We present critic2, a program for the analysis of quantum-mechanical atomic and molecular interactions in periodic solids. This code, a greatly improved version of the previous critic program ...(Otero-de-la Roza et al., 2009), can: (i) find critical points of the electron density and related scalar fields such as the electron localization function (ELF), Laplacian, … (ii) integrate atomic properties in the framework of Bader’s Atoms-in-Molecules theory (QTAIM), (iii) visualize non-covalent interactions in crystals using the non-covalent interactions (NCI) index, (iv) generate relevant graphical representations including lines, planes, gradient paths, contour plots, atomic basins, … and (v) perform transformations between file formats describing scalar fields and crystal structures. Critic2 can interface with the output produced by a variety of electronic structure programs including WIEN2k, elk, PI, abinit, Quantum ESPRESSO, VASP, Gaussian, and, in general, any other code capable of writing the scalar field under study to a three-dimensional grid. Critic2 is parallelized, completely documented (including illustrative test cases) and publicly available under the GNU General Public License.
Program title: CRITIC2
Catalogue identifier: AECB_v2_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECB_v2_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: yes
No. of lines in distributed program, including test data, etc.: 11686949
No. of bytes in distributed program, including test data, etc.: 337020731
Distribution format: tar.gz
Programming language: Fortran 77 and 90.
Computer: Workstations.
Operating system: Unix, GNU/Linux.
Has the code been vectorized or parallelized?: Shared-memory parallelization can be used for most tasks.
Classification: 7.3.
Catalogue identifier of previous version: AECB_v1_0
Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 157
Nature of problem:
Analysis of quantum-chemical interactions in periodic solids by means of atoms-in-molecules and related formalisms.
Solution method:
Critical point search using Newton’s algorithm, atomic basin integration using bisection, qtree and grid-based algorithms, diverse graphical representations and computation of the non-covalent interactions index on a three-dimensional grid.
Additional comments:
!!! The distribution file for this program is over 330 Mbytes and therefore is not delivered directly when download or Email is requested. Instead a html file giving details of how the program can be obtained is sent. !!!
Running time:
Variable, depending on the crystal and the source of the underlying scalar field.
In the second article of the series, we present the Gibbs2 code, a Fortran90 reimplementation of the original Gibbs program Comput. Phys. Commun. 158 (2004) 57 for the calculation of ...pressure–temperature dependent thermodynamic properties of solids under the quasiharmonic approximation. We have taken advantage of the detailed analysis carried out in the first paper to implement robust fitting techniques. In addition, new models to introduce temperature effects have been incorporated, from the simple Debye model contained in the original article to a full quasiharmonic model that requires the phonon density of states at each calculated volume. Other interesting novel features include the empirical energy corrections, that rectify systematic errors in the calculation of equilibrium volumes caused by the choice of the exchange-correlation functional, the electronic contributions to the free energy and the automatic computation of phase diagrams. Full documentation in the form of a userʼs guide and a complete set of tests and sample data are provided along with the source code.
Program title:Gibbs2
Catalogue identifier: AEJI_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJI_v1_0.html
Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland
Licensing provisions: GNU General Public License, v3
No. of lines in distributed program, including test data, etc.: 936 087
No. of bytes in distributed program, including test data, etc.: 8 596 671
Distribution format: tar.gz
Programming language: Fortran90
Computer: Any running Unix/Linux
Operating system: Unix, GNU/Linux
Classification: 7.8
External routines: Part of the minpack, pppack and slatec libraries (downloaded from www.netlib.org) are distributed along with the program.
Nature of problem: Given the static E(V) curve, and possibly vibrational information such as the phonon density of states, calculate the equilibrium volume and thermodynamic properties of a solid at arbitrary temperatures and pressures in the framework of the quasiharmonic approximation.
Additional comments: A detailed analysis concerning the fitting of equations of state has been carried out in the first part of this article, and implemented in the code presented here.
Running time: The tests provided only take a few seconds to run.
► Calculation of thermodynamic properties from first principles data. ► Robust fitting of energy versus volume curves using averages of strain polynomials. ► Models for introducing ab initio temperature effects under the quasiharmonic approximation. ► A Fortran90 program implementing the techniques: Gibbs2.
We describe in this article the techniques developed for the robust treatment of the static energy versus volume theoretical curve in the new version of the quasi-harmonic model code Comput. Phys. ...Commun. 158 (2004) 57. An average of strain polynomials is used to determine, as precisely as the input data allow it, the equilibrium properties and the derivatives of the static E(V) curve. The method provides a conservative estimation of the error bars associated to the fitting procedure. We have also developed the techniques required for detecting, and eventually removing, problematic data points and jumps in the E(V) curve. The fitting routines are offered as an independent octave package, called AsturFit, with an open source license.
Program title:AsturFit
Catalogue identifier: AEIY_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIY_v1_0.html
Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland
Licensing provisions: GPL version 3
No. of lines in distributed program, including test data, etc.: 21 347
No. of bytes in distributed program, including test data, etc.: 620 496
Distribution format: tar.gz
Programming language: GNU Octave
Computer: Workstations
Operating system: Unix, GNU/Linux
Classification: 4.9
External routines: The GSL and OPTIM packages from the octaveforge site (http://octave.sourceforge.net/).
Nature of problem: Fit the total energy versus volume data of a solid to a continuous function and extract the equilibrium properties and the derivatives of the energy, with an estimation of the error introduced by the fitting procedure.
Solution method: The use of averages of strain polynomials allows a robust and reliable representation of the energy curve and its derivatives, together with a statistical estimation of the goodness of the calculated properties.
Additional comments: The techniques discussed have been implemented in Gibbs2, to be included with the second part of this article. Included here is the OCTAVE implementation of the routines, useful for interactive work and also for the creation of independent scripts. Some representative examples are included as test cases with a collection of data sets, test scripts, and model outputs.
Running time: Seconds at most in routine uses of the program. Special tasks like the bootstrap analysis may take up to some minutes.
► Robust fitting of energy versus volume curves using averages of strain polynomials. ► Error bars associated to the fits and thermodynamic properties. ► Detection of noise and problems in the input data. ► An octave package implementing the technique: Asturfit.
Halogen bonds are formed when a Lewis base interacts with a halogen atom in a different molecule, which acts as an electron acceptor. Due to its charge transfer component, halogen bonding is ...difficult to model using many common density-functional approximations because they spuriously overstabilize halogen-bonded dimers. It has been suggested that dispersion-corrected density functionals are inadequate to describe halogen bonding. In this work, we show that the exchange-hole dipole moment (XDM) dispersion correction coupled with functionals that minimize delocalization error (for instance, BH&HLYP, but also other half-and-half functionals) accurately model halogen-bonded interactions, with average errors similar to other noncovalent dimers with less charge-transfer effects. The performance of XDM is evaluated for three previously proposed benchmarks (XB18 and XB51 by Kozuch and Martin, and the set proposed by Bauzá et al.) spanning a range of binding energies up to ∼50 kcal/mol. The good performance of BH&HLYP-XDM is comparable to M06-2X, and extends to the “extreme” cases in the Bauzá set. This set contains anionic electron donors where charge transfer occurs even at infinite separation, as well as other charge transfer dimers belonging to the pnictogen and chalcogen bonding classes. We also show that functional delocalization error results in an overly delocalized electron density and exact-exchange hole. We propose intermolecular Bader delocalization indices as an indicator of both the donor–acceptor character of an intermolecular interaction and the delocalization error coming from the underlying functional.
The accurate calculation of chemical properties using density-functional theory (DFT) requires the use of a nearly complete basis set. In chemical systems involving hundreds to thousands of atoms, ...the cost of the calculations place practical limitations on the number of basis functions that can be used. Therefore, in most practical applications of DFT to large systems, there exists a basis-set incompleteness error (BSIE). In this article, we present the next iteration of the basis-set incompleteness potentials (BSIPs), one-electron potentials designed to correct for basis-set incompleteness error. The ultimate goal associated with the development of BSIPs is to allow the calculation of molecular properties using DFT with near-complete-basis-set results at a computational cost that is similar to a small basis set calculation. In this work, we develop BSIPs for 10 atoms in the first and second rows (H, B–F, Si–Cl) and 15 common basis sets of the Pople, Dunning, Karlsruhe, and Huzinaga types. Our new BSIPs are constructed to minimize BSIE in the calculation of reaction energies, barrier heights, noncovalent binding energies, and intermolecular distances. The BSIPs were obtained using a training set of 15 944 data points. The fitting approach employed a regularized linear least-squares method with variable selection (the LASSO method), which results in a much better fit to the training data than our previous BSIPs while, at the same time, reducing the computational cost of BSIP development. The proposed BSIPs are tested on various benchmark sets and demonstrate excellent performance in practice. Our new BSIPs are also transferable; i.e., they can be used to correct BSIE in calculations that employ density functionals other than the one used in the BSIP development (B3LYP). Finally, BSIPs can be used in any quantum chemistry program that have implemented effective-core potentials without changes to the software.
Inclusion of dispersion effects in density-functional calculations is now standard practice in computational chemistry. In many dispersion models, the dispersion energy is written as a sum of ...pairwise atomic interactions consisting of a damped asymptotic expansion from perturbation theory. There has been much recent attention drawn to the importance of "many-body" dispersion effects, which by their name imply limitations with a pairwise atomic expansion. In this perspective, we clarify what is meant by many-body dispersion, as this term has previously referred to two very different physical phenomena, here classified as electronic and atomic many-body effects. Atomic many-body effects refer to the terms in the perturbation-theory expansion of the dispersion energy involving more than two atoms, the leading contribution being the Axilrod-Teller-Muto three-body term. Conversely, electronic many-body effects refer to changes in the dispersion coefficients of the pairwise terms induced by the atomic environment. Regardless of their nature, many-body effects cause pairwise non-additivity in the dispersion energy, such that the dispersion energy of a system does not equal the sum of the dispersion energies of its atomic pairs taken in isolation. A series of examples using the exchange-hole dipole moment (XDM) method are presented to assess the relative importance of electronic and atomic many-body effects on the dispersion energy. Electronic many-body effects can result in variation in the leading-order
C
6
dispersion coefficients by as much as 50%; hence, their inclusion is critical for good performance of a pairwise asymptotic dispersion correction. Conversely, atomic many-body effects represent less than 1% of the total dispersion energy and are much less significant than higher-order (
C
8
and
C
10
) pairwise terms. Their importance has been previously overestimated through empirical fitting, where they can offset underlying errors stemming either from neglect of higher-order pairwise terms or from the base density functional.
"Many-body" dispersion can refer to two distinct phenomena, here termed electronic and atomic many-body effects, both of which cause the dispersion energy to be non-additive.
Recent progress in the accurate calculation of noncovalent interactions has enabled density-functional theory (DFT) to model systems relevant in biological and supramolecular chemistry. The ...application of DFT methods using atom-centered Gaussian basis sets to large systems is limited by the number of basis functions required to accurately model thermochemistry and, in particular, weak intermolecular interactions. Basis set incompleteness error (BSIE) arising from the use of incomplete basis sets leads to erroneous intermolecular energies, bond dissociation energies, and structures. In this article, we develop a correction for BSIE in DFT calculations using basis set incompleteness potentials (BSIP). BSIPs are atom-based one-electron potentials (ACPs) with the same functional form as effective core potentials (ECP) that are designed to correct the effects of BSIE in properties that are linear mappings of the energy. We present a systematic way of developing general, error-correcting ACPs and apply this technique to generate BSIPs for eight common elements in organic and biological systems (H, C, N, O, F, P, S, and Cl). Two BSIPs were optimized for use with the scaled MINI (MINIs) and MINIs(d) basis sets and were designed to correct for the impacts of BSIE on noncovalent binding energies and intra/intermolecular geometries. BSIPs developed for use with 6-31G*, pc-1, and 6-31+G** basis sets also correct for the effects of BSIE on bond dissociation energies, which enables the study of chemical reactions in very large systems. BSIPs can be used with any density functional in any electronic structure program that implements ECPs. Our BSIPs add very little to the computational cost provided an efficient ECP implementation is used. Our results support the use of BLYP-D3/MINIs-BSIP as a computationally inexpensive and more accurate alternative to other approaches (e.g., B3LYP/6-31G* and BP86/6-31G*) in protein and supramolecular structural studies.
The study of the structure and chemistry of biological systems with density-functional theory requires an accurate description of intermolecular interactions involving charged moieties. While ...dispersion-corrected functionals accurately model noncovalent interactions in neutral systems, a systematic study of the performance and errors associated with intermolecular interactions between charged fragments is missing. We undertake this study by examining the performance of a series of dispersion-corrected functionals with varying degrees of exact exchange for the side-chain protein interactions from the BioFragment Database (BFDb) of Burns et al. (the SSI set). In general, hybrid functionals with 20–30% exact exchange are accurate across the board, with the lowest mean absolute errors of 0.11 kcal/mol obtained from the 20% exact-exchange BLYP and PW86PBE hybrids coupled with the exchange-hole dipole moment (XDM) dispersion model. In addition, our analysis shows that functionals with higher exact-exchange fractions overestimate the electrostatic contributions to the binding energies, and that GGA functionals overestimate zwitterion binding energies due to delocalization error and overestimated charge transfer. In addition, the (quite large) repulsion in the dications is systematically overestimated by all functionals, and the trends for the monoanionic and dianionic dimers can be successfully explained by appealing to the ability of the underlying GGA to describe Pauli repulsion, as given by its exchange enhancement factor. Going beyond studies of biomolecules, this latter result has important implications for selecting appropriate GGA functionals for applications to ionic solids and layered materials containing anion–anion interactions.
Accurate energy ranking is a key facet to the problem of first-principles crystal-structure prediction (CSP) of molecular crystals. This work presents a systematic assessment of B86bPBE-XDM, a ...semilocal density functional combined with the exchange-hole dipole moment (XDM) dispersion model, for energy ranking using 14 compounds from the first five CSP blind tests. Specifically, the set of crystals studied comprises 11 rigid, planar compounds and 3 co-crystals. The experimental structure was correctly identified as the lowest in lattice energy for 12 of the 14 total crystals. One of the exceptions is 4-hydroxythiophene-2-carbonitrile, for which the experimental structure was correctly identified once a quasi-harmonic estimate of the vibrational free-energy contribution was included, evidencing the occasional importance of thermal corrections for accurate energy ranking. The other exception is an organic salt, where charge-transfer error (also called delocalization error) is expected to cause the base density functional to be unreliable. Provided the choice of base density functional is appropriate and an estimate of temperature effects is used, XDM-corrected density-functional theory is highly reliable for the energetic ranking of competing crystal structures.
In this article, we examine the ability of the exchange-hole dipole moment (XDM) model of dispersion to treat large supramolecular systems. We benchmark several XDM-corrected functionals on the S12L ...set proposed by Grimme, which comprises large dispersion-bound host–guest systems, for which back-corrected experimental and Quantum Monte Carlo (QMC) reference data are available. PBE-XDM coupled with the relatively economical and efficient pc-2-spd basis set gives excellent statistics (mean absolute error (MAE) = 1.5 kcal/mol), below the deviation between experimental and QMC data. When compared only to the (more accurate) QMC results, PBE-XDM/pc-2-spd (MAE = 1.2 kcal/mol) outperforms all other dispersion-corrected DFT results in the literature, including PBE-dDsC/QZ4P (6.2 kcal/mol), PBE-NL/def2-QZVP (4.7 kcal/mol), PBE-D2/def2-QZVP′ (3.5 kcal/mol), PBE-D3/def2-QZVP′(2.3 kcal/mol), M06-L/def2-QZVP (1.9 kcal/mol), and PBE-MBD (1.8 kcal/mol), with no significant bias (mean error (ME) = 0.04 kcal/mol). PBE-XDM/pc-2-spd gives binding energies relatively close to the complete basis-set limit and does not necessitate the use of counterpoise corrections, which facilitates its use. The dipole–quadrupole and quadrupole–quadrupole pairwise dispersion terms (C 8 and C 10) are critical for the correct description of the dimers. XDM-corrected functionals different from PBE that work well for small dimers do not yield good accuracy for the large supramolecular systems in the S12L, presenting errors that scale linearly with the dispersion contribution to the binding energy.
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