Solid-state quantum chemistry with ΘΦ (ThetaPhi): Spin-liquids, superconductors, and magnetic superstructures made computationally available.

We present a standalone ΘΦ (ThetaPhi) package capable to read the results of ab initio DFT/PAW quantum-chemical solid-state calculations processed through various tools projecting them to the atomic basis states as an input and to perform on top of this an analysis of so derived electronic structure which includes (among other options) the possibility to obtain a superconducting (Bardeen-Cooper-Schrieffer, BCS), spin-liquid (resonating valence bond, RVB) states/phases as solutions of the electronic structure problem along with the magnetically ordered phases with an arbitrary pitch (magnetic superstructure) vector. Remarkably, different solutions of electronic-structure problems come out as temperature-dependent (exemplified by various superconducting and spin-liquid phases) which feature is as well implemented. All that is exemplified by model calculations on 1D chain, 2D square lattice as well as on more realistic superconducting doped graphene, magnetic phases of iron, and spin-liquid and magnetically ordered states of a simplest nitrogen-based copper pseudo-oxide, CuNCN, resembling socalled metal-oxide framework (MOF) phases by the atomic interlinkage.

Local perturbations of periodic systems. Chemisorption and point defects by GoGreenGo.

We present a software package GoGreenGo-an overlay aimed to model local perturbations of periodic systems due to either chemisorption or point defects. The electronic structure of an ideal crystal is obtained by worldwide-distributed standard quantum physics/chemistry codes, and then processed by various tools performing projection to atomic orbital basis sets. Starting from this, the perturbation is addressed by GoGreenGo with use of the Green's functions formalism, which allows evaluating its effect on the electronic structure, density matrix, and energy of the system. In the present contribution, the main accent is made on processes of chemical nature, such as chemisorption or doping. We address a general theory and its computational implementation supported by a series of test calculations of the electronic structure perturbations for benchmark model solids: simple, face-centered, and body-centered cubium systems. In addition, more realistic problems of local perturbations in graphene lattice, such as lattice substitution, vacancy, and "on-top" chemisorption, are considered.

Relative stability of diamond and graphite as seen through bonds and hybridizations.

The relative stability of the two most important forms of elemental carbon, diamond and graphite, is readdressed from a newly developed perspective as derived from historically well-known roots. Unlike other theoretical studies mostly relying on numerical methods, we consider an analytical model to gain fundamental insight into the reasons for the quasi-degeneracy of diamond and graphite despite their extremely different covalent bonding patterns. We derive the allotropes' relative energies and provide a qualitative picture predicting a quasi-degenerate electronic ground state for graphite (graphene) and diamond at zero temperature. Our approach also gives numerical estimates of the energy difference and interatomic separations in good agreement with experimental data and recent results of hybrid DFT modeling, although obtained with a much smaller numerical but highly transparent effort. An attempt to extend this treatment to the lowest energy allotropes of silicon proves to be successful as well.

Deductive molecular mechanics of four-coordinated carbon allotropes.

Deductive molecular mechanics is applied to study the relative stability and mechanical properties of carbon allotropes containing isolated σ-bonds. Our approach demonstrates numerical accuracy comparable to that of density-functional theory, but achieved with dramatically lower computational costs. We also show how the relative stability of carbon allotropes may be explained from a chemical perspective using the concept of strain of bonds (or rings) in close analogy to theoretical organic chemistry. Besides that, the role of nonbonding electrostatic interactions as the key factor causing the differences in mechanical properties (in particular, hardness) of the allotropes is emphasized and discussed. The ADAMAS program developed on the basis of this study fairly reproduces spatial and electronic structure as well as mechanical properties of carbon allotropes.

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

The computer program LOBSTER (Local Orbital Basis Suite Towards Electronic-Structure Reconstruction) enables chemical-bonding analysis based on periodic plane-wave (PAW) density-functional theory (DFT) output and is applicable to a wide range of first-principles simulations in solid-state and materials chemistry. LOBSTER incorporates analytic projection routines described previously in this very journal [J. Comput. Chem. 2013, 34, 2557] and offers improved functionality. It calculates, among others, atom-projected densities of states (pDOS), projected crystal orbital Hamilton population (pCOHP) curves, and the recently introduced bond-weighted distribution function (BWDF). The software is offered free-of-charge for non-commercial research. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Analytic projection from plane-wave and PAW wavefunctions and application to chemical-bonding analysis in solids.

Quantum-chemical computations of solids benefit enormously from numerically efficient plane-wave (PW) basis sets, and together with the projector augmented-wave (PAW) method, the latter have risen to one of the predominant standards in computational solid-state sciences. Despite their advantages, plane waves lack local information, which makes the interpretation of local densities-of-states (DOS) difficult and precludes the direct use of atom-resolved chemical bonding indicators such as the crystal orbital overlap population (COOP) and the crystal orbital Hamilton population (COHP) techniques. Recently, a number of methods have been proposed to overcome this fundamental issue, built around the concept of basis-set projection onto a local auxiliary basis. In this work, we propose a novel computational technique toward this goal by transferring the PW/PAW wavefunctions to a properly chosen local basis using analytically derived expressions. In particular, we describe a general approach to project both PW and PAW eigenstates onto given custom orbitals, which we then exemplify at the hand of contracted multiple-ζ Slater-type orbitals. The validity of the method presented here is illustrated by applications to chemical textbook examples-diamond, gallium arsenide, the transition-metal titanium-as well as nanoscale allotropes of carbon: a nanotube and the C60 fullerene. Remarkably, the analytical approach not only recovers the total and projected electronic DOS with a high degree of confidence, but it also yields a realistic chemical-bonding picture in the framework of the projected COHP method.

Effective Hamiltonian Crystal Field as applied to magnetic exchange parameters in µ-oxo-bridged Cr(III) dimers.

The calculation of the 3d-intrashell excitations in coordination compounds by means of the Effective Hamiltonian Crystal Field (EHCF) method is generalized to their polynuclear analogues to properly describe several open d-shells and their magnetic interactions. This challenge requires improving the precision of ca. 1000 cm(-1) to ca. 100 cm(-1) characteristic for the spin-reorientation energies. The method follows the successful EHCF paradigm, namely, the concerted usage of McWeeny's group-function approximation and Löwdin's partitioning technique, for an effective description of the multicenter d-systems. The novel approach is implemented in the MagAîxTic package and validated against a series of binuclear complexes of Cr(III) featuring µ-oxygen superexchange paths. The trends in the compound series in terms of exchange constants are correctly reproduced, despite differing details of composition and structure, and the numerical results agree by order of magnitude with available experimental data and other theoretical methods.

High-resolution neutron diffraction study of CuNCN: new evidence of structure anomalies at low temperature.

Copper carbodiimide (CuNCN) is the nitrogen-containing analogue of cupric oxide. Based on high-resolution neutron-diffraction data, CuNCN's lattice parameters are derived as a function of the temperature. In accordance with a recent synchrotron study, a clear trend in the cell parameter a is observed accompanying the changing magnetic behavior. With decreasing temperature, a slowly decreases to a minimum at ~100 K after which it rises again. The same trend-albeit more pronounced-is observed for the c lattice parameter at ~35 K. The herein presented neutron powder-diffraction data also support the conjectured sequence of transitions from the high-temperature one-dimensional resonating valence-bond (RVB) state to a transient two-dimensional RVB state and eventually, at lowest temperatures, into another two-dimensional RVB state, presumably the ground state.

Electronic Structure and d-d Spectrum of Metal-Organic Frameworks with Transition-Metal Ions.

The electronic structure of metal-organic frameworks (MOFs) containing transition metal (TM) ions represents a significant and largely unresolved computational challenge due to limited solutions to the quantitative description of low-energy excitations in open d-shells. These excitations underpin the magnetic and sensing properties of TM MOFs, including the observed remarkable spin-crossover phenomenon. We introduce the effective Hamiltonian of crystal field approach to study the d-d spectrum of MOFs containing TM ions; this is a hybrid QM/QM method based on the separation of crystal structure into d- and s,p-subsystems treated at different levels of theory. We test the method on model frameworks, carbodiimides, and hydrocyanamides and a series of M-MOF-74 (M = Fe, Co, Ni) and compare the computational predictions to experimental data on magnetic properties and Mössbauer spectra.

Phenomenological model of spin crossover in molecular crystals as derived from atom-atom potentials.

The method of atom-atom potentials, previously applied to the analysis of pure molecular crystals formed by either low-spin (LS) or high-spin (HS) forms (spin isomers) of Fe(II) coordination compounds (Sinitskiy et al., Phys. Chem. Chem. Phys., 2009, 11, 10983), is used to estimate the lattice enthalpies of mixed crystals containing different fractions of the spin isomers. The crystals under study were formed by LS and HS isomers of Fe(phen)(2)(NCS)(2) (phen = 1,10-phenanthroline), Fe(btz)(2)(NCS)(2) (btz = 5,5',6,6'-tetrahydro-4H,4'H-2,2'-bi-1,3-thiazine), and Fe(bpz)(2)(bipy) (bpz = dihydrobis(1-pyrazolil)borate, and bipy = 2,2'-bipyridine). For the first time the phenomenological parameters Γ pertinent to the Slichter-Drickamer model (SDM) of several materials were independently derived from the microscopic model of the crystals with use of atom-atom potentials of intermolecular interaction. The accuracy of the SDM was checked against the numerical data on the enthalpies of mixed crystals. Fair semiquantitative agreement with the experimental dependence of the HS fraction on temperature was achieved with use of these values. Prediction of trends in Γ values as a function of chemical composition and geometry of the crystals is possible with the proposed approach, which opens a way to rational design of spin crossover materials with desired properties.

d-d Spectra of transition-metal carbodiimides and hydrocyanamides as derived from many-particle effective Hamiltonian calculations.

We apply the local many-particle method of the Effective Hamiltonian of Crystal Field (EHCF) to analyze the magnetic ground state and the low-energy excitation spectra of the transition-metal carbodiimides MNCN with M = Fe-Ni. Experimentally, these materials represent a uniform group of (high-spin) antiferromagnetic, optically transparent, colored insulators with absorption lines in the visible spectrum. These findings are fully supported by the EHCF numerical modeling. In all three cases, we arrive at high-spin ground states in agreement with the results of previous magnetic measurements as well as the presence of the d-d intrashell transitions for the visible absorption spectra. Remarkably enough, the EHCF approach resolves the controversial case of FeNCN which was earlier predicted to be metallic by density-functional theory even when including explicit electronic correlation (GGA+U). We also address the ground state and the low-energy excitation spectra of the transition-metal hydrocyanamides of the general formula M(NCNH)(2) with M = Fe-Ni, another uniform group of optically transparent colored insulators. EHCF also arrives at high-spin ground states and visible d-d intrashell transitions.

Crystal orbital Hamilton population (COHP) analysis as projected from plane-wave basis sets.

Simple, yet predictive bonding models are essential achievements of chemistry. In the solid state, in particular, they often appear in the form of visual bonding indicators. Because the latter require the crystal orbitals to be constructed from local basis sets, the application of the most popular density-functional theory codes (namely, those based on plane waves and pseudopotentials) appears as being ill-fitted to retrieve the chemical bonding information. In this paper, we describe a way to re-extract Hamilton-weighted populations from plane-wave electronic-structure calculations to develop a tool analogous to the familiar crystal orbital Hamilton population (COHP) method. We derive the new technique, dubbed "projected COHP" (pCOHP), and demonstrate its viability using examples of covalent, ionic, and metallic crystals (diamond, GaAs, CsCl, and Na). For the first time, this chemical bonding information is directly extracted from the results of plane-wave calculations.

Hydrogen-bond networks in water clusters (H2O)20: an exhaustive quantum-chemical analysis.

Water aggregates allow for numerous configurations due to different distributions of hydrogen bonds. The total number of possible hydrogen-bond networks is very large even for medium-sized systems. We demonstrate that targeted ultra-fast methods of quantum chemistry make an exhaustive analysis of all configurations possible. The cage of (H(2)O)(20) in the form of the pentagonal dodecahedron is a common motif in water structures. We calculated the spatial and electronic structure of all hydrogen-bond configurations for three systems: idealized cage (H(2)O)(20) and defect cages with one or two hydrogen bonds broken. More than 3 million configurations studied provide unique data on the structure and properties of water clusters. We performed a thorough analysis of the results with the emphasis on the cooperativity in water systems and the structure-property relations.

Synthesis, characterization, and quantum-chemical studies of Ni(CN)2MX (M = Rb, Cs; X = Cl, Br).

A new series of coordination-network compounds containing Ni(CN)(2) and MX (M = Rb, Cs; X = Cl, Br) quasi two-dimensional sheets has been synthesized and structurally characterized. The tetragonal crystal structure (I4/mmm, no. 139) can be derived from the distorted perovskite type. Chemically, the Lewis-acidic Ni(CN)(2) moieties accept halide ligands, resulting both in slightly elongated [Ni(NC)(4)X(2)](4-) octahedra and strongly elongated [Ni(CN)(4)X(2)](4-) octahedra that are charge-balanced by M(+) cations. Quantum-chemical calculations of the effective Hamiltonian crystal field (EHCF) type indicate the simultaneous presence of high- and low-spin Ni(2+) in a 1:1 ratio, in agreement with GGA+U and UV studies reported here. Our magnetic susceptibility data also corroborate the theoretical findings. An analysis of the magnetic superexchange paths in the new series of compounds is performed as well as that of the tentative magnetic state of the series.

Electronic and magnetic structure of transition-metal carbodiimides by means of GGA+U theory.

The electronic structures and magnetic properties of MNCN (M = Fe, Co, and Ni) have been investigated by density-functional theory including explicit electronic correlation through an ad hoc Coulomb potential (GGA+U). The results evidence CoNCN and NiNCN as type-II anti-ferromagnetic semiconductors (that is, intralayer ferromagnetic and interlayer anti-ferromagnetic), in accordance with experimental observations. Just like the prototype MnNCN, the MNCN phases, with M = Ni and Co, thus resemble the corresponding MO monoxides with respect to their magnetic and transport properties. By contrast, FeNCN remains (semi)metallic even upon applying a strong Coulomb correlation potential. This, most probably, is in contradiction with its observed optical transparency and expected insulating behavior and points toward a serious density-functional theory problem.

Modeling molecular crystals formed by spin-active metal complexes by atom-atom potentials.

We apply the atom-atom potentials to molecular crystals of iron(II) complexes with bulky organic ligands. The crystals under study are formed by low-spin or high-spin molecules of Fe(phen)(2)(NCS)(2) (phen = 1,10-phenanthroline), Fe(btz)(2)(NCS)(2) (btz = 5,5',6,6'-tetrahydro-4H,4'H-2,2'-bi-1,3-thiazine), and Fe(bpz)(2)(bipy) (bpz = dihydrobis(1-pyrazolil)borate, and bipy = 2,2'-bipyridine). All molecular geometries are taken from the X-ray experimental data and assumed to be frozen. The unit cell dimensions and angles, positions of the centers of masses of molecules, and the orientations of molecules corresponding to the minimum energy at 1 atm and 1 GPa are calculated. The optimized crystal structures are in a good agreement with the experimental data. Sources of the residual discrepancies between the calculated and experimental structures are discussed. The intermolecular contributions to the enthalpy of the spin transitions are found to be comparable with its total experimental values. It demonstrates that the method of atom-atom potentials is very useful for modeling molecular crystals undergoing the spin transitions.

Instrumental resolution as a function of scattering angle and wavelength as exemplified for the POWGEN instrument.

The method of angular- and wavelength-dispersive (e.g. two-dimensional) Rietveld refinement is a new and emerging tool for the analysis of neutron diffraction data measured at time-of-flight instruments with large area detectors. Following the approach for one-dimensional refinements (using either scattering angle or time of flight), the first step at each beam time cycle is the calibration of the instrument including the determination of instrumental contributions to the peak shape variation to be expected for diffraction patterns measured by the users. The aim of this work is to provide the users with calibration files and - for the later Rietveld refinement of the measured data - with an instrumental resolution file (IRF). This article will elaborate on the necessary steps to generate such an IRF for the angular- and wavelength-dispersive case, exemplified for the POWGEN instrument. A dataset measured on a standard diamond sample is used to extract the profile function in the two-dimensional case. It is found that the variation of reflection width with 2θ and λ can be expressed by the standard equation used for evaluating the instrumental resolution, which yields a substantially more fundamental approach to the parameterization of the instrumental contribution to the peak shape. Geometrical considerations of the POWGEN instrument and sample effects lead to values for Δθ, Δt and ΔL that yield a very good match to the extracted FWHM values. In a final step the refinement results are compared with the one-dimensional, i.e. diffraction-focused, case.

Atomic motions in the layered copper pseudochalcogenide CuNCN indicative of a quantum spin-liquid scenario.

We explore the thermodynamic properties of the layered copper(II) carbodiimide CuNCN by heat-capacity measurements and investigate the corresponding thermal atomic motions by means of neutron powder diffraction as well as inelastic neutron scattering. The experiments are complemented by a combination of density-functional calculations, phonon analysis and analytic theory. The existence of a soft flexural mode-bending of the layers, characteristic for the material structure-is established in the phonon spectrum of CuNCN by giving characteristic temperature-dependent contributions to the heat capacity and atomic displacement parameters. The agreement with the neutron data allows us to extract a residual-on top of the lattice-presumably spinon contribution to the heat capacity [Formula: see text], speaking in favor of the spin-liquid picture of the electronic phases of CuNCN.

A Rietveld refinement method for angular- and wavelength-dispersive neutron time-of-flight powder diffraction data.

This paper introduces a two-dimensional extension of the well established Rietveld refinement method for modeling neutron time-of-flight powder diffraction data. The novel approach takes into account the variation of two parameters, diffraction angle 2θ and wavelength λ, to optimally adapt to the varying resolution function in diffraction experiments. By doing so, the refinement against angular- and wavelength-dispersive data gets rid of common data-reduction steps and also avoids the loss of high-resolution information typically introduced by integration. In a case study using a numerically simulated diffraction pattern of Rh0.81Fe3.19N taking into account the layout of the future POWTEX instrument, the profile function as parameterized in 2θ and λ is extracted. As a proof-of-concept, the resulting instrument parameterization is then utilized to perform a typical refinement of the angular- and wavelength-dispersive diffraction pattern of CuNCN, yielding excellent residuals within feasible computational efforts. Another proof-of-concept is carried out by applying the same approach to a real neutron diffraction data set of CuNCN obtained from the POWGEN instrument at the Spallation Neutron Source in Oak Ridge. The paper highlights the general importance of the novel approach for data analysis at neutron time-of-flight diffractometers and its possible inclusion within existing Rietveld software packages.