CRYSTAL23: A Program for Computational Solid State Physics and Chemistry

The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998. Nowadays, it is acknowledged by a broad community of solid state chemists and physicists that the inclusion of a fraction of Fock exchange in the exchange-correlation potential of the density functional theory is key to a better description of many properties of materials (electronic, magnetic, mechanical, spintronic, lattice-dynamical, etc.). Here, the main developments made to the program in the last five years (i.e., since the previous release, Crystal17) are presented and some of their most noteworthy applications reviewed.

Benchmark Density Functional Theory Approach for the Calculation of Bond Dissociation Energies of the M-O2 Bond: A Key Step in Water Splitting Reactions

A very fascinating aspect in quantum chemical research is to determine the accurate and cost-effective methods for the calculation of electronic and structural properties through a benchmark study. The current study focuses on the performance evaluation of density functional theory methods for the accurate measurement of bond dissociation energies (BDEs) of chemically important M-O₂ bonds in water splitting reactions. The BDE measurement has got noteworthy attention due to its importance in all areas of chemistry. For BDE measurements of M-O₂ bonds in five metal complexes with oxygen molecules, 14 density functionals (DFs) are chosen from seven classes of DFs with two series of mixed basis sets. A combination of pseudopotential and Pople basis sets [LANL2DZ & 6-31G(d) and SDD & 6-31+G(d)] are used as a series of mixed basis sets. The B3LYP-GD3BJ functional with LANL2DZ & 6-31G(d) gives outstanding results due to low deviations, error, and the best Pearson's correlation (R) between the experimental and theoretical data. Our study suggested an efficient, low-cost, precise, and accurate B3LYP-GD3BJ/LANL2DZ & 6-31G(d) level of theory for BDE of the M-O₂ bond, which may be useful for chemists working in the field of energy generation and utilization.

Controlling the aqueous growth of urea crystals with different growth inhibitors: a molecular-scale study

Molecular scale understanding of the mechanism of solution-mediated nucleation and the growth of crystalline materials in the presence of growth inhibitors together with the process parameters continues to attract the interest of the scientific community though much headway has been made in recent years. Growth inhibitors can be added to solution of a crystallizing parent molecule to alter the rate of growth of different crystal faces, size and shape of the crystalline materials. In this work, we investigated the effects of a number of shape-controlling inhibitors, such as acetone, biuret and biurea, on the growth kinetics of the various faces of aqueous-grown urea crystals as a means to predictably control the crystal growth morphology. We combined the adsorption energy landscape of various auxiliaries with the kinetics of the molecular growth processes to develop an analytical model to compute the rate of growth as a function of supersaturation and the additive concentration. The model relates the kinetic and thermodynamic aspects of the adsorption of the solute, solvent and additive to provide a quantitative description of the crystal growth. Ab initio periodic dispersion-corrected density functional theory using the hybrid exchange-correlation functional was employed to determine the interfacial structure of the adsorption of various auxiliaries at crystalline surfaces. The calculated adsorption energies of different auxiliaries were employed to examine the role played by these auxiliaries during the aqueous crystallization of urea crystals containing small amounts of additives. Our results showed that the growth of (110), (111) and (1̄1̄1̄) faces were nearly unaltered by the addition of moderate amounts of acetone as it has lower adsorption energies with the surfaces of these faces. Nevertheless, the presence of acetone in the solution reasonably impeded the growth of the (001) face. The addition of biuret or biurea in the solution led to a higher adsorption energy at (001) and (111) faces. Consequently, the low concentration of these additives severely obstructed the growth of (001) and (111) faces as most of the adsorption sites were occupied by these additives. On the other hand, these additives were weakly adsorbed at the (110) face and, hence, the growth of the (110) face largely remained unaltered. Moreover, unlike biuret, biurea considerably inhibited the growth of the (1̄1̄1̄) face. Our results are in agreement with the experimental and computational results reported in the literature.

r2SCAN-3c: A "Swiss army knife" composite electronic-structure method

The recently proposed r²SCAN meta-generalized-gradient approximation (mGGA) of Furness and co-workers is used to construct an efficient composite electronic-structure method termed r²SCAN-3c. To this end, the unaltered r²SCAN functional is combined with a tailor-made triple-ζ Gaussian atomic orbital basis set as well as with refitted D4 and geometrical counter-poise corrections for London-dispersion and basis set superposition error. The performance of the new method is evaluated for the GMTKN55 database covering large parts of chemical space with about 1500 data points, as well as additional benchmarks for non-covalent interactions, organometallic reactions, and lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r²SCAN-3c: It by far surpasses its predecessor B97-3c at only twice the cost and provides one of the best results of all semi-local density-functional theory (DFT)/QZ methods ever tested for the GMTKN55 database at one-tenth of the cost. Specifically, for reaction and conformational energies as well as non-covalent interactions, it outperforms prominent hybrid-DFT/QZ approaches at two to three orders of magnitude lower cost. Perhaps, the most relevant remaining issue of r²SCAN-3c is self-interaction error (SIE), owing to its mGGA nature. However, SIE is slightly reduced compared to other (m)GGAs, as is demonstrated in two examples. After all, this remarkably efficient and robust method is chosen as our new group default, replacing previous composite DFT and partially even expensive high-level methods in most standard applications for systems with up to several hundreds of atoms.

Vibrational Frequencies of Cerium-Oxide-Bound CO: A Challenge for Conventional DFT Methods

In ceria-based catalysis, the shape of the catalyst particle, which determines the exposed crystal facets, profoundly affects its reactivity. The vibrational frequency of adsorbed carbon monoxide (CO) can be used as a sensitive probe to identify the exposed surface facets, provided reference data on well-defined single crystal surfaces together with a definitive theoretical assignment exist. We investigate the adsorption of CO on the CeO_{2}(110) and (111) surfaces and show that the commonly applied DFT(PBE)+U method does not provide reliable CO vibrational frequencies by comparing with state-of-the-art infrared spectroscopy experiments for monocrystalline CeO_{2} surfaces. Good agreement requires the hybrid DFT approach with the HSE06 functional. The failure of conventional density-functional theory (DFT) is explained in terms of its inability to accurately describe the facet- and configuration-specific donation and backdonation effects that control the changes in the C─O bond length upon CO adsorption and the CO force constant. Our findings thus provide a theoretical basis for the detailed interpretation of experiments and open up the path to characterize more complex scenarios, including oxygen vacancies and metal adatoms.

Extension and evaluation of the D4 London-dispersion model for periodic systems

We present an extension of the DFT-D4 model [J. Chem. Phys., 2019, 150, 154122] for periodic systems. The main new ingredients are additional reference polarizabilities for highly-coordinated group 1-5 elements derived from pseudo-periodic electrostatically-embedded cluster calculations. To illustrate the performance of the updated method, several test cases are considered, for which we compare D4 to its predecessor D3(BJ), as well as to a comprehensive set of other dispersion-corrected methods. The largest improvements are observed for solid-state polarizabilities of 16 inorganic salts, where the D4 model achieves an unprecedented accuracy, surpassing its predecessor as well as other, computationally much more demanding approaches. For cell volumes and lattice energies of two sets of chemically diverse molecular crystals, the accuracy gain is less pronounced compared to the already excellently performing D3(BJ) method. For the challenging adsorption energies of small organic molecules on metallic as well as on ionic surfaces, DFT-D4 provides values in good agreement with experimental and/or high-level references. These results suggest the application of the proposed D4 model as a physically improved yet computationally efficient dispersion correction for standard DFT calculations as well as low-cost approaches like semi-empirical or even force-field models.

Elucidating the structure and dynamics of CO ad-layers on MgO surfaces

The combination of quantum-mechanical simulations and infrared absorption spectroscopy measurements provides a clear picture for a long standing puzzle in surface science: the actual structure and vibrational dynamics of the low-temperature ordered CO monolayer adsorbed on (001) MgO surfaces. The equilibrium structure of the commensurate (4 × 2) adsorbed phase consists of three CO molecules per primitive cell (surface coverage of 75%) located at two inequivalent sites: one molecule seats upright on top of a Mg site while two molecules, tilted off the normal to the surface, are symmetrically positioned relative to the upright one with anti-parallel projections on the surface. This configuration, long believed to be incompatible with measured polarization infrared spectra, is shown to reproduce all observed spectral features, including a new, unexpected one: the vanishing anharmonicity of CO stretching modes in the monolayer.

Silicate-mediated interstellar water formation: A theoretical study

Water is one of the most abundant molecules in the form of solid ice phase in the different regions of the interstellar medium (ISM). This large abundance cannot be properly explained by using only traditional low temperature gas-phase reactions. Thus, surface chemical reactions are believed to be major synthetic channels for the formation of interstellar water ice. Among the different proposals, hydrogenation of atomic O (i.e., 2H + O → H2O) is a chemically "simple" and plausible reaction toward water formation occurring on the surfaces of interstellar grains. Here, novel theoretical results concerning the formation of water adopting this mechanism on the crystalline (010) Mg2SiO4 surface (a unequivocally identified interstellar silicate) are presented. The investigated reaction aims to simulate the formation of the first water ice layer covering the silicate core of dust grains. Adsorption of the atomic O as a first step of the reaction has been computed, results indicating that a peroxo (O 2 2 - ) group is formed. The following steps involve the adsorption, diffusion and reaction of two successive H atoms with the adsorbed O atom. Results indicate that H diffusion on the surface has barriers of 4-6 kcal mol-1, while actual formation of OH and H2O present energy barriers of 22-23 kcal mol-1. Kinetic study results show that tunneling is crucial for the occurrence of the reactions and that formation of OH and H2O are the bottlenecks of the overall process. Several astrophysical implications derived from the theoretical results are provided as concluding remarks.

Carbon monoxide adsorption at forsterite surfaces as models of interstellar dust grains: An unexpected bathochromic (red) shift of the CO stretching frequency

Carbon monoxide (CO) is one of the most abundant species in the interstellar medium (ISM). In the colder regions of the ISM, it can directly adsorb onto exposed Mg cations of forsterite (Fo, Mg₂SiO₄), one of the main constituents of the dust grains. Its energetic of adsorption can strongly influence the chemico-physical evolution of cold interstellar clouds; thus, a detailed description of this process is desirable. We recently simulated the CO adsorption on crystalline Fo surfaces by computer ab initio methods and, surprisingly, reported cases where the CO stretching frequency underwent a bathochromic (red) shift (i.e., it is lowered with respect to the CO gas phase frequency), usually not experimentally observed for CO adsorbed onto oxides with non-d cations, like the present case. Here, we elucidate in deep when and under which conditions this case may happen and concluded that this red shift may be related to peculiar surface sites occurring at the morphologically complex Fo surfaces. The reasons for the red shift are linked to both the quadrupolar nature of the CO molecule and the role of dispersion interactions with surfaces of complex morphology. The present work, albeit speculative, suggests that, at variance with CO adsorption on simple oxides like MgO, the CO spectrum may exhibit features at lower frequencies than the reference gas frequency when CO is adsorbed on complex oxides, even in the absence of transition metal ions.

When the Surface Matters: Prebiotic Peptide-Bond Formation on the TiO2 (101) Anatase Surface through Periodic DFT-D2 Simulations

The mechanism of the peptide-bond formation between two glycine (Gly) molecules has been investigated by means of PBE-D2* and PBE0-D2* periodic simulations on the TiO₂ (101) anatase surface. This is a process of great relevance both in fundamental prebiotic chemistry, as the reaction univocally belongs to one of the different organizational events that ultimately led to the emergence of life on Earth, as well as from an industrial perspective, since formation of amides is a key reaction for pharmaceutical companies. The efficiency of the surface catalytic sites is demonstrated by comparing the reactions in the gas phase and on the surface. At variance with the uncatalyzed gas-phase reaction, which involves a concerted nucleophilic attack and dehydration step, on the surface these two steps occur along a stepwise mechanism. The presence of surface Lewis and Brönsted sites exerts some catalytic effect by lowering the free energy barrier for the peptide-bond formation by about 6 kcal mol^-1 compared to the gas-phase reaction. Moreover, the co-presence of molecules acting as proton-transfer assistants (i.e., H₂ O and Gly) provide a more significant kinetic energy barrier decrease. The reaction on the surface is also favorable from a thermodynamic standpoint, involving very large and negative reaction energies. This is due to the fact that the anatase surface also acts as a dehydration agent during the condensation reaction, since the outermost coordinatively unsaturated Ti atoms strongly anchor the released water molecules. Our theoretical results provide a comprehensive atomistic interpretation of the experimental results of Martra et al. (Angew. Chem. Int. Ed. 2014, 53, 4671), in which polyglycine formation was obtained by successive feedings of Gly vapor on TiO₂ surfaces in dry conditions and are, therefore, relevant in a prebiotic context envisaging dry and wet cycles occurring, at mineral surfaces, in a small pool.

Interaction of organic compounds with chondritic silicate surfaces. Atomistic insights from quantum chemical periodic simulations

The interaction of 14 different probe organic molecules with the crystalline (010) forsterite Mg₂SiO₄ surface has been studied at quantum chemical level by means of B3LYP-D2* periodic simulations. The probe molecules are representatives of the class of soluble organic compounds found in carbonaceous meteorites, namely: aliphatic and aromatic hydrocarbons, alcohols, carbonyl compounds, amines, amides, nitrogen heterocycles, carboxylic and hydroxycarboxylic acids, sulfonic and phosphonic acids, amino acids, and carbohydrates. With the exception of the aliphatic and aromatic hydrocarbons, the interaction takes place mainly between the O and N electron donor atoms of the molecules and the outermost Mg surface cations, and/or by hydrogen bonds of H atoms of the molecules with O surface atoms. Dispersion also contributes to the final interaction energies. Each surface/molecule complex has also been characterized by computing its harmonic vibrational spectrum, in which the most significant frequency perturbations caused by the surface interaction are described. With the calculated interaction energies, a trend of the intrinsic affinity of the probe molecules with the silicate surface has been obtained. However, this affinity scale does not correlate with the experimental abundances of the class of compounds found in the Murchison meteorite. A brief discussion of this lack of correlation and the factors that can help us to understand the abundances is provided.

On the structure of superbasic (MgO)n sites solvated in a faujasite zeolite

Theory and experiment reveal the structure of magnesium oxide nanoclusters in a superbasic faujasite zeolite.

Role of tailor-made additives in controlling vapour growth asymmetry along the polar axis of α-resorcinol crystals: a molecular-scale study

The role of different tailor-made additives and conformers of resorcinol have been investigated to elucidate the mechanism of unidirectional vapour growth of α-resorcinol crystal. Our results show the growth anisotropy is linked with the surface stabilization of the slow growing face.

Nucleobases-decorated boron nitride nanoribbons for electrochemical biosensing: a dispersion-corrected DFT study

The study suggests that BNNRs may act as superior material for future sensing and DNA sequencing applications.

First-principles calculations of the electronic structure and bonding in metal cluster-fullerene materials considered within the superatomic framework

Inspired by recent success of synthesizing cluster assembled compounds we address the question to what extent the three new materials [Co₆Se₈(PEt₃)₆][C₆₀]₂, [Cr₆Te₈(PEt₃)₆][C₆₀]₂, and [Ni₉Te₆(PEt₃)₈]C₆₀, upon forming bulk compounds, imitate atomic analogues. Although experimental results suggest the latter, a theoretical approach is the method of choice for offering a conclusive answer and for studying the actual superatomic character. The concept of superatoms for describing atom-imitating clusters is very intriguing since it allows chemists to apply their chemical intuition - a useful tool for predicting new materials - when it comes to inter-cluster reactions. Thus, we systematically study the lattice structure, the intercluster binding, and the electronic structure by density functional theory and assess them in terms of their superatomic features. We show that collective properties arise upon bulk formation, which promotes arguments for the formation of solids in which the constituent clusters have a superatomic character that determines some form of chemical bonding. Additionally, we find evidence for the formation of superatomic states. Unfortunately, however, due to the mixing of electronic states of transition metals and chalcogen atoms, no typical electronic shell closing in the cluster cores can be identified.

Structural, electronic, magnetic and chemical properties of B-, C- and N-doped MgO(001) surfaces

Doping of simple oxide materials can give rise to new exciting physical and chemical properties and open new perspectives for a variety of possible applications. Here we use density functional theory calculations to investigate the B-, C- and N-doped MgO(001) surfaces. We have found that the investigated dopants induce magnetization of the system amounting to 3, 2 and 1 μB for B, C and N, respectively. The dopants are found to be in the X(2-) state and tend to segregate to the surface. These impurity sites also present the centers of altered chemical reactivity. We probe the chemisorption properties of the doped MgO(001) surfaces with the CO molecule and atomic O. The adsorption of CO is much stronger on B- and C-doped MgO(001) compared to pure MgO(001) as the impurity sites serve as potent electron donors. The situation is similar to the case of atomic oxygen, for which we find the adsorption energy of -8.78 eV on B-doped MgO(001). The surface reactivity changes locally around the dopant atom, which is mainly restricted to its first coordination shell. The presented results suggest doped MgO as a versatile multifunctional material with possible use as an adsorbent or a catalyst.

Theoretical study of adsorption of amino acids on graphene and BN sheet in gas and aqueous phase with empirical DFT dispersion correction

Suitability of BN nanosheet/graphene towards the adsorption of amino acids established by dispersion corrected DFT calculations.

First-principle modelling of forsterite surface properties: Accuracy of methods and basis sets

The seven main crystal surfaces of forsterite (Mg2 SiO4 ) were modeled using various Gaussian-type basis sets, and several formulations for the exchange-correlation functional within the density functional theory (DFT). The recently developed pob-TZVP basis set provides the best results for all properties that are strongly dependent on the accuracy of the wavefunction. Convergence on the structure and on the basis set superposition error-corrected surface energy can be reached also with poorer basis sets. The effect of adopting different DFT functionals was assessed. All functionals give the same stability order for the various surfaces. Surfaces do not exhibit any major structural differences when optimized with different functionals, except for higher energy orientations where major rearrangements occur around the Mg sites at the surface or subsurface. When dispersions are not accounted for, all functionals provide similar surface energies. The inclusion of empirical dispersions raises the energy of all surfaces by a nearly systematic value proportional to the scaling factor s of the dispersion formulation. An estimation for the surface energy is provided through adopting C6 coefficients that are more suitable than the standard ones to describe O-O interactions in minerals. A 2 × 2 supercell of the most stable surface (010) was optimized. No surface reconstruction was observed. The resulting structure and surface energy show no difference with respect to those obtained when using the primitive cell. This result validates the (010) surface model here adopted, that will serve as a reference for future studies on adsorption and reactivity of water and carbon dioxide at this interface.

Interstellar H adsorption and H₂ formation on the crystalline (010) forsterite surface: a B3LYP-D2* periodic study

The physisorption/chemisorption of atomic hydrogen on a slab model of the Mg2SiO4 forsterite (010) surface mimicking the interstellar dust particle surface has been modeled using a quantum mechanical approach based on periodic B3LYP-D2* density functional calculations (DFT) combined with flexible polarized Gaussian type basis sets, which allows a balanced description of the hydrogen/surface interactions for both minima and activated complexes. Physisorption of hydrogen is barrierless, very weak and occurs either close to surface oxygen atoms or on Mg surface ions. The contribution of dispersion interactions accounts for almost half of the adsorption energy. Both the hydrogen adsorption energy and barrier to hydrogen jump between equivalent surface sites are overestimated compared to experimental results meant to simulate the interstellar conditions in the laboratory. The hydrogen atom exclusively chemisorbs at the oxygen site of the forsterite (010) surface, forming a SiOH surface group and its spin density being entirely transferred to the neighboring Mg ion. Barrier for chemisorption allows rapid attachment of H at the surface at 100 K, but prevents the same process from occurring at 10 K. From this H-chemisorbed state, the second hydrogen chemisorption mainly occurs on the neighboring Mg ion, thus forming a Mg-H surface group, giving rise to a surface species stabilized by favorable electrostatic interactions between the OHH-Mg pair. The formation of molecular hydrogen at the (010) forsterite surface adopting a Langmuir-Hinshelwood mechanism takes place either starting from two physisorbed H atoms with an almost negligible kinetic barrier through a spin-spin coupling driven reaction or from two chemisorbed H atoms with a barrier surmountable even at T higher than 10 K. We also suggest that a nanosized model of the interstellar dust built from a replica of the forsterite unit cell is able to adsorb half the energy released by the H2 formation by increasing its temperature by about 50 K which could then radiate in about 0.02 s.

The effect of electron correlation on the adsorption of hydrogen fluoride and water on magnesium fluoride surfaces

Periodic DFT and local MP2 calculations elucidate the role of electron correlation in the adsorption of H₂O and HF on MgF₂ surfaces.

Accurate adsorption energies of small molecules on oxide surfaces: CO-MgO(001)

A hybrid MP2:DFT + D optimization method is applied using a 3 × 3 × 2 cluster model (Mg9O9) embedded in a 4 × 4 × 4 slab model. The calculated CO-Mg(2+) distance is 248 pm, and the calculated CO frequency (blue) shift is 20 cm(-1), 6 cm(-1) larger than the experimental value. For the structure obtained, MP2 calculations with basis set extrapolation on a series of cluster models of increasing size are performed. Taking into account the difference in the periodic limit at the DFT + D level, 20.9 ± 0.7 kJ mol(-1) is obtained as the estimate for the full periodic MP2 limit for the energy of CO desorption from the MgO(001) surface. CCSD(T) corrections are evaluated for the Mg9O9 cluster model using an augmented double-zeta basis set. Basis set extension effects are examined for smaller models. For a loading of Θ = 1/8, the estimated CCSD(T) value is 21.0 ± 1.0 kJ mol(-1), which is 0.4 ± 1.0 kJ mol(-1) larger than the (electronic) desorption energy derived in this study from TPD desorption barriers reported in the literature.

System-dependent dispersion coefficients for the DFT-D3 treatment of adsorption processes on ionic surfaces

Dispersion-corrected density functional theory calculations (DFT-D3) were performed for the adsorption of CO on MgO and C(2) H(2) on NaCl surfaces. An extension of our non-empirical scheme for the computation of atom-in-molecules dispersion coefficients is proposed. It is based on electrostatically embedded M(4)X(4) (M=Na, Mg) clusters that are used in TDDFT calculations of dynamic dipole polarizabilities. We find that the C(MM)(6) dispersion coefficients for bulk NaCl and MgO are reduced by factors of about 100 and 35 for Na and Mg, respectively, compared to the values of the free atoms. These are used in periodic DFT calculations with the revPBE semi-local density functional. As demonstrated by calculations of adsorption potential energy curves, the new C(6) coefficients lead to much more accurate energies (E(ads)) and molecule-surface distances than with previous DFT-D schemes. For NaCl/C(2) H(2) we obtained at the revPBE-D3(BJ) level a value of E(ads) =-7.4 kcal mol(-1) in good agreement with experimental data (-5.7 to -7.1 kcal mol(-1)). Dispersion-uncorrected DFT yields an unbound surface state. For the MgO/CO system, the computed revPBE-D3(BJ) value of E(ads) =-4.1 kcal mol(-1) is also in reasonable agreement with experimental results (-3.0 kcal mol(-1)) when thermal corrections are taken into account. Our new dispersion correction also improves computed lattice constants of the bulk systems significantly compared to plain DFT or previous DFT-D results. The extended DFT-D3 scheme also provides accurate non-covalent interactions for ionic systems without empirical adjustments and is suggested as a general tool in surface science.