Getaway from the Geometry Factor Error in the Molecular Property Calculations: Efficient pecG-n (n = 1, 2) Basis Sets for the Geometry Optimization of Molecules Containing Light p Elements.

The basis of all molecular property quantum chemical calculations is the correct equilibrium geometry. In this paper, new efficient pecG-n (n = 1, 2) basis sets for the geometry optimization of molecules containing hydrogen and p elements of 2-3 periods are proposed. These basis sets were optimized via the property-energy consistent (PEC) algorithm directed to the minimization of the molecular energy gradient relative to the bond lengths. New basis sets are compact and give equilibrium geometries of very high quality, which is comparable to that provided by considerably larger energy-optimized basis sets. The equilibrium geometries obtained with the pecG-n (n = 1, 2) basis sets and the other basis sets of diverse quality were tested in the CCSD calculations of different second-order molecular properties, including NMR shielding constants, static polarizabilities, and static magnetizabilities. As a result, new basis sets have demonstrated far superior performance as compared to the other energy-optimized basis sets of the same or close sizes commonly used at the geometry optimization stage.

On the Efficiency of the Density Functional Theory (DFT)-Based Computational Protocol for 1H and 13C Nuclear Magnetic Resonance (NMR) Chemical Shifts of Natural Products: Studying the Accuracy of the pecS-n (n = 1, 2) Basis Sets.

The basis set issue has always been one of the most important factors of accuracy in the quantum chemical calculations of NMR chemical shifts. In a previous paper, we developed new pecS-n (n = 1, 2) basis sets purposed for the calculations of the NMR chemical shifts of the nuclei of the most popular NMR-active isotopes of 1-2 row elements and successfully approbated these on the DFT calculations of chemical shifts in a limited series of small molecules. In this paper, we demonstrate the performance of the pecS-n (n = 1, 2) basis sets on the calculations of as much as 713 1H and 767 13C chemical shifts of 23 biologically active natural products with complicated stereochemical structures, carried out using the GIAO-DFT(PBE0) approach. We also proposed new alternative contraction schemes for our basis sets characterized by less contraction depth of the p-shell. New contraction coefficients have been optimized with the property-energy consistent (PEC) method. The accuracies of the pecS-n (n = 1, 2) basis sets of both the original and newly contracted forms were assessed on massive benchmark calculations of proton and carbon chemical shifts of a vast variety of natural products. It was found that less contracted pecS-n (n = 1, 2) basis sets provide no noticeable improvement in accuracy. These calculations represent the most austere test of our basis sets as applied to routine calculations of the NMR chemical shifts of real-life compounds.

New efficient pecS-n (n = 1, 2) basis sets for quantum chemical calculations of 31P NMR chemical shifts.

The basis sets that are used in the quantum chemical calculations of 31P NMR chemical shifts have always been one of the most important factors of accuracy. Regardless of what high-quality approach is employed, using basis sets of insufficient flexibility in the important angular regions may give poor results and lead to misassignments of the signals in the 31P NMR spectra. In this work, it was found that the existing nonrelativistic basis sets for phosphorus atom of double- and triple-ζ quality, specialized for the 31P NMR chemical shifts calculations, are essentially undersaturated in the d-angular space that occurred to play a significant role in the overall accuracy of these calculations. This problem has been thoroughly investigated, and new pecS-n (n = 1, 2) basis sets for phosphorus chemical shifts calculations were proposed. The exponents and contraction coefficients for the pecS-n basis sets were generated with the property-energy consistent method that has been introduced in our earlier paper, and has been proven useful in the creation of efficient property-oriented basis sets. New basis sets were optimized using the GIAO-DFT method with the B97-2 functional. Extensive benchmark calculations showed that the pecS-1 and pecS-2 basis sets provide very good accuracy, characterized by the corrected mean absolute percentage errors against the experiment of about 7.03 and 4.42 ppm, respectively. In particular, the accuracy of 31P NMR chemical shifts calculations achieved with the pecS-2 basis set is one of the most favorable accuracies for today. We believe that our new pecS-n (n = 1, 2) basis sets for phosphorus atom will prove useful in modern large-scale quantum chemical calculations of 31P NMR chemical shifts.

New pecJ-n (n = 1, 2) Basis Sets for Selenium Atom Purposed for the Calculations of NMR Spin-Spin Coupling Constants Involving Selenium.

We present new compact pecJ-n (n = 1, 2) basis sets for the selenium atom developed for the quantum-chemical calculations of NMR spin-spin coupling constants (SSCCs) involving selenium nuclei. These basis sets were obtained at the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes (SOPPA(CCSD)) level with the property-energy consistent (PEC) method, which was introduced in our previous papers. The existing SSCC-oriented selenium basis sets are rather large in size, while the PEC method gives more compact basis sets that are capable of providing accuracy comparable to that reached using the property-oriented basis sets of larger sizes generated with a standard even-tempered technique. This is due to the fact that the PEC method is very different in its essence from the even-tempered approaches. It generates new exponents through the total optimization of angular spaces of trial basis sets with respect to the property under consideration and the total molecular energy. New basis sets were tested on the coupled cluster singles and doubles (CCSD) calculations of SSCCs involving selenium in the representative series of molecules, taking into account relativistic, solvent, and vibrational corrections. The comparison with the experiment showed that the accuracy of the results obtained with the pecJ-2 basis set is almost the same as that provided by a significantly larger basis set, aug-cc-pVTZ-J, while that achieved with a very compact pecJ-1 basis set is only slightly inferior to the accuracy provided by the former.

On the Utmost Importance of the Basis Set Choice for the Calculations of the Relativistic Corrections to NMR Shielding Constants.

The investigation of the sensitivity of the relativistic corrections to the NMR shielding constants (σ) to the configuration of angular spaces of the basis sets used on the atoms of interest was carried out within the four-component density functional theory (DFT). Both types of relativistic effects were considered, namely the so-called heavy atom on light atom and heavy atom on heavy atom effects, though the main attention was paid to the former. As a main result, it was found that the dependence of the relativistic corrections to σ of light nuclei (exemplified here by 1H and 13C) located in close vicinity to a heavy atom (exemplified here by In, Sn, Sb, Te, and I) on the basis set used on the light spectator atom was very much in common with that of the Fermi-contact contribution to the corresponding nonrelativistic spin-spin coupling constant (J). In general, it has been shown that the nonrelativistic J-oriented and σ-oriented basis sets, artificially saturated in the tight s-region, provided much better accuracy than the standard nonrelativistic σ-oriented basis sets when calculating the relativistic corrections to the NMR shielding constants of light nuclei at the relativistic four-component level of the DFT theory.

New pecJ-n (n = 1, 2) Basis Sets for High-Quality Calculations of Indirect Nuclear Spin-Spin Coupling Constants Involving 31P and 29Si: The Advanced PEC Method.

In this paper, we presented new J-oriented basis sets, pecJ-n (n = 1, 2), for phosphorus and silicon, purposed for the high-quality correlated calculations of the NMR spin-spin coupling constants involving these nuclei. The pecJ-n basis sets were generated using the modified version of the property-energy consistent (PEC) method, which was introduced in our earlier paper. The modifications applied to the original PEC procedure increased the overall accuracy and robustness of the generated basis sets in relation to the diversity of electronic systems. Our new basis sets were successfully tested on a great number of spin-spin coupling constants, involving phosphorus or/and silicon, calculated within the SOPPA(CCSD) method. In general, it was found that our new pecJ-1 and pecJ-2 basis sets are very efficient, providing the overall accuracy that can be characterized by MAEs of about 3.80 and 1.98 Hz, respectively, against the benchmark data obtained with a large dyall.aae4z+ basis set of quadruple-ζ quality.

New pecS-n (n = 1, 2) basis sets for quantum chemical calculations of the NMR chemical shifts of H, C, N, and O nuclei.

This paper demonstrates the performance of our previously suggested property-energy consistent method on the example of the generation of effective basis sets, pecS-1 and pecS-2, suited for the calculation of hydrogen, carbon, nitrogen, and oxygen chemical shifts. The new basis sets were successfully approbated in the GIAO-DFT calculations of the chemical shifts of 35 molecules using six different functionals. The pecS-1 basis set demonstrated very good accuracy, which makes this small basis set an effective means for the large-scale computations. At the same time, the pecS-2 basis set also gave very accurate results, thus putting it on a par with the other commensurate basis sets suited for the chemical shifts calculations.

Computational 199 Hg NMR.

Theoretical background and fundamental results dealing with the computation of mercury chemical shifts and spin-spin coupling constants are reviewed with a special emphasis on their stereochemical behavior and applications.

An efficient method for generating property-energy consistent basis sets. New pecJ-n (n = 1, 2) basis sets for high-quality calculations of indirect nuclear spin-spin coupling constants involving 1H, 13C, 15N, and 19F nuclei.

This paper presents a new method of generating property-energy consistent (PEC) basis sets that can be applied to any arbitrary molecular property. The PEC method generates a basis set that is optimized for the molecular property under interest, providing the least possible total molecular energy. The main algorithm of the PEC approach involves Monte Carlo simulations to generate random exponents in the predetermined range. In this work, the PEC method is introduced in the example of generation of new pecJ-n (n = 1, 2) basis sets suited for high-quality correlated calculations of indirect nuclear spin-spin coupling constants involving the most popular NMR-active nuclei: 1H, 13C, 15N, and 19F.

Efficient J-oriented tin basis sets for the correlated calculations of indirect nuclear spin-spin coupling constants.

New J-oriented tin basis sets, acvXz-J (X = 2, 3, 4), have been developed at the level of the second-order polarization propagator approximation with the coupled-cluster single and double amplitudes, SOPPA (CCSD), for the purpose of correlated calculations of indirect nuclear spin-spin coupling constants involving tin nucleus. High-quality coupled-cluster calculations of several tin-proton and tin-carbon spin-spin coupling constants, performed with one of the newly developed basis sets, namely, the acv3z-J, taking into account relativistic, solvent, and vibrational corrections showed that the acv3z-J basis set is capable to provide reliable results, as compared with the experimental data.

Quantum chemical calculations of 77 Se and 125 Te nuclear magnetic resonance spectral parameters and their structural applications.

An accurate quantum chemical (QC) modeling of 77 Se and 125 Te nuclear magnetic resonance (NMR) spectra is deeply involved in the NMR structural assignment for selenium and tellurium compounds that are of utmost importance both in organic and inorganic chemistry nowadays due to their huge application potential in many fields, like biology, medicine, and metallurgy. The main interest of this review is focused on the progress in QC computations of 77 Se and 125 Te NMR chemical shifts and indirect spin-spin coupling constants involving these nuclei. Different computational methodologies that have been used to simulate the NMR spectra of selenium and tellurium compounds since the middle of the 1990s are discussed with a strong emphasis on their accuracy. A special accent is placed on the calculations resorting to the relativistic methodologies, because taking into account the relativistic effects appreciably influences the precision of NMR calculations of selenium and, especially, tellurium compounds. Stereochemical applications of quantum chemical calculations of 77 Se and 125 Te NMR parameters are discussed so as to exemplify the importance of integrated approach of experimental and computational NMR techniques.

A New Basis Set for the Calculation of 13C NMR Chemical Shifts within a Non-empirical Correlated Framework.

A new basis set of triple-ζ quality for carbon, 3z-S, is developed and tested at the DFT, MP2, and CCSD(T) levels, taking into account solvent and vibrational corrections for a number of molecules ranging from the smallest fluoromethane, CH3F, to the largest 5,10,15,20-tetraphenylporphyrin, C44H30N4. The proposed highly economical 3z-S basis set has been proven to provide very good accuracy in all examinations, comparable to that of the NMR-oriented Jensen's pcS-2 basis set, which is about 50% larger than 3z-S.

Correlated ab initio calculations of one-bond 31 P77 Se and 31 P125 Te spin-spin coupling constants in a series of PSe and PTe systems accounting for relativistic effects (part 2).

Synthetic chalcogen-phosphorus chemistry permanently makes new challenges to computational Nuclear Magnetic Resonance (NMR) spectroscopy, which has proven to be a powerful tool of structural analysis of chalcogen-phosphorus compounds. This paper reports on the calculations of one-bond 31 P77 Se and 31 P125 Te NMR spin-spin coupling constants (SSCCs) in the series of phosphine selenides and tellurides. The applicability of the combined computational approach to the one-bond 31 P77 Se and 31 P125 Te SSCCs, incorporating the composite nonrelativistic scheme, built of high-accuracy correlated SOPPA (CC2) and Coupled Cluster Single and Double (CCSD) methods and the Density Functional Theory (DFT) relativistic corrections (four-component level), was examined against the experiment and another scheme based on the four-component relativistic DFT method. A special J-oriented basis set (acv3z-J) for selenium and tellurium atoms, developed previously by the authors, was used throughout the NMR calculations in this work at the first time. The proposed computational methodologies (combined and 'pure') provided a reasonable accuracy for 31 P77 Se and 31 P125 Te SSCCs against experimental data, characterizing by the mean absolute percentage errors of about 4% and 1%, and 12% and 8% for selenium and tellurium species, respectively. The present study reports typical relativistic corrections to 77 Se31 P and 125 Te31 P SSCCs, calculated within the four-component DFT formalism for a broad series of tertiary phosphine selenides and tellurides with different substituents at phosphorus.

Hierarchical Basis Sets for the Calculation of Nuclear Magnetic Resonance Spin-Spin Coupling Constants Involving Either Selenium or Tellurium Nuclei.

New basis sets, acvXz-J (X = 2, 3, 4), were designed for tellurium and selenium atoms for the calculation of indirect nuclear spin-spin coupling constants involving selenium or tellurium nuclei. Saturation of angular spaces was performed in an even-tempered manner till achieving the convergence of spin-spin coupling constants under consideration. The high-accuracy correlated SOPPA(CCSD) method was employed in this procedure. Saturated basis sets were contracted by approximately 30% using the coefficients obtained from the atomic self-consistent field (SCF) closed-shell calculations of selenium and tellurium anions, Se2- and Te2-. Final basis sets of acvXz-J showed sufficiently high accuracy in comparison with previous special basis sets.

On the heavy atom on light atom relativistic effect in the NMR shielding constants of phosphine tellurides.

The relativistic HALA effect has been shown to depend on the spatial deformation of the lone electron pairs of a heavy atom, as demonstrated for alkyl and alkene phosphine tellurides. It was found that HALA effect on phosphorous nuclear magnetic resonance shielding constant is strongly dependent on the spatial arrangements of light substituents on phosphorus, resulting in the deformation of the lone electron pairs of tellurium.

Calculation of 125Te NMR Chemical Shifts at the Full Four-Component Relativistic Level with Taking into Account Solvent and Vibrational Corrections: A Gateway to Better Agreement with Experiment.

Four-component relativistic calculations of 125Te NMR chemical shifts were performed in the series of 13 organotellurium compounds, potential precursors of the biologically active species, at the density functional theory level under the nonrelativistic and four-component fully relativistic conditions using locally dense basis set scheme derived from relativistic Dyall's basis sets. The relativistic effects in tellurium chemical shifts were found to be of as much as 20-25% of the total calculated values. The vibrational and solvent corrections to 125Te NMR chemical shifts are about, accordingly, 6 and 8% of their total values. The PBE0 exchange-correlation functional turned out to give the best agreement of calculated tellurium shifts with their experimental values giving the mean absolute percentage error of 4% in the range of ∼1000 ppm, provided all corrections are taken into account.