ANO Basis Sets Research Articles

Valence-to-core X-ray emission spectroscopy of transition metal tetrahalides: mechanisms governing intensities.

Valence-to-core (VtC) X-ray emission spectroscopy offers the opportunity to probe the valence electronic structure of a system filtered by selection rules. From this, the nature of its ligands can be inferred. While a preceding 1s ionization creates a core hole, in VtC XES this core hole is filled with electrons from mainly ligand based orbitals. In this work, we investigated the trends in the observed VtC intensities for a series of transition metal halides, which spans the first row transition metals from manganese to copper. Further, with the aid of computational studies, we corroborated these trends and identified the mechanisms and factors that dictate the observed intensity trends. Small amounts of metal p contribution to the ligand orbitals are known to give rise to intensity of a VtC transition. By employing an LCAO (linear combination of atomic orbitals) approach, we were able to assess the amount of metal p contribution to the ligand molecular orbitals, as well as the role of the transition dipole moment and correlate these factors to the experimentally observed intensities. Finally, by employing an ano (atomic natural orbital) basis set within the calculations, the nature of the metal p contribution (3p vs. 4p) was qualitatively assessed and their trends discussed within the same transition metal halide series.

The challenge of ab initio calculations of small neon clusters.

Weakly bound neon dimer, trimer and tetramers are studied at HF and CCSD(T) levels using Dunning, ANO and SIGMA-s basis sets. Their ground-state binding energies are studied along with some structural properties. SIGMA-s basis sets have been developed explicitly for this issue but in a manner that can be readily applied to other atoms for the study of larger weakly bound systems. The difficulties for attaining accurate results on these systems are assessed by the computation of total, atomization and correlation energies, as well as equilibrium distances, with several basis sets of increasing size, ranging from non-augmented to double-augmented versions. Extrapolations are proposed to predict stabilization energies and the results are compared with previously published data.

Can G4-like composite Ab Initio methods accurately predict vibrational harmonic frequencies?

Minimally empirical G4-like composite wavefunction theories [E. Semidalas and J. M. L. Martin, J. Chem. Theory Comput. 16, 4238–4255 and 7507–7524 (2020)] trained against the large and chemically diverse GMTKN55 benchmark suite have demonstrated both accuracy and cost-effectiveness in predicting thermochemistry, barrier heights, and noncovalent interaction energies. Here, we assess the spectroscopic accuracy of top-performing methods: G4-n, cc-G4-n, and G4-n-F12, and validate them against explicitly correlated coupled-cluster CCSD(T*)(F12*) harmonic vibrational frequencies and experimental data from the HFREQ2014 dataset, of small first- and second-row polyatomics. G4-T is three times more accurate than plain CCSD(T)/def2-TZVP, while G4-T ano is two times superior to CCSD(T)/ano-pVTZ. Combining CCSD(T)/ano-pVTZ with MP2-F12 in a parameter-free composite scheme results to a root-mean-square deviation of 5 cm − 1 relative to experiment, comparable to CCSD(T) at the complete basis set limit. Application to the harmonic frequencies of benzene reveals a significant advantage of composites with ANO basis sets – MP2/ano-pVmZ and [CCSD(T)-MP2]/ano-pVTZ (m = Q or 5) – over similar protocols based on CCSD(T)/def2-TZVP. Overall, G4-type composite energy schemes, particularly when combined with ANO basis sets in CCSD(T), are accurate and comparatively inexpensive tools for computational vibrational spectroscopy.

Accuracy of Different Electronic Basis Set Families for Anharmonic Molecular Vibrations: A Comprehensive Benchmark Study.

In this work, the accuracy and convergence of different electronic basis set families for the computation of anharmonic molecular vibrational spectroscopic calculations are benchmarked. A series of 39 different basis sets from different families following their hierarchy are assessed on VSCF and VSCF-PT2 algorithms with commonly used MP2 and DFT based B3LYP-D potentials for a set of molecular systems. Such an effort has been validated in a previous work ( J. Phys. Chem. A 2020, 124, 9203-9221) with split-valence basis sets for fundamentals and intensities. Here, fundamental transitions, vibrationally excited states, and intensities are compared with the experimental data to estimate the accuracy for a series of Jensen, Dunning, Calendar, Karlsruhe, and Sapporo basis set families. The convergence of basis sets are also compared with the large ANO basis set. Comprehensive statistical error analysis in terms of accuracy and precision was carried out to assess the performance of each basis set. It is observed that the improvement for the calculated harmonic and anharmonic values from the smaller basis sets to the medium (i.e., triple-ξ) is considerable. Beyond this, from medium to large basis sets, the convergence is slow and mostly posits nearly converged values. Basis sets with and without diffuse functions offer characteristically different accuracies and convergence patterns. Finally, recommendations are given on the choice of basis set chosen as black-box which can balance between accuracy and computational time, estimation of the errors, and their selections especially for large molecules.

Generation of Basis Sets for Accurate Molecular Calculations: Application to Helium Atom and Dimer

A new approach for basis set generation is reported and tested in helium atom and dimer. The basis sets thus computed, named sigma, range from DZ to 5Z and consist of the same composition as Dunning basis sets but with a different treatment of contractions. The performance of the sigma sets is analyzed for energy and other properties of He atom and He dimer, and the results are compared with those obtained with Dunning and ANO basis sets. The sigma basis sets and their extended versions up to triple augmented provide better energy values than Dunning basis sets of the same composition, and similar values to those attained with the currently available ANO. Extrapolation to complete basis set of correlation energy is compared between the sigma basis sets and those of Dunning, showing the better performance of the former in this respect.

New compact density matrix averaged ANO basis sets for relativistic calculations.

When including relativistic effects in quantum chemical calculations, basis sets optimized for relativistic Hamiltonians such as the atomic natural orbital-relativistic core-correlated (ANO-RCC) basis set have to be used to avoid large errors that appear upon contraction of the basis set. While the large size of the ANO-RCC basis set in terms of primitive basis functions allows for highly accurate calculations, it also hinders its applicability to large sized systems due to the computational costs. To tackle this problem, a new compact relativistic ANO basis set, the ANO-eXtra Small (XS) basis set, is introduced for elements H-Ca. The number of primitive basis functions in ANO-XS is about half that of the ANO-RCC basis set. This greatly reduces the computational costs in the integral calculations especially when used in combination with Cholesky decomposition. At the same time, the ANO-XS basis set is able to predict molecular properties such as bond lengths and excitation energies with reasonable errors compared to the larger ANO-RCC basis set. The main intention for the ANO-XS basis set is to be used in conjunction with the ANO-RCC basis set for large systems that can be divided with regions demanding different qualities of basis sets. This is exemplified in CASPT2 calculations for an Ir(C3H4N)3 complex, where substituting the larger ANO-RCC for the compact ANO-XS basis set at the ligand atoms yields only minor differences for a large number of excited states compared to calculations employing the ANO-RCC basis set on all atoms. Thus, accurate calculations including relativistic effects for large systems become more affordable with the new ANO-XS basis set.

The Total Ground State Energies and First Ionization Energies of the Incomplete 3d-Transition Metal-Elements Atoms

We studied the incomplete 3d-transition metal-lements, scandium through nikel, atoms and their corresponding cations by diffusion Monte Carlo (DMC) method with three different basis sets, namely VTZ_ANO, Stuttgart RSC 1997 ECP, and CRENBL ECP. Our calculations for total ground state energy and first ionization potential, agree very well with studies used LANL2DZB3LYP as basis sets, and with the experimental values of first ionization potential. Moreover, we found that the calculations with VTZ_ANO basis set are more accurate than those with the other two basis sets.

Applications to metal K pre-edges of transition metal dimers illustrate the approximate origin independence for the intensities in the length representation

ABSTRACTX-ray absorption spectroscopy (XAS) in the metal K pre-edge is a standard probe of electronic and geometric structure of transition metal complexes. Simulating the K pre-edge spectra requires contributions beyond the electric dipole, but if that term is non-zero, the second-order terms, e.g. electric quadrupoles, are no longer origin-independent. In the velocity representation, complete origin independence can be achieved by including all terms to the same order in the oscillator strength. Here, we implement that approach in the length representation and use it for restricted active space (RAS) simulations of metal K pre-edges of iron monomers and dimers. Complete origin independence is not achieved and the size of the remaining errors depends on the electric dipole oscillator strength and its ratio in length and velocity representations. The error in the origin independence is in the ANO basis sets two orders of magnitude smaller than the value of the individual contributions. For systems with strong electric dipole contributions, the errors are not significant within 3 Å from a metal centre, far enough to handle many multi-metal systems. Furthermore, we discuss the convergence of the multipole expansion, the possibility to assign spectral contributions, and the origin of negative absorption intensities.

A Density Functional Theory and ab Initio Investigation of the Oxidation Reaction of CO by IO Radicals.

To get an insight into the possible reactivity between iodine oxides and CO, a first step was to study the thermochemical properties and kinetic parameters of the reaction between IO and CO using theoretical chemistry tools. All stationary points involved were optimized using the Becke's three-parameter hybrid exchange functional coupled with the Lee-Yang-Parr nonlocal correlation functional (B3LYP) and the Møller-Plesset second-order perturbation theory (MP2). Single-point energy calculations were performed using the coupled cluster theory with the iterative inclusion of singles and doubles and the perturbative estimation for triple excitations (CCSD(T)) and the aug-cc-pVnZ (n = T, Q, and 5) basis sets on geometries previously optimized at the aug-cc-pVTZ level. The energetics was then recalculated using the one-component DK-CCSD(T) approach with the relativistic ANO basis sets. The spin-orbit coupling for the iodine containing species was calculated a posteriori using the restricted active space state interaction method in conjunction with the multiconfigurational perturbation theory (CASPT2/RASSI) employing the complete active space (CASSCF) wave function as the reference. The CCSD(T) energies were also corrected for BSSE for molecular complexes and refined with the extrapolation to CBS limit while the DK-CCSD(T) values were refined with the extrapolation to FCI. The exploration of the potential energy surface revealed a two-steps mechanism with a trans and a cis pathway. The rate constants for the direct and complex mechanism were computed as a function of temperature (250-2500 K) using the canonical transition state theory. The three-parameter Arrhenius expressions obtained for the direct and indirect mechanism at the DK-CCSD(T)-cf level of theory is 1.49 × 10(-17) × T(1.77) exp(-47.4 (kJ mol(-1))/RT).

Beryllium dimer: a bond based on non-dynamical correlation.

The bond nature in beryllium dimer has been theoretically investigated using high-level ab initio methods. A series of ANO basis sets of increasing quality, going from sp to spdf ghi contractions, has been employed, combined with HF, CAS-SCF, CISD, and MRCI calculations with several different active spaces. The quality of these calculations has been checked by comparing the results with valence Full-CI calculations, performed with the same basis sets. It is shown that two quasi-degenerated partly occupied orbitals play a crucial role to give a qualitatively correct description of the bond. Their nature is similar to that of the edge orbitals that give rise to the quasi-degenerated singlet-triplet states in longer beryllium chains.

Quantum-chemical ab initio investigation of the vibrational spectrum of halon 1113 and its anharmonic force field: A joint experimental and computational approach

Halon 1113 (chlorotrifluoroethene), used in the synthesis of fluorocarbon-based polymers, has been recently detected in the atmosphere and it is a potential source of chlorine atoms. In this work, the vibrational properties of chlorotrifluoroethene are studied in the 125–5000cm−1 region by coupling Fourier-transform infrared spectroscopy and high-level ab initio calculations. The vibrational analysis is performed over the whole spectral range and band intensities are obtained in the range 400–3100cm−1. Ab initio calculations of the anharmonic force field are performed at the coupled cluster level of theory employing either cc-pVTZ or ANO basis sets. Vibration perturbation theory is applied to obtain spectroscopic parameters from the computed anharmonic force fields. The present results provide a solid interpretation of chlorotrifluoroethene vibrational spectrum, and they represent a significant reference for future studies on this molecule, being also the first published data on absorption cross sections and ab initio calculations.

On the Relaxation Mechanisms of 6-Azauracil

The nonadiabatic photochemistry of 6-azauracil has been studied by means of the CASPT2//CASSCF protocol and double-ζ plus polarization ANO basis sets. Minimum energy states, transition states, minimum energy paths, and surface intersections have been computed in order to obtain an accurate description of several potential energy hypersurfaces. It is concluded that, after absorption of ultraviolet radiation (248 nm), two main relaxation mechanisms may occur, via which the lowest (3)(ππ*) state can be populated. The first one takes place via a conical intersection involving the bright (1)(ππ*) and the lowest (1)(nπ*) states, ((1)ππ*/(1)nπ*)(CI), from which a low-energy singlet-triplet crossing, ((1)nπ*/(3)ππ*)(STC), connecting the (1)(nπ*) state to the lowest (3)(ππ*) triplet state is accessible. The second mechanism arises via a singlet-triplet crossing, ((1)ππ*/(3)nπ*)(STC), leading to a conical intersection in the triplet manifold, ((3)nπ*/(3)ππ*)(CI), evolving to the lowest (3)(ππ*) state. Further radiationless decay to the ground state is possible through a (gs/(3)ππ*)(STC).

Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods?

The performance of several families of basis sets for correlated wave function calculations on molecules is studied. The widely used correlation-consistent basis set family cc-pVXZ (n = D, T, Q, 5) is compared to a systematic series of atomic natural orbital basis sets (ano-pVXZ). These basis sets are built from the cc-pV6Z primitives in atomic multireference average coupled pair functional (MR-ACPF) calculations. Segmented basis sets optimized for self-consistent field calculations (def2-SVP, def2-TZVPP, and def2-QZVPP as well as "pc-n", n = 1, 2, 3) were also tested. Reference Hartree-Fock energies are determined with the uncontracted aug-cc-pV6Z basis set for a set of 21 small molecules built from H, B, C, N, O, and F. Reference coupled cluster CCSD(T) correlation energies were determined from extrapolation at the cc-pV5Z/cc-pV6Z level. It is found that the ano-pVXZ basis sets outperform the other basis sets. The error in the SCF energies compared to cc-pVXZ basis sets is reduced by about a factor of 3 at each cardinal number. In addition, the ano-pVXZ consistently recovers more correlation energy than their competitors at each cardinal number. The ability of the four families of basis sets to extrapolate SCF and correlation energies to the basis set limit has been investigated. A conclusion by Truhlar is confirmed that the optimum exponent for correlation energy extrapolations at the DZ/TZ level is ∼2.4. All TZ/QZ basis set pairs lead to an optimum exponent close to the expected value of 3. The SCF energy extrapolation proposed by Petersson and co-workers is found to be effective. At the DZ/TZ level, errors in total energies of less than 2 mEh are found for the test set, while at the TZ/QZ level one obtains the total energies within ∼0.3 mEh of the basis set limit. For extrapolation, the "cc" and "ano" bases are found to be similarly successful. Extrapolation results were compared to explicitly correlated calculations with dedicated basis sets (cc-pVXZ-F12) as well as the ano-pVXZ bases. It is found that the ano-pVXZ+ basis sets perform as well as the cc-pVXZ-F12 family (both are of comparable size); additional improvement should be possible by reoptimizing the ANO basis sets for explicitly correlated calculations. The error of the extrapolated energies is about 2-3 times smaller than what was found in the explicitly correlated calculations. However, the error in the explicitly correlated calculations is more systematic, and hence the same conclusion may not hold for the computation of energy differences.

Mixed Valence Character of Anionic Linear Beryllium Chains: A CAS-SCF and MR-CI Study

A theoretical investigation on the mixed valence behavior, or bistability, of a series of anionic linear chains composed of beryllium atoms is presented. Calculations on Be(N)- (with N = 7, ..., 13) were performed at CAS-SCF and MR-CI levels by using an ANO basis set containing 6s4p3d2f contracted orbitals for each atom. Our results show a consistent gradual shift between different classes of mixed valence compounds as the number of beryllium atoms increases, from strong coupling (class III) toward valence-trapped (class II). Indeed, in the largest cases (N > 10), the anionic chains were found to become asymptotically closer to class I, where the coupling vanishes. The intramolecular electron-transfer parameters V(ab), E(barr), and E(opt) were calculated for each atomic chain. It is shown that the decrease of V(ab) with increasing N follows an exponential pattern.

Electronic Bistability in Linear Beryllium Chains

A theoretical investigation on the mixed-valence behavior (bistability) of a series of cationic linear chains composed of beryllium atoms, Be(N)(+) (with N = 6,..., 12), is presented. The calculations were performed at CAS-SCF and MR-CI levels by using an ANO basis set containing 6s4p3d2f orbitals for each atom. Our results show a consistent gradual shift between different classes of mixed-valence compounds as the number of beryllium atoms increases, from class III strong coupling toward class II valence trapped. Indeed, in the largest cases (N > 10), the cationic chains were found to be closer to class I, where the coupling vanishes. The intramolecular electron transfer parameters V(ab), E(a), and E(opt) were calculated for each atomic chain. It is shown that the decrease of V(ab) with increasing N follows an exponential pattern.

An investigation of the electronic structure of some 3-monosubstituted-2-methylpropenes through computational chemistry and photoelectron spectroscopy

The photoelectron (PE) spectra of some 3-monosubstituted 2-methylpropenes H 2C C(CH 3)CH 2X [X = Cl, Br, I, OH, OMe, OEt, SH, SMe, SEt, N(Me) 2 and N(Et) 2] have been recorded. A preliminary analysis is presented indicating some trends in the ionization potentials associated with application of OVGF method and NBO analysis from MP2/6-31G(d,p) and cc-pVDZ level of theory indicating that the more effective hyperconjugation effect leads to the most stable conformers. The sensitivity of the outermost ionization energies of selected molecules with respect to the level of theory was analyzed. Application of the CASPT2 method with ANO basis set and geometries from MP2 calculations provided results in excellent agreement with the experimental data.

Theoretical Study of Oxidative Additions of H2 and MeCN to a Nickel(0) Complex: Significantly Large Correlation Effects and Characteristic Features of the Reaction

Oxidative addition of H2 to Ni(PH3)2 was theoretically studied as a prototype of nickel-catalyzed sigma-bond activation reaction, where CASSCF, CASPT2, CCSD(T), broken symmetry (Bs) MP2 to MP4(SDTQ), and DFT methods were employed. The CASPT2 method yields a reliable potential energy curve (PEC) when the active space consists of 10 electrons and 10 orbitals including five outer 3d' orbitals. The CCSD(T) method presents almost the same PEC as the CASPT2-calculated one, when either the ANO or the cc-pVTZ basis set is used for Ni. Bs-MP4(SDTQ)-calculated PEC is similar to those calculated by the CASPT2/ANO method, while the PEC is not smooth around the transition state. In the DFT calculation, ANO, cc-pVTZ, and triple-zeta quality basis sets (SDB) with Stuttgart-Dresden-Bonn effective core potentials (ECPs) must be used for Ni. The DFT-calculated reaction energy is somewhat smaller than the CASPT2- and CCSD(T)-calculated values, while B3PW91 and mPW1PW91 present moderately better energy changes than BLYP, B1LYP, and B3LYP. Oxidative addition of MeCN to Ni(PH3)2 was investigated by the DFT(B3PW91) and CCSD(T) methods. Almost the same activation barrier was calculated by these methods, when cc-pVTZ was employed for Ni. However, the DFT method moderately underestimates the binding energy of the reactant complex and the reaction energy compared to the CCSD(T) method. This oxidative addition exhibits interesting characteristic features, as follows: The barrier height relative to infinite separation is lower, and the product is more stable than those of the oxidative addition of C2H6. These differences are discussed in detail in terms of Ni-Me and Ni-CN bond energies and the participation of the CN pi* orbital to stabilization interaction in the transition state.

CuNO2 and Cu(+)NO2 Revisited: A Comparative ab Initio and DFT Study.

We have reinvestigated CuNO2 and Cu(+)NO2 at ab initio as well as at pure and hybrid DFT levels of approximation employing large ANO basis sets. The systems were fully optimized using the CCSD(T), QCISD(T), BPW91, PBE, PBE0, and B3LYP methods. Several stationary points (minima and transition structures) were found on the related potential energy surfaces (PES). The C2v bidentate η(2)-O,O isomer is calculated to be the most stable species on the CuNO2 PES, followed by two monodentate isomers [Formula: see text] the Cs η(1)-O and C2v η(1)-N species which are higher in energy by 12 and 14 kcal/mol, respectively, at CCSD(T)/Basis-II (where Basis-II is 21s15p10d6f4g/8s7p5d3f2g for Cu; 14s9p4d3f/5s4p3d2f for O and N). On the Cu(+)NO2 PES, the Cs monodentate η(1)-O trans (0 kcal/mol) and cis (+3 kcal/mol at CCSD(T)/Basis-II) isomers are found, followed by the C2v monodentate η(1)-N isomer (+14 kcal/mol at CCSD/Basis-II). In contrast to the pure DFT, the hybrid DFT methods perform reasonably well for predicting the relative stabilities (except for η(1)-N of CuNO2) and structures; however, their predictions of the bond dissociation energies are less reliable (for CuNO2 the difference is as much as 10 kcal/mol compared to the CCSD(T) values). The performance of the QCISD(T) method was analyzed, and, furthermore, the issue of symmetry breaking was investigated.

Van der Waals interactions and dipole polarizabilities of lanthanides: Tm(F2)–He and Yb(S1)–He potentials

Anisotropic dipole polarizabilities of Tm(2F), Tm+2(2F), and Yb(1S) are calculated using the finite-field multireference averaged quadratic coupled cluster (MR-AQCC) (Tm and Tm+2) and RCCSD(T) (Yb) methods with small-core relativistic pseudopotentials ECP28MWB combined with the augmented ANO basis sets. The lanthanide atoms are strongly polarizable with the scalar part originating from the 6s electrons and the tensorial part from the open 4f shells. The adiabatic interaction potentials 2Sigma+, 2Pi, 2Delta, and 2Phi of Tm(2F)-He and Tm+2(2F)-He were examined by the multireference approaches, multireference configuration interaction and MR-AQCC, using the basis sets designed in the polarizability calculations. A closed-shell lanthanide system Yb(1S)-He was included for comparison. The Tm-He 2Sigma+, 2Pi, 2Delta, and 2Phi interaction potentials are very shallow and nearly degenerate (within 0.01 cm(-1)), with the well depths in the range of 2.35-2.36 cm(-1) at R=6.17 A. The basis-set saturated well depths are expected to be larger by ca. 25%, as estimated using the bond-function augmented basis set. The interactions of lanthanide atoms with He are one order of magnitude less anisotropic than those involving first-row transition metal atoms. The suppression of anisotropy is chiefly attributed to the screening effected by the 6s shell. When these electrons are removed as in the di-cation complex Tm+2(2F)-He, the potentials deepen to a thousand wave number range and their anisotropy is enhanced 500-fold.

THE ESTIMATIONS OF INNER-SHELL IONIZATION ENERGIES FOR ALKYL HALIDES: A DESIGNATED SINGLE-CONFIGURATION CASSCF APPROACH AND ADVANCED CORRECTION

Based on the Franck–Condon principle, vertical ionization energies regarding the inner-shell valence electrons of alkyl halides and their unsaturated analogues were evaluated with a designated single-configuration complete active self-consistent field (CASSCF) approach as well as the advanced correction with configuration interaction. Excitations corresponding to the elimination of one electron from a specific molecular orbital of these species were calculated by the deviation between the energy of the SCF-optimized neutral structure and of its cation. The freezing over the outer orbitals with identical symmetry was achieved while performing the CASSCF ionization calculation for the inner orbitals. These energy evaluations utilized Pople's 6-31G*, 6-311G** and Roos' ANO basis sets. Computed results agreed well with the experimental data. The characters for the molecular orbitals of corresponding vertical ionizations could be qualitatively assigned by the MOLDEN visualization program.