Comment on “Assessment of exchange correlation functionals” [A.J. Cohen, N.C. Handy, Chem. Phys. Lett. 316 (2000) 160–166]

"On-the-fly" Crystal : How to reliably and automatically characterize and construct potential energy surfaces

In this work, the Crystal  code, developed previously by the authors to find "holes" as well as legitimate transition states in existing potential energy surface (PES) functions [JPC Lett. 11, 6468 (2020)], is retooled to perform on-the-fly "direct dynamics"-type PES explorations, as well as automatic construction of new PES functions. In all of these contexts, the chief advantage of Crystal  over other methods is its ability to globally map the PES, thereby determining the most relevant regions of configuration space quickly and reliably-even when the dimensionality is rather large. Here, Crystal  is used to generate a uniformly spaced grid of density functional theory (DFT) or ab initio points, truncated over the relevant regions, which can then be used to either: (a) hone in precisely on PES features such as minima and transition states, or; (b) create a new PES function automatically, via interpolation. Proof of concept is demonstrated via application to three molecular systems: water (H2 O), (reduced-dimensional) methane (CH4 ), and methylene imine (CH2 NH).

SOLUBILITY OF Ca(II), Ni(II), Nd(III) AND Pu(IV) IN THE PRESENCE OF PROXY LIGANDS FOR THE DEGRADATION OF POLYACRYLONITRILE IN CEMENTITIOUS SYSTEMS

The solubility of Ca(OH)2(cr), β-Ni(OH)2(cr), Nd(OH)3(s) and PuO2(ncr, hyd) was investigated in cement porewater solutions containing glutarate (GTA), a-hydroxyisobutarate (HIBA) and 3-hydroxybutarate (HBA). These ligands were proposed as probable degradation...

Machine learning of free energies in chemical compound space using ensemble representations: Reaching experimental uncertainty for solvation

Free energies govern the behavior of soft and liquid matter, and improving their predictions could have a large impact on the development of drugs, electrolytes, or homogeneous catalysts. Unfortunately, it is challenging to devise an accurate description of effects governing solvation such as hydrogen-bonding, van der Waals interactions, or conformational sampling. We present a Free energy Machine Learning (FML) model applicable throughout chemical compound space and based on a representation that employs Boltzmann averages to account for an approximated sampling of configurational space. Using the FreeSolv database, FML's out-of-sample prediction errors of experimental hydration free energies decay systematically with training set size, and experimental uncertainty (0.6 kcal/mol) is reached after training on 490 molecules (80% of FreeSolv). Corresponding FML model errors are on par with state-of-the art physics based approaches. To generate the input representation for a new query compound, FML requires approximate and short molecular dynamics runs. We showcase its usefulness through analysis of solvation free energies for 116k organic molecules (all force-field compatible molecules in the QM9 database), identifying the most and least solvated systems and rediscovering quasi-linear structure-property relationships in terms of simple descriptors such as hydrogen-bond donors, number of NH or OH groups, number of oxygen atoms in hydrocarbons, and number of heavy atoms. FML's accuracy is maximal when the temperature used for the molecular dynamics simulation to generate averaged input representation samples in training is the same as for the query compounds. The sampling time for the representation converges rapidly with respect to the prediction error.

Polyradical Character of Triangular Non-Kekulé Structures, Zethrenes, p-Quinodimethane-Linked Bisphenalenyl, and the Clar Goblet in Comparison: An Extended Multireference Study

In this work, two different classes of polyaromatic hydrocarbon (PAH) systems have been investigated in order to characterize the amount of polyradical character and to localize the specific regions of chemical reactivity: (a) the non-Kekulé triangular structures phenalenyl, triangulene and a π-extended triangulene system with high-spin ground state and (b) PAHs based on zethrenes, p-quinodimethane-linked bisphenalenyl, and the Clar goblet containing varying polyradical character in their singlet ground state. The first class of structures already have open-shell character because of their high-spin ground state, which follows from the bonding pattern, whereas for the second class the open-shell character is generated either because of the competition between the closed-shell quinoid Kekulé and the open-shell singlet biradical resonance structures or the topology of the π-electron arrangement of the non-Kekulé form. High-level ab initio calculations based on multireference theory have been carried out to compute singlet–triplet splitting for the above-listed compounds and to provide insight into their chemical reactivity based on the polyradical character by means of unpaired densities. Unrestricted density functional theory and Hartree–Fock calculations have been performed for comparison also in order to obtain better insight into their applicability to these types of complicated radical systems.

A computationally efficient double hybrid density functional based on the random phase approximation

A new double hybrid density functional (PWRB95) based on GGA orbitals and RPA is presented and its performance is investigated compared to standard DFT and wavefunction methods.

The electronic states of a double carbon vacancy defect in pyrene: a model study for graphene

The unpaired density changes from the polyradical to closed shell character upon geometry relaxation.

Dimers of boroglycine and methylamine boronic acid: a computational comparison of the relative importance of dative versus hydrogen bonding

Boronic acids are widely used in materials science, pharmacology, and the synthesis of biologically active compounds. In this Article, geometrical structures and relative energies of dimers of boroglycine, H2N-CH2-B(OH)2, and its constitutional isomer H3C-NH-B(OH)2, were computed using second-order Møller-Plesset perturbation theory and density functional theory; Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis sets were employed for the MP2 calculations, and the Pople 6-311++G(d,p) basis set was employed for a majority of the DFT calculations. Effects of an aqueous environment were incorporated into the results using PCM and COSMO-RS methodology. The lowest-energy conformer of the H2N-CH2-B(OH)2 dimer was a six-membered ring structure (chair conformation; Ci symmetry) with two intermolecular B:N dative-bonds; it was 14.0 kcal/mol lower in energy at the MP2/aug-cc-pVDZ computational level than a conformer with the classic eight-centered ring structure (Ci symmetry) in which the boroglycine monomers are linked by a pair of H-O...H bonds. Compared to the results of MP2 calculations with correlation-consistent basis sets, DFT calculations using the PBE1PBE and TPSS functionals with the 6-311++G(d,p) basis set were significantly better at predicting relative conformational energies of the H2N-CH2-B(OH)2 and H3C-NH-B(OH)2 dimers than corresponding calculations using the BLYP, B3LYP, OLYP, and O3LYP functionals, particularly with respect to dative-bonded structures.

Intramolecular Mixed-Valence State Through Silicon or Germanium Double Bridges in Rigid Bis(Tetrathiafulvalenes)

The synthesis and characterization of two ortho-dimethyltetrathiafulvalene (o-DMTTF)-based rigid dimers containing dimethylsilicon (Me(2)Si) or dimethylgermanium (Me(2)Ge) linkers are described. Single-crystal X-ray analysis reveals planar geometry for the central 1,4-disilicon or 1,4-digermanium six-membered rings. DFT calculations provide optimized conformations in agreement with the experimental ones, and also emphasize the role of the heteroatomic linkers in the conjugation between the two redox active units. Cyclic voltammetry measurements show sequential oxidation into radical cation, and then dication species. Solution EPR measurements on the radical-cation species indicate full delocalization of the unpaired electron over both electroactive TTF units, with an associated coupling of 0.42 G with twelve equivalent protons. DFT calculations afford fully planar geometry for the radical-cation species and confirm the experimental isotropic coupling constant. Single-crystal X-ray analyses of two charge-transfer compounds obtained upon chemical oxidation, formulated as [(Me(2)Si)(2)(o-DMTTF)(2)].1/2[TCNQ].1/2[TCNQF(4)] and [(Me(2)Ge)(2)(o-DMTTF)(2)].[TCNQ], demonstrate the occurrence of genuine mixed-valence radical-cation species, as well as a three-dimensional network of short S...S intermolecular contacts. Temperature-dependent conductivity measurements demonstrate semiconducting behavior for both charge-transfer compounds, with an increase of the absolute value of the conductivity upon applying external pressure. Band structure calculations reveal peculiar pseudo-two-dimensional electronic structures, also confirming electronic interactions through SiMe(2) and GeMe(2) bridges.

Structure of the Boronic Acid Dimer and the Relative Stabilities of Its Conformers

Despite the widespread use of boronic acids in materials science and as pharmaceutical agents, many aspects of their structure and reactivity are not well understood. In this research the boronic acid dimer, [HB(OH)(2)](2), was studied by second-order Møller-Plesset (MP2) perturbation theory and coupled cluster methodology with single and double excitations (CCSD). Pople split-valence 6-31+G*, 6-311G**, and 6-311++G** and Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis sets were employed for the calculations. A doubly hydrogen-bonded conformer (1) of the dimer was consistently found to be lowest in energy; the structure of 1 was planar (C(2h)) at most computational levels employed but was significantly nonplanar (C(2)) at the MP2/6-311++G** and CCSD/6-311++G** levels, the result of an intrinsic problem with Pople-type sp-diffuse basis functions on heavy atoms. The dimerization energy, enthalpy, and free energy for the formation of (1) from the exo-endo conformer of the monomer were -10.8, -9.2, and +1.2 kcal/mol, respectively, at the MP2/aug-cc-pVTZ level. Several other hydrogen-bonded conformers of the dimer were local minima on the potential energy surface (PES) and ranged from 2 to 5 kcal/mol higher in energy than 1. Nine doubly OH-bridged conformers, in which the boron atoms were tetracoordinated, were also local minima on the PES, but they were all greater than 13 kcal/mol higher in energy than 1; doubly H-bridged structures proved to be transition states. MP2 and CCSD results were compared to those from the BLYP, B3LYP, OLYP, O3LYP, PBE1PBE, and TPSS functionals with the 6-311++G** and aug-cc-pVTZ basis sets; the PBE1PBE functional performed best relative to the MP2 and CCSD results. Self-consistent reaction field (SCRF) calculations predict that boronic acid dimerization is less favorable in solution than in vacuo.

Growing Graphene Sheets from Reactions with Methyl Radicals: A Quantum Chemical Study

Hydrogen abstraction reactions by methyl radicals on the zigzag and armchair edges of perylene are studied by density functional theory (DFT) to explore various growth pathways that seem to be in line with experimental observations. The DFT approach is validated by comparing the results obtained from calculations with six different functionals with those obtained from correlated ab initio methods, thereby emphasizing the calculation of reaction barriers. A useful compromise between accuracy and computational cost is provided by DFT, and possible pathways are studied in detail at this level of calculation. Our computational study is carried out by ordering, as a first step, all of the isomers that arise from the abstraction of one or two H atoms from 1,12-dimethyl-1,12-dihydroperylene and 3,4-dimethyl-3,4-dihydroperylene with respect to their energies. Subsequently, only those pathways that connect low-energy isomers are investigated. The calculations reveal that the selected pathways are favored thermodynamically, and also that the reaction barriers are somewhat higher than the energy locally available for the respective reaction. Notably, in the case of 3,4-dimethyl-3,4-dihydroperylene, the first two reaction steps have no or only a very low reaction barrier. The final conclusion of our study is that a cascade of reactions is possible that leads to the growth of a graphene sheet on a graphite surface.

Excited State Proton Transfer in 3-Methyl-7-Azaindole Dimer. Symmetry Control

The concerted double proton transfer undergone by the C(2)(h) dimer of 7-azaindole upon electronic excitation has also been reported to occur in 3-methyl-7-azaindole monocrystals and in dimers of this compound under free-jet conditions. However, the results obtained in this work for the 3-methyl-7-azaindole dimer formed in a 10(-4) M solution of the compound in 2-methylbutane suggest that the dimer produces no fluorescent signal consistent with a double proton transfer in the liquid phase or in a matrix. In this paper, the spectroscopic behavior of the doubly hydrogen bonded dimer of 3-methyl-7-azaindole is shown to provide a prominent example of molecular symmetry control over the spectroscopy of a substance. This interpretation opens up a new, interesting research avenue for exploring the ability of molecular symmetry to switch between proton-transfer mechanisms. It should be noted that symmetry changes in the 3-methyl-7-azaindole dimer are caused by an out-of-phase internal rotation of the two methyl groups.

Comparison of density functionals for energy and structural differences between the high- [5T2g:(t2g)4(eg)2] and low- [1A1g:(t2g)6(eg)0] spin states of iron(II) coordination compounds. II. More functionals and the hexaminoferrous cation, [Fe(NH3)6]2+

The ability of different density functionals to describe the structural and energy differences between the high- [(5)T(2g):(t(2g))(4)(e(g))(2)] and low- [(1)A(1g):(t(2g))(6)(e(g))(0)] spin states of small octahedral ferrous compounds is studied. This work is an extension of our previous study of the hexaquoferrous cation, [Fe(H(2)O)(6)](2+), [J. Chem. Phys. 120, 9473 (2004)] to include a second compound-namely, the hexaminoferrous cation, [Fe(NH(3))(6)](2+)-and several additional functionals. In particular, the present study includes the highly parametrized generalized gradient approximations (GGAs) known as HCTH and the meta-GGA VSXC [which together we refer to as highly parametrized density functionals (HPDFs)], now readily available in the GAUSSIAN03 program, as well as the hybrid functional PBE0. Since there are very few experimental results for these molecules with which to compare, comparison is made with best estimates obtained from second-order perturbation theory-corrected complete active space self-consistent field (CASPT2) calculations, with spectroscopy oriented configuration interaction (SORCI) calculations, and with ligand field theory (LFT) estimations. While CASPT2 and SORCI are among the most reliable ab initio methods available for this type of problem, LFT embodies many decades of empirical experience. These three methods are found to give coherent results and provide best estimates of the adiabatic low-spin-high-spin energy difference, DeltaE(LH) (adia), of 12 000-13 000 cm(-1) for [Fe(H(2)O)(6)](2+) and 9 000-11 000 cm(-1) for [Fe(NH(3))(6)](2+). All functionals beyond the purely local approximation produce reasonably good geometries, so long as adequate basis sets are used. In contrast, the energy splitting, DeltaE(LH) (adia), is much more sensitive to the choice of functional. The local density approximation severely over stabilizes the low-spin state with respect to the high-spin state. This "density functional theory (DFT) spin pairing-energy problem" persists, but is reduced, for traditional GGAs. In contrast the hybrid functional B3LYP underestimates DeltaE(LH) (adia) by a few thousands of wave numbers. The RPBE GGA of Hammer, Hansen, and Norskov gives good results for DeltaE(LH) (adia) as do the HPDFs, especially the VSXC functional. Surprisingly the HCTH functionals actually over correct the DFT spin pairing-energy problem, destabilizing the low-spin state relative to the high-spin state. Best agreement is found for the hybrid functional PBE0.

Characterization of synthetic oxomanganese complexes and the inorganic core of the O2-evolving complex in photosystem II: Evaluation of the DFT/B3LYP level of theory

The capabilities and limitations of the Becke-3-Lee-Yang-Parr (B3LYP) hybrid density functional are investigated as applied to studies of mixed-valent multinuclear oxomanganese complexes. Benchmark calculations involve the analysis of structural, electronic and magnetic properties of di-, tri- and tetra-nuclear Mn complexes, previously characterized both chemically and spectroscopically, including the di-mu-oxo bridged dimers [Mn(III)Mn(IV)(mu-O)(2)(H(2)O)(2)(terpy)(2)](3+) (terpy=2,2':6,2''-terpyridine) and [Mn(III)Mn(IV)(mu-O)(2)(phen)(4)](3+) (phen=1,10-phenanthroline), the Mn trimer [Mn(3)O(4)(bpy)(4)(H(2)O)(2)](4+) (bpy=2,2'-bipyridine), and the tetramer [Mn(4)O(4)L(6)](+) with L=Ph(2)PO(2)(-). Furthermore, the density functional theory (DFT) B3LYP level is applied to analyze the hydrated Mn(3)O(4)CaMn cluster completely ligated by water, OH(-), Cl(-), carboxylate and imidazole ligands, analogous to the '3+1 Mn tetramer' of the oxygen-evolving complex of photosystem II. It is found that DFT/B3LYP predicts structural and electronic properties of oxomanganese complexes in pre-selected spin-electronic states in very good agreement with X-ray and magnetic experimental data, even when applied in conjunction with rather modest basis sets. However, it is conjectured that the energetics of low-lying spin-states is beyond the capabilities of the DFT/B3LYP level, constituting a limitation to mechanistic studies of multinuclear oxomanganese complexes where until now the performance of DFT/B3LYP has raised little concern.

On the photophysics of all-transpolyenes: Hexatriene versus octatetraene

The disparate photophysical behavior of trans-1,3,5-hexatriene (nonfluorescent) and trans-1,3,5,7-octatetraene (with two fluorescence emissions) in the gas phase is explained in terms of the tendency of their 1B(u) excited states to rotate about their terminal carbon-carbon single bonds in order to adopt a quasiplanar molecular form of lower energy than the 1B(u) state in the parent all-trans structure. The origin of their disparate photophysical behavior is that such a transformation is subject to a small energy barrier in octatetraene; the barrier produces two minima (two fluorescence emissions) in the corresponding potential-energy curve. Instead of an energy barrier, hexatriene gives a 1,3-diene species which falls to the ground state so rapidly that no emission is produced.

Semiempirical GGA-type density functional constructed with a long-range dispersion correction

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 C(6) x 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 C(6) x 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.

Spectral broadening and diffusion by torsional motion in biphenyl

We have studied biphenyl by time-dependent density-functional theory. In particular, we have analyzed the dependence of singlet excitation energies and transition dipoles on the torsional angle between the phenyl groups. The torsional spectrum has been computed quantum mechanically as well as semiclassically in order to understand how this influences the broadening of absorption and luminescence spectra. Our results are in best agreement with supersonic jet spectroscopy data, but also fit astonishingly well to spectra of biphenyl in condensed phase. Furthermore, we compare the torsional and vibrational relaxation and discuss qualitatively the general consequences for poly-para-phenylenes and related conjugated polymers as poly-thiophenes, considering, in particular, how side chains and solvents may affect the optical spectra.

The molecular symmetry and electronic spectroscopy of 7-azaindole dimer: Its proton-transfer channels

The potential-energy surfaces for the proton transfer in the doubly hydrogen-bonded dimer of 7-azaindole in its lowest excited electronic states were examined. The dimer with C2h symmetry in its lowest excited electronic states, 2Ag and 1Bu, undergoes concerted double-proton transfer via transition states of the same symmetry placed at energies 4.55 and 4.70 kcal/mol higher, respectively. This suggests that the activation barriers for the double-proton transfer, if any, are lower than 1 kcal/mol. Emission from the dimers resulting from the double-proton transfer involves a Stokes shift of 5605 cm(-1), as theoretically estimated from the 0-0 components of the absortion and emission transitions of the dimer. Surprisingly, however, the calculations suggest that the green emission cannot arise from the 2Ag state generated by a double-proton transfer, because this structure possesses an imaginary frequency. In the 7-azaindole dimer of Cs symmetry, the first excited electronic state, a', lies 4.9 kcal/mol below 1Bu. This excited state a' can be the starting point for single-proton transfers giving a zwitterionic form that can dissociate into the protonated and deprotonated forms of 7-azaindole, the former being electronically excited. This situation of lower symmetry is consistent with the mutational scheme proposed by Goodman [Nature (London) 378, 237 (1995)].

Study of 7-azaindole in its first four singlet states

The molecular structure and properties of 7-azaindole in its first four singlet states were studied with a view to improving current understanding of the photophysical behavior of its C(2h) dimer. This dimer, which exhibits a double proton transfer via its two hydrogen bonds upon electronic excitation, has for 35 years been used as a model for the photophysical behavior of DNA base pairs. Electronic excitation of 7-azaindole simultaneously increases its acidity and basicity; these changes facilitate a concerted mechanism for the double proton transfer in the dimer. In this work, we found the acidity and basicity changes to occur only in its first pi,pi(*) excited singlet state.

Benchmarking approximate density functional theory. I.s/d excitation energies in 3d transition metal cations

The performance of a number of different implementations of density functional theory (DFT) for predicting the s/d interconfigurational energies of the 3d transition metal cations is investigated. Systematic comparisons of computed results with experimental data indicate that gradient corrected correlation functionals, like the LYP GGA, efficiently correct the flaws of the LDA, but reveal shortcomings in the treatment of exchange by currently available GGAs. The admixture of exact exchange in hybrid functionals eventually leads to largely reduced errors. Several basis sets available for the 3d elements are tested in combination with the B3LYP functional. Finally, the influence of variations of the admixture of exact exchange is systematically tested. The results reveal that computed s/d excitation energies obtained for the individual ions depend in markedly different ways on the amount of exact exchange admixture and that there is no single optimal and transferable exchange parameter to create a hybrid functional that yields improved results for all ions alike. Several of the recently devised functionals perform as good as or slightly better than the B3LYP functional in the present study. But given the fact that the B3LYP functional has been identified as the most successful DFT method in an overwhelming number of systematic investigations in very many areas of chemical research, there is no persuasive motivation to recommend its replacement by one of the other functionals, as much less is known about their robustness.