an xc treatment on the level of long-range corrected hybrids. Nevertheless, particularly the robustness of ΔSCF with respect to state crossings as well as its numerical efficiency suggest this approach as a promising route to dynamical studies of larger azobenzene-containing systems.}",
    issn = {0021-9606},
    doi = {10.1063/1.3664305},
}

@article{DeltaSCF2,
  title = {Δ self-consistent field method to obtain potential energy surfaces of excited molecules on surfaces},
  author = {Gavnholt, Jeppe and Olsen, Thomas and Engelund, Mads and Schi\o{}tz, Jakob},
  journal = {Phys. Rev. B},
  volume = {78},
  issue = {7},
  pages = {075441},
  numpages = {10},
  year = {2008},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.78.075441},
}

@article{DeltaSCF3,
    author = {Maurer, Reinhard J. and Reuter, Karsten},
    title = "{Excited-state potential-energy surfaces of metal-adsorbed organic molecules from linear expansion Δ-self-consistent field density-functional theory (ΔSCF-DFT)}",
    journal = {The Journal of Chemical Physics},
    volume = {139},
    number = {1},
    pages = {014708},
    year = {2013},
    month = {07},
    abstract = "{Accurate and efficient simulation of excited state properties is an important and much aspired cornerstone in the study of adsorbate dynamics on metal surfaces. To this end, the recently proposed linear expansion Δ-self-consistent field method by Gavnholt et al. [Phys. Rev. B 78, 075441 (2008)]10.1103/PhysRevB.78.075441 presents an efficient alternative to time consuming quasi-particle calculations. In this method, the standard Kohn-Sham equations of density-functional theory are solved with the constraint of a non-equilibrium occupation in a region of Hilbert-space resembling gas-phase orbitals of the adsorbate. In this work, we discuss the applicability of this method for the excited-state dynamics of metal-surface mounted organic adsorbates, specifically in the context of molecular switching. We present necessary advancements to allow for a consistent quality description of excited-state potential-energy surfaces (PESs), and illustrate the concept with the application to Azobenzene adsorbed on Ag(111) and Au(111) surfaces. We find that the explicit inclusion of substrate electronic states modifies the topologies of intra-molecular excited-state PESs of the molecule due to image charge and hybridization effects. While the molecule in gas phase shows a clear energetic separation of resonances that induce isomerization and backreaction, the surface-adsorbed molecule does not. The concomitant possibly simultaneous induction of both processes would lead to a significantly reduced switching efficiency of such a mechanism.}",
    issn = {0021-9606},
    doi = {10.1063/1.4812398},
}

@article{Muller2016,
    author = {M\"{u}ller, Moritz and Diller, Katharina and Maurer, Reinhard J. and Reuter, Karsten},
    title = "{Interfacial charge rearrangement and intermolecular interactions: Density-functional theory study of free-base porphine adsorbed on Ag(111) and Cu(111)}",
    journal = {The Journal of Chemical Physics},
    volume = {144},
    number = {2},
    pages = {024701},
    year = {2016},
    month = {01},
    abstract = "{ We employ dispersion-corrected density-functional theory to study the adsorption of tetrapyrrole 2H-porphine (2H-P) at Cu(111) and Ag(111). Various contributions to adsorbate-substrate and adsorbate-adsorbate interactions are systematically extracted to analyze the self-assembly behavior of this basic building block to porphyrin-based metal-organic nanostructures. This analysis reveals a surprising importance of substrate-mediated van der Waals interactions between 2H-P molecules, in contrast to negligible direct dispersive interactions. The resulting net repulsive interactions rationalize the experimentally observed tendency for single molecule adsorption. }",
    issn = {0021-9606},
    doi = {10.1063/1.4938259},
}

@phdthesis{Maurer2014,
        author = {Maurer, Reinhard Johann},
        title = {First-Principles Description of the Isomerization Dynamics of Surface-Adsorbed Molecular Switches},
        year = {2014},
        school = {Technische Universität München},
        pages = {212},
        abstract = {This work investigates adsorbed molecular switches on the example of coinage-metal adsorbed azobenzene molecules. Employing state-of-the-art first-principles methodology, an accurate model of the structure and energetics is established. With this model the loss of thermodynamic prerequisites to molecular function can be explained and future design strategies are discussed. On the basis of this a possible future approach towards an explicit dynamical simulation is proposed.},
        url = {https://mediatum.ub.tum.de/1190934},
}

@article{Troullier1991,
  title = {Efficient pseudopotentials for plane-wave calculations},
  author = {Troullier, N. and Martins, Jos\'e Lu\'{i}s},
  journal = {Phys. Rev. B},
  volume = {43},
  issue = {3},
  pages = {1993--2006},
  numpages = {0},
  year = {1991},
  month = {Jan},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.43.1993},
}

@article{Vanderbilt1990,
  title = {Soft self-consistent pseudopotentials in a generalized eigenvalue formalism},
  author = {Vanderbilt, David},
  journal = {Phys. Rev. B},
  volume = {41},
  issue = {11},
  pages = {7892--7895},
  numpages = {0},
  year = {1990},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.41.7892},
}

@article{Becke1990,
    author = {Becke, A. D. and Edgecombe, K. E.},
    title = "{A simple measure of electron localization in atomic and molecular systems}",
    journal = {The Journal of Chemical Physics},
    volume = {92},
    number = {9},
    pages = {5397-5403},
    year = {1990},
    month = {05},
    abstract = "{We introduce in this work a new approach to the identification of localized electronic groups in atomic and molecular systems. Our approach is based on local behavior of the Hartree–Fock parallel‐spin pair probability and is completely independent of unitary orbital transformations. We derive a simple ‘‘electron localization function’’ (ELF) which easily reveals atomic shell structure and core, binding, and lone electron pairs in simple molecular systems as well.}",
    issn = {0021-9606},
    doi = {10.1063/1.458517},
}

@article{Silvi1994,
author={Silvi, B.
and Savin, A.},
title={Classification of chemical bonds based on topological analysis of electron localization functions},
journal={Nature},
year={1994},
month={Oct},
day={01},
volume={371},
number={6499},
pages={683-686},
abstract={The definitions currently used to classify chemical bonds (in terms of bond order, covalency versus ionicity and so forth) are derived from approximate theories1--3 and are often imprecise. Here we outline a first step towards a more rigorous means of classification based on topological analysis of local quantum-mechanical functions related to the Pauli exclusion principle. The local maxima of these functions define 'localization attractors', of which there are only three basic types: bonding, non-bonding and core. Bonding attractors lie between the core attractors (which themselves surround the atomic nuclei) and characterize the shared-electron interactions. The number of bond attractors is related to the bond multiplicity. The spatial organization of localization attractors provides a basis for a well-defined classification of bonds, allowing an absolute characterization of covalency versus ionicity to be obtained from observable properties such as electron densities.},
issn={1476-4687},
doi={10.1038/371683a0},
}

@article{Jarvis2001,
author = {Jarvis, Emily A. A. and Carter, Emily A.},
title = "{Metallic Character of the Al2O3(0001)-(√31 × √31)R ± 9° Surface Reconstruction}",
journal = {The Journal of Physical Chemistry B},
volume = {105},
number = {18},
pages = {4045-4052},
year = {2001},
doi = {10.1021/jp003587c},
}