Auxiliary basis sets for density fitting-MP2 calculations: Nonrelativistic triple-zeta all-electron correlation consistent basis sets for the 3d elements Sc-Zn

Auxiliary basis sets for density fitting second-order Moller-Plesset perturbation theory (DF-MP2) have been optimized for use with the triple-zeta nonrelativistic all-electron correlation consistent orbital basis sets, cc-pVTZ-NR and aug-cc-pVTZ-NR, for the 3d elements Sc-Zn. The relative error in using these auxiliary basis sets is found to be around four orders of magnitude smaller than that from utilizing triple-zeta orbital basis sets rather than corresponding quadruple-zeta basis sets, in calculation of the correlation energy for a test set of 54 small to medium sized transition metal complexes.     

Zero-point vibrational corrections to isotropic hyperfine coupling constants in polyatomic molecules

The present work addresses isotropic hyperfine coupling constants in polyatomic systems with a particular emphasis on a largely neglected, but a posteriori significant, effect, namely zero-point vibrational corrections. Using the density functional restricted-unrestricted approach, the zero-point vibrational corrections are evaluated for the allyl radical and four of its derivatives. In addition for establishing the numerical size of the zero-point vibrational corrections to the isotropic hyperfine coupling constants, we present simple guidelines useful for identifying hydrogens for which such corrections are significant. Based on our findings, we critically re-examine the computational procedures used for the determination of hyperfine coupling constants in general as well as the practice of using experimental hyperfine coupling constants as reference data when benchmarking and optimizing exchange-correlation functionals and basis sets for such calculations.     

Density functional theory study of 14N isotropic hyperfine coupling constants of organic radicals

Nitrogen hyperfine coupling constants (hfccs) of organic radicals have been calculated by density functional theory (DFT) methodology. The capability of the B3LYP functional, combined with 6-31G*, TZVP and EPR-III basis sets, to reproduce experimental nitrogen coupling constant data has been analyzed for 109 neutral, cationic and anionic radicals, all of them containing at least one nitrogen atom. The results indicate that the selection of the basis set plays an important role in the accuracy of DFT calculations of hfccs, mainly in relation with the composition of the primitive functions and the quantum number of those functions. The main conclusion obtained is the high reliability of the scheme B3LYP/6-31G* for the prediction of nitrogen hfccs with very low computational cost.     

Hyperfine coupling constants of the azafullerenes C19N, C59N, C69N, and C75N

The isomers of the nitrogen-substituted fullerenes (azafullerenes) C19N, C59N, C69N, and C75N are examined using all-electron Gaussian atomic orbital basis density functional theory, to determine the doublet radical geometries and hyperfine coupling constants. We find that the inaccuracy of previously calculated hyperfine coupling constants of C59N resulted from a poor treatment of the geometry optimization. We find that UB3LYP minimization of the radical geometry in the 6-31G basis, followed by single-point evaluation of the hyperfine constants in which an expanded basis is used on the atomic sites of interest, forms an efficient compromise between computational cost and accuracy with respect to experimental hyperfine constants. Using this approach, we assign the hyperfine signals observed in experiments on the C69N radical by calculating the hyperfine coupling constants for all five of the isomers and examine the electron spin density distribution. Finally, we present predicted hyperfine coupling constants for the isomers of C19N and C75N for use in the interpretation of future experiments.     

Approximate STO functions for the first-row transition metal atoms

Slater type orbital (STO) basis sets for the atoms Sc-Zn have been derived using a technique based on the distance between subspaces. The accuracy for several properties of these basis sets has been tested. Basis sets studied are of both single- and double-zeta sizes, although this technique can be generalized for any size. Uniform quality criteria through the series of atoms Sc-Zn are difficulty to establish due to the varying number of d electrons. A comparative study at the atomic level of the quality of STO basis sets (both the two new basis sets and Clementi's basis sets) for the first-row transition elements has been carried out. Results show that the new basis sets provide better simulation for several properties. Molecular calculations on compounds with these atoms using a Gaussian expansion fitted according to the new values of optimized STOs are also included. The results obtained are similar to those reported when STO-3G basis set is used.     

Evaluation of a new procedure for quantum-chemical estimates of constants of isotropic hyperfine coupling with protons in free radicals

A new procedure for quantum-chemical estimates of the constants of isotropic hyperfine coupling (IHFC) with protons using the orbital spin populations calculated in the basis set of symmetrically orthogonalized (according to Löwdin) atomic orbitals is tested taking 16 well-studied simplest π-electron and σ-electron radicals as examples. The most probable reasons for and possible ways of correcting large deviations of calculated IHFC constants from experimental values are considered. The efficiency of the semiempirical MNDORU scheme, which makes it possible to consistently estimate the delocalization and spin-polarization contributions to the constants of IHFC with protons in free radicals, is demonstrated.     

L-tryptophan radical cation electron spin resonance studies: connecting solution-derived hyperfine coupling constants with protein spectral interpretations

Fast-flow electron spin resonance (ESR) spectroscopy has been used to detect a free radical formed from the reaction of l-tryptophan with Ce (4+) in an acidic aqueous environment. Computer simulations of the ESR spectra from l-tryptophan and several isotopically modified forms strongly support the conclusion that the l-tryptophan radical cation has been detected by ESR for the first time. The hyperfine coupling constants (HFCs) determined from the well-resolved isotropic ESR spectra support experimental and computational efforts to understand l-tryptophan's role in protein catalysis of oxidation-reduction processes. l-Tryptophan HFCs facilitated the simulation of fast-flow ESR spectra of free radicals from two related compounds, tryptamine and 3-methylindole. Analysis of these three compounds' beta-methylene hydrogen HFC data along with equivalent l-tyrosine data has led to a new computational method that can distinguish between these two amino acid free radicals in proteins without dependence on isotope labeling, electron-nuclear double resonance, or high-field ESR. This approach also produces geometric parameters (dihedral angles for the beta-methylene hydrogens) that should facilitate protein site assignment of observed l-tryptophan radicals as has been done for l-tyrosine radicals.     

Basis set error estimation for DFT calculations of electronic g‐tensors for transition metal complexes

We present a detailed study of the basis set dependence of electronic g‐tensors for transition metal complexes calculated using Kohn–Sham density functional theory. Focus is on the use of locally dense basis set schemes where the metal is treated using either the same or a more flexible basis set than used for the ligand sphere. The performance of all basis set schemes is compared to the extrapolated complete basis set limit results. Furthermore, we test the performance of the aug‐cc‐pVTZ‐J basis set developed for calculations of NMR spin‐spin and electron paramagnetic resonance hyperfine coupling constants. Our results show that reasonable results can be obtain when using small basis sets for the ligand sphere, and very accurate results are obtained when an aug‐cc‐pVTZ basis set or similar is used for all atoms in the complex. © 2014 Wiley Periodicals, Inc.     

Basis set limit electronic excitation energies, ionization potentials, and electron affinities for the 3d transition metal atoms: Coupled cluster and multireference methods

Recently developed correlation consistent basis sets for the first row transition metal elements Sc-Zn have been utilized to determine complete basis set (CBS) scalar relativistic electron affinities, ionization potentials, and 4s(2)3d(n-2)-4s(1)d(n-1) electronic excitation energies with single reference coupled cluster methods [CCSD(T), CCSDT, and CCSDTQ] and multireference configuration interaction with three reference spaces: 3d4s, 3d4s4p, and 3d4s4p3d'. The theoretical values calculated with the highest order coupled cluster techniques at the CBS limit, including extrapolations to full configuration interaction, are well within 1 kcal/mol of the corresponding experimental data. For the early transition metal elements (Sc-Mn) the internally contracted multireference averaged coupled pair functional method yielded excellent agreement with experiment; however, the atomic properties for the late transition metals (Mn-Zn) proved to be much more difficult to describe with this level of theory, even with the largest reference function of the present work.     

Compact and efficient basis sets of s- and p-block elements for model core potential method

We propose compact and efficient valence-function sets for s- and p-block elements from Li to Rn to appropriately describe valence correlation in model core potential (MCP) calculations. The basis sets are generated by a combination of split MCP valence orbitals and correlating contracted Gaussian-type functions in a segmented form. We provide three types of basis sets. They are referred to as MCP-dzp, MCP-tzp, and MCP-qzp, since they have the quality comparable with all-electron correlation consistent basis sets, cc-pVDZ, cc-pVTZ, and cc-pVQZ, respectively, for lighter atoms. MCP calculations with the present basis sets give atomic correlation energies in good agreement with all-electron calculations. The present MCP basis sets systematically improve physical properties in atomic and molecular systems in a series of MCP-dzp, MCP-tzp, and MCP-qzp. Ionization potentials and electron affinities of halogen atoms as well as molecular spectroscopic constants calculated by the best MCP set are in good agreement with experimental values.     

Isomers of Au8

Using newly developed correlation consistent basis sets for gold, the relative energies for the neutral Au8 geometric isomers have been re-evaluated and the vertical ionization potentials calculated. The results using the correlation consistent basis sets show that second-order Moller-Plesset perturbation theory calculations strongly favor nonplanar Au8 structures for all basis sets that were employed. However, the general trend at the coupled cluster singles and doubles with perturbative triples level of theory is to increasingly favor planar structures as the basis set is improved. The effects of basis set and the effects of core-valence correlation are discussed.     

Comparison of the experimental, semi-experimental and ab initio equilibrium structures of acetylene: influence of relativisitic effects and of the diagonal Born-Oppenheimer corrections

The equilibrium structure of acetylene (also named ethyne) has been reinvestigated to resolve the small discrepancies noted between different determinations. The size of the system as well as the large amount of available experimental data provides the quite unique opportunity to check the magnitude and relevance of various contributions to equilibrium structure as well as to verify the accuracy of experimental results. With respect to pure theoretical investigation, quantum-chemical calculations at the coupled-cluster level have been employed together with extrapolation to the basis set limit, consideration of higher excitations in the cluster operator, inclusion of core correlation effects as well as relativistic and diagonal Born-Oppenheimer corrections. In particular, it is found that the extrapolation to the complete basis set limit, the inclusion of higher excitations in the electronic-correlation treatment and the relativistic corrections are of the same order of magnitude. It also appears that a basis set as large as a core-valence quintuple-zeta set is required for accurately accounting for the inner-shell correlation contribution. From a pure experimental point of view, the equilibrium structure has been determined using very accurate rotational constants recently obtained by a "global analysis" (that is to say that all non-negligible interactions are explicitly included in the Hamiltonian matrix) of rovibrational spectra. Finally, a semi-experimental equilibrium structure (where the equilibrium rotational constants are obtained from the experimental ground state rotational constants and computed rovibrational corrections) has been obtained from the available experimental ground-state rotational constants for ten isotopic species corrected for computed vibrational corrections. Such a determination led to the revision of the ground-state rotational constants of two isotopologues, thus showing that structural determination is a good method to identify errors in experimental rotational constants. The three structures are found in a very good agreement, and our recommended values are r(CC) = 120.2958(7) pm and r(CH) = 106.164(1) pm.     

An ab initio study of the vibronic, spin-orbit, and magnetic hyperfine structure in the X2Pi electronic state of NCO

In the present study we give the results of the ab initio calculations on the vibronic, spin-orbit, and magnetic hyperfine structure in the X (2)Pi electronic state of the NCO radical. The calculations of the potential surfaces and the electronic mean values of the hyperfine coupling constants are carried out by means of the density functional theory approach (B3LYP functional combined with an atomic orbital basis set suitable for calculations of the hyperfine structure). The vibronic levels, spin-orbit splitting, and the vibronic mean values of the components of the hyperfine tensor in the vibronic species are calculated using a variational method. The results of the calculations are in good agreement with the available experimental data.     

Spectroscopic Parameters of X3∑-, a1△, and A'3△ Electronic States of SO Radical

The potential energy curves (PECs) of three low-lying electronic states (X³∑^-, a¹△, and A^'3△) of SO radical have been studied by ab initio quantum chemical method. The calcula-tions were carried out with the full valence complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration in-teraction (MRCI) approach in combination with correlation-consistent basis sets. Effects of the core-valence correlation and relativistic corrections on the PECs are taken into account. The core-valence correlation correction is carried out with the cc-pCVDZ basis set. The way to consider the relativistic correction is to use the second-order Douglas-Kroll Hamiltonian approximation, and the correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit by the two-point energy extrapolation scheme. With these PECs, the spectroscopic parameters are determined.     

Exchange coupling in transition-metal complexes via density-functional theory: comparison and reliability of different basis set approaches

Theoretical methods based on density-functional theory with Gaussian, plane waves, and numerical basis sets were employed to evaluate the exchange coupling constants in transition-metal complexes. In the case of the numerical basis set, the effect of different computational parameters was tested. We analyzed whether and how the use of pseudopotentials affects the calculation of the exchange coupling constants. For the three different basis sets, a comparison of the exchange coupling constants and spin distributions shows that both the plane-wave and the numerical basis set approaches are accurate and reliable alternatives to the more established Gaussian basis functions.     

Toward spectroscopic accuracy for open-shell systems: molecular structure and hyperfine coupling constants of H2CN, H2CP, NH2, and PH2 as test cases

In the present paper, we investigate the molecular structure and hyperfine couplings of a series of σ radicals containing first- and second-row atoms (H(2)CN,H(2)CP,NH(2),PH(2)) for which accurate gas-phase microwave results are available. The presence of α- and, especially, β-hydrogen atoms makes the evaluation of magnetic properties of these radicals particularly challenging. Geometrical parameters have been computed by the coupled-cluster ansatz in conjunction with hierarchical series of basis sets, thus accounting for extrapolation to the complete basis-set limit. Core correlation as well as higher excitations in the electronic-correlation treatment have also been taken into account. An analogous approach has been employed for evaluating hyperfine coupling constants with particular emphasis given to basis-set, correlation, and geometrical effects. The corresponding vibrational corrections, required for a meaningful comparison to experimental data, have also been investigated. The remarkable agreement with experiment confirms the reliability of the present computational approach, already validated for π radicals, thus establishing the way for setting up a benchmark database for magnetic properties.     

含自旋轨道角动量耦合的耦合簇理论研究Zn2和Cd2二聚物的结构和光谱常数

在二分量相对论有效势和与之匹配的基组aug-cc-pvnz-pp (n=Q, 5)的基础上, 结合电子相关能的完备基组外推和四阶多项式拟合, 我们用含自旋轨道角动量耦合的耦合簇方法研究了Zn₂和Cd₂的结构和光谱常数. 尽管Zn₂和Cd₂的自旋轨道角动量耦合效应不及Hg₂的明显, 但还是把自旋轨道角动量耦合放在耦合簇迭代计算中, 以获得更加合理的理论结果. 通过比较, 理论结果与最新发表的实验结果或其他课题组的理论结果吻合得较好, 因此我们的理论计算将有助于丰富对Zn₂和Cd₂光谱性质的认识.     

New accurate reference energies for the G2/97 test set

A recently proposed computational protocol is employed to obtain highly accurate atomization energies for the full G2/97 test set, which consists of 148 diverse molecules. This computational protocol is based on the explicitly correlated coupled-cluster method with iterative single and double excitations as well as perturbative triple excitations, using quadruple-ζ basis sets. Corrections for higher excitations and core/core-valence correlation effects are accounted for in separate calculations. In this manner, suitable reference values are obtained with a mean deviation of -0.75 kJ/mol and a standard deviation of 1.06 kJ/mol with respect to the active thermochemical tables. Often, in the literature, new approximate methods (e.g., in the area of density functional theory) are compared to, or fitted to, experimental heats of formation of the G2/97 test set. We propose to use our atomization energies for this purpose because they are more accurate on average.     

High-level coupled-cluster methods for electron spin resonance spectra: on the experimental spectrum of the silacyclobutane radical cation

The silacyclobutane radical cation is a prototype intermediate in chemical reactions involving Si based organic molecules. In the interest of its full characterization, the experimentally determined isotropic hyperfine coupling constants of the hydrogens in silacyclobutane radical cation (c-SiC(3)(+)) have raised some interesting questions, leading to different interpretations of the spectrum. To help resolve this discrepancy, we report very high-level theoretical results with coupled-cluster theory using its analytical, response density matrix procedure, and recently proposed basis sets that are specific to ESR. The detailed studies of geometries, basis set effects, and electron correlation tend to support the B3LYP/6-31G-based reassignment of the ESR spectrum of the c-SiC(3)(+) radical cation by F?ngstr?m et al.