Diffuse basis functions for explicitly correlated calculations on the heavy p-block: aug-cc-pVnZ-PP-F12 sets for Ga-Kr, In-Xe, and Tl-Rn.

New aug-cc-pVnZ-PP-F12 basis sets (n = D, T, Q) for the heavy p-block elements, Ga-Kr, In-Xe, and Tl-Rn, have been developed by augmenting the cc-pVnZ-PP-F12 sets with additional higher angular momentum diffuse functions. These basis sets have been optimized for use in explicitly correlated F12 calculations, and matching auxiliary basis sets for density fitting of conventional and F12 integrals have also been developed. The new sets have been validated with benchmark CCSD(T)-F12b calculations of electron affinities, where an accelerated convergence to the complete basis set limit is evident. The effect of the additional diffuse functions on electron affinities is shown to be comparable to the effect of correlating the outer-core d electrons.

BasisOpt: A Python package for quantum chemistry basis set optimization.

The accuracy and efficiency of molecular quantum chemical calculations depend critically on the basis set used. However, the development of novel basis sets is hindered because much of the literature relies on the use of opaque processes and tools that are not publicly available. We present here BasisOpt, a tool for the automated optimization of basis sets with an easy-to-use framework. It features an open and accessible workflow for basis set optimization that can be easily adapted to almost any quantum chemistry program, a standardized approach to testing basis sets, and visualization of both the optimized basis sets and the optimization process. We provide examples of usage in realistic basis set optimization scenarios where: (i) a density fitting basis set is optimized for He, Ne, and Ar; (ii) the exponents of the def2-SVP basis are re-optimized for a set of molecules rather than atoms; and (iii) a large, almost saturated basis of sp primitives is automatically reduced to (10s5p) while achieving the lowest energy for such a basis set composition.

Correlation Consistent Basis Sets and Core Polarization Potentials for Al-Ar with ccECP Pseudopotentials.

New correlation consistent basis sets for the second-row atoms (Al-Ar) to be used with the neon-core correlation consistent effective core potentials (ccECPs) have been developed. The basis sets, denoted cc-pV(n+d)Z-ccECP (n = D, T, Q), include the "tight"-d functions that are known to be important for second-row elements. Sets augmented with additional diffuse functions are also reported. Effective core polarization potentials (CPPs) to account for the effect of core-valence correlation have been adjusted for the same elements, and two different forms of the CPP cutoff function have been analyzed. The accuracy of both the basis sets and the CPPs is assessed through benchmark calculations at the coupled-cluster level of theory for atomic and molecular properties. Agreement with all-electron results is much improved relative to the basis sets that originally accompanied the ccECPs; moreover, the combination of cc-pV(n+d)Z-ccECP and CPPs is found to be a computationally efficient and accurate alternative to including core electrons in the correlation treatment.

Radial Potential Energy Functions of Linear Halogen-Bonded Complexes YX···ClF (YX = FB, OC, SC, N2) and the Effects of Substituting X by Second-Row Analogues: Mulliken Inner and Outer Complexes.

Energies of linear, halogen-bonded complexes in the isoelectronic series YX···ClF (YX = FB, OC, or N2) are calculated at several levels of theory as a function of the intermolecular distance r(X···Cl) to yield radial potential energy functions. When YX = OC, a secondary minimum is observed corresponding to lengthened and shortened distances r(ClF) and r(CCl), respectively, relative to the primary minimum, suggesting a significant contribution from the Mulliken inner complex structure [O═C-Cl]+···F-. A conventional weak, halogen-bond complex OC···ClF occurs at the primary minimum. For YX = FB, the primary minimum corresponds to the inner complex [F═B-Cl]+···F-, while the outer complex FB···ClF is at the secondary minimum. The effects on the potential energy function of systematic substitution of Y and X by second-row congeners and of reversing the order of X and Y are also investigated. Symmetry-adapted perturbation theory and natural population analyses are applied to further understand the nature of the various halogen-bond interactions.

Correlation consistent basis sets for explicitly correlated wavefunctions: Pseudopotential-based basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements.

New correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements have been developed specifically for use in explicitly correlated F12 calculations. This includes orbital basis sets for valence only (cc-pVnZ-PP-F12, n = D, T, Q) and outer core-valence (cc-pCVnZ-PP-F12) correlation, along with both of these augmented with additional high angular momentum diffuse functions. Matching auxiliary basis sets required for density fitting and resolution-of-the-identity approaches to conventional and F12 integrals have also been optimized. All of the basis sets are to be used in conjunction with small-core relativistic pseudopotentials [Figgen et al., Chem. Phys. 311, 227 (2005)]. The accuracy of the basis sets is determined through benchmark calculation at the explicitly correlated coupled-cluster level of theory for various properties of atoms and diatomic molecules. The convergence of the properties with respect to the basis set is dramatically improved compared to conventional coupled-cluster calculations, with cc-pVTZ-PP-F12 results close to conventional estimates of the complete basis set limit. The patterns of convergence are also greatly improved compared to those observed from the use of conventional correlation consistent basis sets in F12 calculations.

CHARMM-DYES: Parameterization of Fluorescent Dyes for Use with the CHARMM Force Field.

We present CHARMM-compatible force field parameters for a series of fluorescent dyes from the Alexa, Atto, and Cy families, commonly used in Förster resonance energy transfer (FRET) experiments. These dyes are routinely used in experiments to resolve the dynamics of proteins and nucleic acids at the nanoscale. However, little is known about the accuracy of the theoretical approximations used in determining the dynamics from the spectroscopic data. Molecular dynamics simulations can provide valuable insights into these dynamics at an atomistic level, but this requires accurate parameters for the dyes. The complex structure of the dyes and the importance of this in determining their spectroscopic properties mean that parameters generated by analogy to existing parameters do not give meaningful results. Through validation relative to quantum chemical calculation and experiments, the new parameters are shown to significantly outperform those that can be generated automatically, giving better agreement in both the charge distributions and structural properties. These improvements, in particular with regard to orientation of the dipole moments on the dyes, are vital for accurate simulation of FRET processes.

An ab initio investigation of alkali-metal non-covalent bonds BLiR and BNaR (R = F, H or CH3) formed with simple Lewis bases B: the relative inductive effects of F, H and CH3.

The alkali-metal bonds formed by simple molecules LiR and NaR (R = F, H or CH3) with each of the six Lewis bases B = OC, HCN, H2O, H3N, H2S and H3P were investigated by ab initio calculations at the CCSD(T)/AVTZ and CCSD(T)/awCVTZ levels of theory with the aim of characterising this type of non-covalent interaction. In some complexes, two minima were discovered, especially for those involving the NaR. The higher-energy minimum (referred to as Type I) for a given B was found to have geometry that is isomorphous with that of the corresponding hydrogen-bonded analogue BHF. The lower-energy minimum (when two were present) showed evidence of a significant secondary interaction of R with the main electrophilic region of B (Type II complexes). Energies DCBSe for dissociation of the complexes into separate components were found to be directly proportional to the intermolecular stretching force constant kσ The value of DCBSe could be partitioned into a nucleophilicity of B and an electrophilicity of LiR or NaR, with the order ELiH ⪆ ELiF = ELiCH3 for the LiR and ENaF > ENaH ≈ ENaCH3 for the NaR. For a given B, the order of the electrophilicities is ELiR > ENaR, which presumably reflects the fact that Li+ is smaller than Na+ and can approach the Lewis base more closely. A SAPT analysis revealed that the complexes BLiR and BNaR have larger electrostatic contributions to De than do the hydrogen- and halogen-bonded counterparts BHCl and BClF.

A Linear-Scaling Method for Noncovalent Interactions: An Efficient Combination of Absolutely Localized Molecular Orbitals and a Local Random Phase Approximation Approach.

A novel method for the accurate and efficient calculation of interaction energies in weakly bound complexes composed of a large number of molecules is presented. The new ALMO+RPAd method circumvents the prohibitive scaling of coupled cluster singles and doubles while still providing similar accuracy across a diverse range of weakly bound chemical systems. Linear-scaling procedures for the Fock build are given utilizing absolutely localized molecular orbitals (ALMOs), resulting in the a priori exclusion of basis set superposition errors. A bespoke data structure and algorithm using density fitting are described, leading to linear scaling for the storage and computation of the two-electron integrals. Electron correlation is included through a new, linear-scaling pairwise local random phase approximation approach, including exchange interactions, and decomposed into purely dispersive excitations (RPAxd). Collectively, these allow meaningful decomposition of the interaction energy into physically distinct contributions: electrostatic, polarization, charge transfer, and dispersion. Comparison with symmetry-adapted perturbation theory shows good qualitative agreement. Tests on various dimers and the S66 benchmark set demonstrate results within 0.5 kcal mol-1 of coupled cluster singles and doubles results. On a large cluster of water molecules, we achieve calculations involving over 3500 orbital and 12,000 auxiliary basis functions in under 10 min on a single CPU core.

Syntheses, Structures, and Infrared Spectra of the Hexa(cyanido) Complexes of Silicon, Germanium, and Tin.

The rare octahedral EC6 coordination skeleton type is unknown for complexes with coordination centers consisting of group 14 elements. Here, the first examples of such EC6 species, the hexacoordinate homoleptic cyanido complexes E(CN)62-, E = Si, Ge, Sn, have been synthesized from element halides SiCl4, GeCl4 and SnF4 and isolated as salts with PPN counterions (PPN+ = (Ph3P)2N+) on a scale of 0.2-1 g. Characterization by spectroscopic techniques and by structure determination through single crystal crystallographic methods show that these pseudohalogen complexes have effective octahedral symmetry in solution and in the solid state. Infrared spectra obtained in solution reveal that the T1 u symmetric IR-active vibrations in all three complexes have unusually small oscillator strengths. The observed reluctance of Si(CN)62-, Ge(CN)62-, and Sn(CN)62- to form from chloro-precursors was rationalized in terms of Gibbs free energies, which were found by ab initio calculations at the CCSD(T)-F12b/aug-cc-pVTZ(-PP)-F12 level of theory to be small or even positive. The work demonstrates that E(CN)62- complexes of silicon, germanium and tin are in fact stable at room temperature and exist as well-defined units in the presence of noncoordinating counterions. The results add to our understanding of the chemistry of pseudohalogens and structure and bonding.

Interplay between hydrogen bonding and n→π* interaction in an analgesic drug salicin.

The competition and cooperation between weak intermolecular interactions are important in determining the conformational preferences of molecules. Understanding the relative strengths of these effects in the context of potential drug candidates is therefore essential. We use a combination of gas-phase spectroscopy and quantum-chemical calculations to elucidate the nature of such interactions for the analgesic salicin [2-(hydroxymethyl)phenyl ß-d-glucopyranoside], an analog of aspirin found in willow bark. Of several possible conformers, only three are observed experimentally, and these are found to correspond with the three lowest energy conformers obtained from density functional theory calculations and simulated Franck-Condon spectra. Natural bond orbital analyses show that these are characterized by a subtle interplay between weak n→π* interaction and conventional strong hydrogen bond, with additional insights into this interaction provided by analysis of quantum theory of atoms in molecules and symmetry-adapted perturbation theory calculations. In contrast, the higher energy conformers, which are not observed experimentally, are mostly stabilized by the hydrogen bond with negligible contribution of n→π* interaction. The n→π* interaction results in a preference for the benzyl alcohol group of salicin to adopt a gauche conformation, a characteristic also found when salicin is bound to the ß-glucosidase enzyme. As such, understanding the interplay between these weak interactions has significance in the rationalization of protein structures.

Alkali-Metal Trihalides: M+X3- Ion Pair or MX-X2 Complex?

The alkali-metal trihalides MX3 (M = Li, Na, K, Rb, and Cs; X = Cl, Br, and I) are systematically studied using coupled-cluster methods. Benchmarks using CCSD(T) against diatomic experimental results suggest satisfactory performance for the weighted core-valence basis sets (new basis sets for K, Rb, and Cs) selected for predicting reliable structures and harmonic vibrational frequencies. An isomer search using the B3LYP functional yields a planar, yet asymmetric T-shaped C s structure as the global minimum for all MX3 species. Much higher level CCSD(T) computations show a moderate to strong distortion of the X3- anion by the M+ cation in the respective equilibrium geometries. Most obviously, for LiCl3, the two Cl-Cl distances are separated by 0.786 Å. Even for CsI3, the structure least distorted from the M+X3- model, the two I-I distances differ by 0.243 Å. It does not take much energy to distort the parent anions along an antisymmetric stretch, so this is no surprise. The normal modes of vibration of the MX3 molecules are in better agreement with matrix isolation experiments than previous calculations. And these normal modes reveal that, instead of the well-established antisymmetric and symmetric stretches of the "free" X3- anions, relatively localized and mutually perturbed X-X and M-X stretches are calculated. The suggestion emerges that the MX3 system may be alternatively described as an MX-X2 complex rather than the M+X3- ion pair. This perspective is supported by bonding analyses showing low electron densities at the bond critical points and natural bond orders between the MX and X2 moieties. The thermochemistry of fragmentations of MX3 to MX + X2 versus M+ + X3- also supports the alternative viewpoint of the bonding in this class of molecules.

Structures and Heats of Formation of Simple Alkaline Earth Metal Compounds II: Fluorides, Chlorides, Oxides, and Hydroxides for Ba, Sr, and Ra.

Geometry parameters, vibrational frequencies, heats of formation, bond dissociation energies, cohesive energies, and selected fluoride affinities (difluorides) are predicted for the late alkaline earth (Sr, Ba, and Ra) oxides, fluorides, chlorides, and hydroxides at the coupled cluster theory CCSD(T) level. Additional corrections (scalar relativistic and pseudopotential corrections, vibrational zero-point energies, and atomic spin-orbit effects) were included to accurately calculate the total atomization energies and heats of formation following the Feller-Peterson-Dixon methodology. The calculated values are compared to the experimental data where available. In some cases, especially for Ra compounds, there are no experimental results, or the experimental energetics and geometries are not reliable or have very large error bars. All of the Sr, Ba, and Ra difluorides, dichlorides, and dihydroxides are bent structures with the OMO bond angles decreasing going down the group. The cohesive energies of bulk Be dihalides are predicted to be quite low, while those of Ra are relatively large. The fluoride affinities show that the difluorides are moderately strong Lewis acids and that such trifluorides may form under the appropriate experimental conditions.

UV photodissociation dynamics of CHI2Cl and its role as a photolytic precursor for a chlorinated Criegee intermediate.

Photolysis of geminal diiodoalkanes in the presence of molecular oxygen has become an established route to the laboratory production of several Criegee intermediates, and such compounds also have marine sources. Here, we explore the role that the trihaloalkane, chlorodiiodomethane (CHI2Cl), may play as a photolytic precursor for the chlorinated Criegee intermediate ClCHOO. CHI2Cl has been synthesized and its UV absorption spectrum measured; relative to that of CH2I2 the spectrum is shifted to longer wavelength and the photolysis lifetime is calculated to be less than two minutes. The photodissociation dynamics have been investigated using DC slice imaging, probing ground state I and spin-orbit excited I* atoms with 2 + 1 REMPI and single-photon VUV ionization. Total translational energy distributions are bimodal for I atoms and unimodal for I*, with around 72% of the available energy partitioned in to the internal degrees of freedom of the CHICl radical product, independent of photolysis wavelength. A bond dissociation energy of D0 = 1.73 ± 0.11 eV is inferred from the wavelength dependence of the translational energy release, which is slightly weaker than typical C-I bonds. Analysis of the photofragment angular distributions indicate dissociation is prompt and occurs primarily via transitions to states of A'' symmetry. Complementary high-level MRCI calculations, including spin-orbit coupling, have been performed to characterize the excited states and confirm that states of A'' symmetry with highly mixed singlet and triplet character are predominantly responsible for the absorption spectrum. Transient absorption spectroscopy has been used to measure the absorption spectrum of ClCHOO produced from the reaction of CHICl with O2 over the range 345-440 nm. The absorption spectrum, tentatively assigned to the syn conformer, is at shorter wavelengths relative to that of CH2OO and shows far weaker vibrational structure.

Prescreening and efficiency in the evaluation of integrals over ab initio effective core potentials.

New, efficient schemes for the prescreening and evaluation of integrals over effective core potentials (ECPs) are presented. The screening is shown to give a rigorous, and close bound, to within on average 10% of the true value. A systematic rescaling procedure is given to reduce this error to approximately 0.1%. This is then used to devise a numerically stable recursive integration routine that avoids expensive quadratures. Tests with coupled clusters with single and double excitations and perturbative triple calculations on small silver clusters demonstrate that the new schemes show no loss in accuracy, while reducing both the power and prefactor of the scaling with system size. In particular, speedups of roughly 40 times can be achieved compared to quadrature-based methods.

Approaching the Hartree-Fock Limit through the Complementary Auxiliary Basis Set Singles Correction and Auxiliary Basis Sets.

Auxiliary basis sets for use in the resolution of the identity (RI) approximation in explicitly correlated methods are presented for the elements H-Ar. These extend the cc-pVnZ-F12/OptRI (n = D-Q) auxiliary basis sets of Peterson and co-workers by the addition of a small number of s- and p-functions, optimized so as to yield the greatest complementary auxiliary basis set (CABS) singles correction to the Hartree-Fock energy. The new sets, denoted OptRI+, also lead to a reduction in errors due to the RI approximation and hence an improvement in correlation energies. The atomization energies and heats of formation for a test set of small molecules, and spectroscopic constants for 27 diatomics, calculated at the CCSD(T)-F12b level, are shown to have improved error distributions for the new auxiliary basis sets with negligible additional effort. The OptRI+ sets retain all of the desirable properties of the original OptRI, including the production of smooth potential energy surfaces, while maintaining a compact nature.

Interplay among Electrostatic, Dispersion, and Steric Interactions: Spectroscopy and Quantum Chemical Calculations of π-Hydrogen Bonded Complexes.

π-Hydrogen bonding interactions are ubiquitous in both materials and biology. Despite their relatively weak nature, great progress has been made in their investigation by experimental and theoretical methods, but this becomes significantly more complicated when secondary intermolecular interactions are present. In this study, the effect of successive methyl substitution on the supramolecular structure and interaction energy of indole⋅⋅⋅methylated benzene (ind⋅⋅⋅n-mb, n=1-6) complexes is probed through a combination of supersonic jet experiments and benchmark-quality quantum chemical calculations. It is demonstrated that additional secondary interactions introduce a subtle interplay among electrostatic and dispersion forces, as well as steric repulsion, which fine-tunes the overall structural motif. Resonant two-photon ionization and IR-UV double-resonance spectroscopy techniques are used to probe jet-cooled ind⋅⋅⋅n-mb (n=2, 3, 6) complexes, with redshifting of the N-H IR stretching frequency showing that increasing the degree of methyl substitution increases the strength of the primary N-H⋅⋅⋅π interaction. Ab initio harmonic frequency and binding energy calculations confirm this trend for all six complexes. Electronic spectra of the three dimers are broad and structureless, with quantum chemical calculations revealing that this is likely to be due to multiple tilted conformations of each dimer possessing similar stabilization energies.

Gaussian basis sets for use in correlated molecular calculations. XI. Pseudopotential-based and all-electron relativistic basis sets for alkali metal (K-Fr) and alkaline earth (Ca-Ra) elements.

New correlation consistent basis sets based on pseudopotential (PP) Hamiltonians have been developed from double- to quintuple-zeta quality for the late alkali (K-Fr) and alkaline earth (Ca-Ra) metals. These are accompanied by new all-electron basis sets of double- to quadruple-zeta quality that have been contracted for use with both Douglas-Kroll-Hess (DKH) and eXact 2-Component (X2C) scalar relativistic Hamiltonians. Sets for valence correlation (ms), cc-pVnZ-PP and cc-pVnZ-(DK,DK3/X2C), in addition to outer-core correlation [valence + (m-1)sp], cc-p(w)CVnZ-PP and cc-pwCVnZ-(DK,DK3/X2C), are reported. The -PP sets have been developed for use with small-core PPs [I. S. Lim et al., J. Chem. Phys. 122, 104103 (2005) and I. S. Lim et al., J. Chem. Phys. 124, 034107 (2006)], while the all-electron sets utilized second-order DKH Hamiltonians for 4s and 5s elements and third-order DKH for 6s and 7s. The accuracy of the basis sets is assessed through benchmark calculations at the coupled-cluster level of theory for both atomic and molecular properties. Not surprisingly, it is found that outer-core correlation is vital for accurate calculation of the thermodynamic and spectroscopic properties of diatomic molecules containing these elements.

Halogen Bonding with Phosphine: Evidence for Mulliken Inner Complexes and the Importance of Relaxation Energy.

Intermolecular halogen bonding in complexes of phosphine and dihalogens has been theoretically investigated using explicitly correlated coupled cluster methods and symmetry-adapted perturbation theory. The complexes H3P···ClF, H3P···BrF, and H3P···IF are demonstrated to possess unusually strong interactions that are accompanied by an increase in the induction component of the interaction energy and significant elongation of the X-Y halogen distance on complex formation. The combination of these factors is indicative of Mulliken inner complexes, and criteria for identifying this classification are further developed. The importance of choosing an electronic structure method that describes both dispersion and longer range interactions is demonstrated, along with the need to account for the change in geometry on complexation formation via relaxation energy and overall stabilization energies.

Near-UV photodissociation dynamics of CH2I2.

The near-UV photodissociation dynamics of CH2I2 has been investigated using a combination of velocity-map (slice) ion imaging and ab initio calculations characterizing the excited states. Ground state I((2)P3/2) and spin-orbit excited I*((2)P1/2) atoms were probed using 2 + 1 resonance-enhanced multiphoton ionization (REMPI) or with single-photon VUV ionization. Two-color ion images were recorded at pump wavelengths of 355 nm, 266 nm and 248 nm, and one-color ion images at the REMPI wavelengths of ∼304 nm and ∼280 nm. Analysis of the ion images shows that, regardless of iodine spin-orbit state, ∼20% of the available energy is partitioned into translation E(T) at all excitation wavelengths indicating that the CH2I co-fragment is formed highly internally excited. The translational energy distributions comprise a slow, "statistical" component that peaks near zero and faster components that peak away from zero. The slow component makes an increasingly large contribution to the distribution as the excitation wavelength is decreased. The C-I bond dissociation energy of D0 = 2.155 ± 0.008 eV is obtained from the trend in the E(T) release of the faster components with increasing excitation energy. The I and I* ion images are anisotropic, indicating prompt dissociation, and are characterized by ß parameters that become increasingly positive with increasing E(T). The decrease in ß at lower translational energies can be attributed to deviation from axial recoil. MRCI calculations including spin-orbit coupling have been performed to identify the overlapping features in the absorption spectrum and characterize one-dimensional cuts through the electronically excited potential energy surfaces. The excited states are of significantly mixed singlet and triplet character. At longer wavelengths, excitation directly accesses repulsive states primarily of B1 symmetry, consistent with the observed 〈ß〉, while shorter wavelengths accesses bound states, also of B1 symmetry that are crossed by repulsive states.

Optimized Basis Sets for the Environment in the Domain-Specific Basis Set Approach of the Incremental Scheme.

Minimal basis sets, denoted DSBSenv, based on the segmented basis sets of Ahlrichs and co-workers have been developed for use as environmental basis sets for the domain-specific basis set (DSBS) incremental scheme with the aim of decreasing the CPU requirements of the incremental scheme. The use of these minimal basis sets within explicitly correlated (F12) methods has been enabled by the optimization of matching auxiliary basis sets for use in density fitting of two-electron integrals and resolution of the identity. The accuracy of these auxiliary sets has been validated by calculations on a test set containing small- to medium-sized molecules. The errors due to density fitting are about 2-4 orders of magnitude smaller than the basis set incompleteness error of the DSBSenv orbital basis sets. Additional reductions in computational cost have been tested with the reduced DSBSenv basis sets, in which the highest angular momentum functions of the DSBSenv auxiliary basis sets have been removed. The optimized and reduced basis sets are used in the framework of the domain-specific basis set of the incremental scheme to decrease the computation time without significant loss of accuracy. The computation times and accuracy of the previously used environmental basis and that optimized in this work have been validated with a test set of medium- to large-sized systems. The optimized and reduced DSBSenv basis sets decrease the CPU time by about 15.4% and 19.4% compared with the old environmental basis and retain the accuracy in the absolute energy with standard deviations of 0.99 and 1.06 kJ/mol, respectively.