Computational convergence of electronic structure calculations of transition metal ligand complexes

Calculations of binding energies and optimum geometries of compounds of the series M(H₂O)⁺ with M = Sc to Zn have been carried out and compared with gas-phase experimental data and with the Rosi and Bauschlicher MCPF calculations. Hartree–Fock calculations and correlated calculations at MP2, MP4, and QCISD(T) levels were used to test the dependence of the results upon the level of correlation. A test of basis set dependence was also carried out, using parallel calculations on four basis sets ranging in size from a small DZ set to a TZ contraction. Correlation levels above MP2 and elaboration of the metal d-function basis set to (4d/3d) size or greater were both necessary for convergence with the most uniformly reliable results obtained from QCISD(T) calculations on a basis set with a (6d/4d) contraction for the d-function space. However, MP2 or higher-level calculations with a contracted four or five d function set [(5d/3d) or (4d/3d)] are capable of yielding results on binding energies and geometries close to the current gas-phase experimental uncertainty on electrostatically bound transition metal complexes. © 1993 John Wiley & Sons, Inc.     

Anharmonic force field and spectroscopic constants of silene: an ab initio study

High-level ab initio calculations with large basis sets are reported for silene, H₂C=SiH₂. Correlated harmonic force fields are obtained from coupled cluster CCSD(T) calculations with the cc-pVQZ basis (cc-pVTZ for H) while the anharmonic force fields are computed at the MP2/TZ2Pf level. There is excellent agreement with the available experimental data, in particular the equilibrium geometry and the fundamental vibrational frequencies. Many other spectroscopic constants are predicted for the C _{2 v} isotopomers of silene. Received: 27 May 1998 / Accepted: 23 July 1998 / Published online: 9 October 1998     

A charge-conserving approximation method for ab initio calculations

A new method is presented for approximate ab initio calculations in quantum chemistry. It is called CCAM (charge conserving approximation method). The calculation method does not include the use of empirical parameters. We use Slater type orbitals as basis set, replacing STO's by STO-2G functions to evaluate three- and four-center integrals and making the STO-2G two-orbital charge distributions have the same total charge as STO. The results are presented for test calculations on five molecules. In view of these results, CCAM is better than ab initio calculations over STO-6G in the results on total energies, kinetic energies and occupied orbital energies. In atomic populations, dipole moments and unoccupied orbital energies, CCAM is also satisfactory. We estimate that CCAM would be as fast as ab initio calculations over STO-2G in evaluating molecular integrals.     

Order of stabilities in water nanoclusters: Insight from some recent double‐hybrid functionals

In the present work, the applicability of some of the recently proposed and modern double‐hybrid (DH) models and other density functional theory (DFT) approximations has been analyzed for a difficult test, the order of stability in low‐energy isomers of water nanoclusters. In particular, we aim to systematically investigate for these functionals the role played by several factors such as dispersion correction, integrand functions upon which the DHs are based, and different spin scaling for the perturbative term in DH calculations of the relative energies for various isomers of water nanoclusters (H₂O)₂₀. From the obtained results, the superior performance of DHs with respect to the functionals from previous rungs is confirmed. It is shown that the dispersion corrected DHs perform better than noncorrected counterparts. Plus, the DH models based on cubic integrand (CI) and quadratic integrand (QI) functions are nearly equivalent in performance. We also find that using only contributions of electron pairs with opposite spin for the perturbative correlation part through scaled opposite spin scheme does not represent a significant improvement on accuracy of the results. Putting all the results together, the dispersion corrected parameterized DHs and parameter‐free DH models involving CI and QI functions outperform other approximations for relative energies of water 20‐mers. Altogether, predicting the correct order of the stability in water nanoclusters may be considered as another Achilles' heel in DFT calculations, although more analyses in this context are still needed. © 2016 Wiley Periodicals, Inc.     

The methyl isocyanide isomerization: A CNDO/2 study with partitioning of energy

Ab initio LCAO MO SCF calculations have been carried out to predict core electron binding energies and shifts in fluoro- and chloro-methanes. The quality of the calculations ranges from a better than double zeta basis set to minimal STO (3 G) basis set. Predictions of binding energies and shifts are made using Koopmans' theorem, hole state calculations and equivalent cores calculations. Using a flexible basis set there is very little difference in the prediction of shifts by these three methods but for minimal basis set calculations the equivalent cores calculations give the best results.     

DFT Investigation on the Insertion Reaction of an Isocyanide into the（Silyl）（silylene）molybdenum Si-C Bond

The chemistry of silylene-transition-metal complexes LnM(=SiR2)SiR3 is one of the attractive synthetic targets in organometallic chemistry for such complexes are key intermediates in many transition metal-catalyzed systems.In the present work,the novel insertion reactions of an isocyanide into the Cp*Mo(CO)2(=SiMe2)(SiMe3) Si-C bond were investigated extensively by using the DFT method.The effective core potentials(ECP) with a double-ζ valence basis set(LanL2DZ) were employed for Mo and Si and the standard 6-31G basis set for all other atoms.Polarization functions[22] were added for Si(ζd = 0.262),C(ζd = 0.8) and N(ζd = 0.8).The effect of solvent was evaluated with the standard PCM model.Our calculations show that the two-step channel is energetically favorable,and the solvation mode has minor influence on the relative energies.     

The electronic structure of small sodium clusters

Ab initio molecular orbital calculations using the STO3-21G basis set has been carried out for the cluster series Na _n ⁺ , Na _n , and Na _n ^– (wheren=2–7). The basis set is shown to be reliable compared with more extensive basis sets at the Hartree-Fock level. Thirty-one optimized structures are reported and discussed, many of which (especially for the anions) have not been considered. The STO3-21G//STO3-21G calculations suggest that for most of the species the optimum geometries are planar. In particular, the optimized structures for the anionic species should provide a starting point for more sophisticated configuration interaction calculations.     

Ab initio calculations of guanidinium–carboxylate interaction

Ab initio calculations (self-consistent-field Hartree–Fock) using 6-31G and STO -4G basis sets are used to investigate the interaction between guanidinium and methylguanidinium ion with the carboxylate group of formate. Binding energies and optimum geometries are obtained and compared with reported results using a smaller basis set (STO -3G). The importance of this interaction in proteinsubstrate binding is discussed.     

Double hybrids and time-dependent density functional theory: An implementation and benchmark on charge transfer excited states

In this paper we present the implementation and benchmarking of a Time Dependent Density Functional Theory approach in conjunction with Double Hybrid (DH) functionals. We focused on the analysis of their performance for through space charge-transfer (CT) excitations which are well known to be very problematic for commonly used functionals, such as global hybrids.Two different families of functionals were compared, each of them containing pure, hybrid and double-hybrid functionals.The results obtained show that, beside the robustness of the implementation, these functionals provide results with an accuracy comparable to that of adjusted range-separated functionals, with the relevant difference that for DHs no parameter is tuned on specific compounds thus making them more appealing for a general use. Furthermore, the algorithm described and implemented is characterized by the same computational cost scaling as that of the ground state algorithm employed for MP2 and double hybrids.     

Analysis of fourth-order Møller–Plesset limit energies: the importance of three-electron correlation effects

Fourth-order M?ller–Plesset (MP4) correlation energies are computed for 28 atoms and simple molecules employing Dunning's correlation-consistent polarized-valence m-zeta basis sets for m=2, 3, 4, and 5. Extrapolation formulas are used to predict MP4 energies for infinitely large basis sets. It is shown that both total and partial MP4 correlation energies can be extrapolated to limit values and that the sum of extrapolated partial MP4 energies equals the extrapolated total MP4 correlation energy within calculational accuracy. Therefore, partial MP4 correlation energies can be presented in the form of an MP4 spectrum reflecting the relative importance of different correlation effects. Typical trends in calculated correlation effects for a given class of electron systems are independent of the basis set used. As first found by Cremer and He [(1996) J Phys Chem 100:6173], one can use MP4 spectra to distinguish between electron systems with well-separated electron pairs and systems for which electrons cluster in a confined region of atomic or molecular space. MP4 spectra for increasing size of the basis set reveal that smaller basis set calculations underestimate the importance of three-electron correlation effects for both classes by overestimating the importance of pair correlation effects. The minimum size of a basis set required for reliable MP4 calculations is given by a valence triple-zeta polarized basis, which even in the case of anions performs better than a valence double-zeta basis augmented by diffuse functions. Received: 14 June 2000 / Accepted: 16 June 2000 / Published online: 24 October 2000     

Methods for the calculation of Voh in OH?O hydrogen bonds

Ab initio calculations are reported for dimerization-induced changes, Δk, in the harmonic force constant k of the H-bonded OH in water dimer. Two dimer geometries are considered. Δk is obtained by considering the perturbation of a given monomer OH potential by the interaction energy in the dimer in question. The interaction energy is partitioned to identify the role of the various contributions to Δk. The sensitivity of Δk to the choice of the one-electron basis set is studied by using five different basis sets, some of which have a set of bond functions in the H? O bond. At the correlated level, correction for basis set superposition error is found to be essential. A comparison is made of the correlation contribution to Δk as given by the CEPA1, MP2, MP3, and MP4 methods. Of these, MP2 gives exaggerated results. Nevertheless, for economical and reasonably accurate calculations on large systems the MP2 approach in the ESPB basis set is advocated. The most accurate calculations yield a shift Δv_0-;1 of – 121 cm^?1 for the uncoupled donor O-H vibrational frequency in water dimer.     

The error due to neglecting the core spin–orbit splitting in valence ZORA calculations with frozen core approximation and its elimination

In valence zeroth-order regular approximation (ZORA) calculations with frozen core approximation, when the basis set optimized to the related scalar relativistic ZORA calculations is used, neglecting the core spin–orbit splitting may result in additional basis set truncation errors. It is found that the error is negligible for most elements except the 6p-block elements. When the basis set is extended by a p-type STO function put on the 6p element atoms with the ζ value proper to 5p_1/2 orbitals, the error can be reduced to be negligible. The calculated atomic properties related to valence orbitals can be improved greatly by use of this extended basis set. The frozen core approximation calculations of some molecules containing Tl, Pb and Bi with closed shells show that neglecting the core spin–orbit splitting only slightly affects the calculated bond lengths and bond energies, and the calculated molecular property can also be improved slightly by use of the extended basis sets.     

Physical nature of silane⋯carbene dimers revealed by state-of-the-art ab initio calculations

Using the SAPT2 + 3(CCD)δMP2 method in complete basis set (CBS) limit, it is shown that the interactions in the recently studied silane⋯carbene dimers are mainly dispersive in nature. Consequently, slow convergence of dispersion energy also forces slow convergence of the interaction energy. Therefore, obtaining very accurate values requires extrapolation of the correlation part to the CBS limit. The most accurate values obtained at the CCSD(T)/CBS level of theory show that the studied silane⋯carbene dimers are rather weakly bound, with interaction energies ranging from about −1.9 to −1.3 kcal/mol. Comparing to CCSD(T)/CBS, it will be shown that SCS-MP2 and MP2C methods clearly underestimate and methods based on SAPT2+ and having some third-order corrections, as well as the MP2 method, overestimate values of interaction energies. Popular SAPT(DFT) method performs better than SCS-MP2 and MP2C; nevertheless, underestimation is still considerable. The underestimation is slightly quenched if third-order dispersion energy and its exchange counterpart is added to the SAPT(DFT). The closest value of CCSD(T)/CBS has been given by the SAPT2 + (3)(CCD)δMP2 method in quadruple-ζ basis set. © 2019 Wiley Periodicals, Inc.     

Density-functional generalized-gradient and hybrid calculations of electromagnetic properties using Slater basis sets

In this paper we extend our density-functional theory calculations, with generalized gradient approximation and hybrid functionals, using Slater-type orbitals (STOs), to the determination of second-order molecular properties. The key to the entire methodology involves the fitting of all STO basis function products to an auxiliary STO basis, through the minimization of electron-repulsion integrals. The selected properties are (i) dipole polarizabilities, (ii) nuclear magnetic shielding constants, and (iii) nuclear spin-spin coupling constants. In all cases the one-electron integrals involving STOs were evaluated by quadrature. The implementation for (ii) involved some complexity because we used gauge-including atomic orbitals. The presence of two-electron integrals on the right-hand side of the coupled equations meant that the fitting procedure had to be implemented. For (iii) in the hybrid case, fitting procedures were again required for the exchange contributions. For each property we studied a number of small molecules. We first obtained an estimate of the basis set limit using Gaussian-type orbitals (GTOs). We then showed how it is possible to reproduce these values using a STO basis set. For (ii) a regular TZ2P quality STO basis was adequate; for (i) the addition of one set of diffuse functions (determined by Slater's rules) gave the required accuracy; for (iii) it was necessary to add a set of 1s functions, including one very tight function, to give the desired result. In summary, we show that it is possible to predict second-order molecular properties using STO basis sets with an accuracy comparable with large GTO basis sets. We did not encounter any major difficulties with either the selection of the bases or the implementation of the procedures. Although the energy code (especially in the hybrid case) may not be competitive with a regular GTO code, for properties we find that STOs are more attractive.     

Theoretical studies of organometallic compounds. I. All electron and pseudopotential calculations of Ti(CH3)nCl4 − n (n = 0–4)

The performance of effective core potentials (ECP) and model potentials (MP) has been studied by calculating the geometries and reaction energies of isodesmic reactions for the molecules Ti(CH₃)_nCl_{4 ? n} (n = 0–4) at the Hartree–Fock level of theory. The results are compared with data from all electron calculations and experimental results as far as available. The all electron calculations were performed with a 3-21G basis set from Hehre and a (53321/521/41) basis set from Huzinaga. For the ECP calculations the potentials developed by Hay and Wadt, and for the MP calculations, the model potentials developed by Sakai and Huzinaga, are employed. © 1992 by John Wiley & Sons, Inc.     

On the existence of SH3, SeH3, and TeH3: Discrepancies between all-electron and pseudopotential calculations

Ab initio calculations using both pseudopotential and double and triple-ζ all-electron basis sets, with and without electron correlation (MP2, QCISD), have been performed on the λ⁴-sulfanyl (SH₃), λ⁴-selanyl (SeH₃), and λ⁴-tellanyl (TeH₃) radicals. All-electron basis sets of double-ζ quality predict that SH₃ and SeH₃ correspond to transition states on their respective potential energy surfaces. In contrast, the pseudopotentials of Hay and Wadt predict that SH₃ and SeH₃ correspond to local minima at the QCISD level of theory while the pseudopotentials of Christiansen and Stevens predict transition states. By comparison, TeH₃ proved to be a local minimum at all levels of theory. Interestingly, when a very large (triple-ζ) all-electron basis set was used, SH₃ proved to be a transition state; however, in this instance the potential energy surface was found to be much flatter than in the case for which a double-ζ basis set was used, suggesting that further improvements in the basis set may lead to a local minimum. Further improvements in the all-electron selenium basis also led to a local minimum for SeH₃ at the QCISD level of theory. © 1995 by John Wiley & Sons, Inc.     

Oxidation energies of shuttle molecules candidates in lithium-ion batteries from double-hybrid models

As promising candidates for protecting against both overcharge and overdischarge of lithium-ion batteries, the shuttle molecules should be named. Considering the action mechanism of these molecules, it is turned out that their oxidation energies are important factors. Alongside the experimental efforts, computational chemistry within density functional theory (DFT) can play imperative roles in this respect. In the present contribution, in order to predict the oxidation energies of shuttle molecules the double-hybrid (DH) approximations from DFT are of concern. In particular, applicability of the recently proposed DHs including parameterized, parameter-free, and spin-opposite-scaled functionals is evaluated for our purpose. With more or less different accountabilities of the DHs under study, it is revealed that from the parameterized and parameter-free approximations, the B2-PLYP and Perdew-Burke-Ernzerhof (PBE)-cubic integrand DH (CIDH) functionals, respectively, have the lowest deviations while the SOS0-PBE0-DH is the winner against others within the category of spin-opposite-scaled DHs. Perusing the role of both nonlocal exchange and correlation contributions in the energy expression of DHs on the predicted oxidation energies unveils that the high fractions of these terms do not guarantee better performance, but an appropriate proportion between the two is needed to achieve a reliable accuracy. Although this study ascertains the efficiency of DHs for describing the oxidation energies of shuttle molecules candidates, we hope that our findings can function as an inspiring avenue to develop novel DH approximations with a broad range of applications in electrochemistry.     

Ab initio MO Calculations of benzene + TCNE and naphthalene + TCNE complexes with STO-3G π-split basis set

Ab initio SCF MO calculations have been carried out on benzene + TCNE (tetracyanoethylene) and naphthalene + TCNE complexes with the STO -3G, STO -3G π-split (STO -3G for π orbitals and a split basis for π orbitals), and 4–31G basis sets. The interaction energy, gross charges, dipole moment, and the electron density in the middle plane of the complexes have also been evaluated. The STO -3G π-split basis set is appropriate for the calculation of large π–π stacking complexes from two points of view, production of reliable results and ease of computations. The approximation scheme based on the semiorthogonalized orgitals is revealed to be very efficient to save CPU time and storage in such calculations. The stable conformation and the charge-transfer interaction of the two complexes are discussed on the basis of the calculated quantities.     

An ab initio study on HXC(double bond)O …︁ HY molecular complexes (X,Y = F,Cl)

Post-Hartree-Fock calculations were carried out to predict the stabilities and properties of four HClCO …︁ HCl, HClCO …︁ HF, HFCO …︁ HCl, and HFCO …︁ HF molecular complexes. Full geometry optimizations and vibrational frequency calculations were performed for all systems using standard 6-311G (d, p) and 6-311G (2d,2p) basis sets at the MP 2 level of theory. Single-point calculations of the interaction energies were carried out for all complexes at the MP 4(SDTQ ) level with the 6-311G (d, p) basis set. All systems were found to be stable and their predicted molecular parameters match well available (very scarce) experimental data. © 1996 John Wiley & Sons, Inc.     

Application of combined Hartree–Fock–Roothaan theory to molecules with arbitrary number of closed and open shells

In this study, the applicability of the combined Hartree–Fock–Roothaan (CHFR) theory of atomic-molecular and nuclear systems (Guseinov, J Math Chem 42:177, 2007) to the molecules is demonstrated using minimal basis set of Slater type orbitals (STO). As an example of application of CHFR theory, the calculations have been performed for the ground state of electronic configuration of methylene molecule CH ₂ which has two open shells. The results of computer calculations for the orbital, kinetic and total energies, linear combination coefficients of symmetrized molecular orbitals and virial ratios are presented.