Polarization-Consistent versus Correlation-Consistent Basis Sets in Predicting Molecular and Spectroscopic Properties

Compared to the correlation-consistent basis sets, it is not known if polarization-consistent pc-n basis sets, which were initially developed for HF and DFT calculations, can provide a monotonic and faster convergence toward the basis-set limit for results at correlated levels as well as better accuracy for a similar number of basis functions. It is also not known whether the pc-n basis sets can compute second derivatives of energy, such as nuclear magnetic shielding tensors, efficiently. To address these questions, the pc-n (n = 1−4), cc-pVxZ, and/or aug-cc-pVxZ (x = D, T, Q, 5, and 6) basis sets were used to compute the molecular and/or spectroscopic parameters of H2, H2O, and NH3 at the RHF, B3-LYP, MP2, and/or CCSD(T) levels of theory. The results show that compared to the cc-pVxZ and/or aug-cc-pVxZ basis sets the pc-n basis sets yield faster convergence toward the basis-set limit but equivalent molecular and/or spectroscopic parameters in the basis-set limit at the RHF, DFT, MP2, and CCSD(T) levels. Because the pc-n basis sets show faster convergence, fewer basis-set functions are needed to reach the accuracy obtained with the aug-cc-pVxZ basis sets, enabling faster calculations and less computer storage space. The results also show that the pc-n basis sets, in conjunction with the “locally dense” basis-set approach, could be applied to predict accurate parameters; thus, they could be used to estimate accurate molecular or spectroscopic properties (e.g., NMR parameters) for larger systems such as the active site of enzymes

Toward Hartree−Fock- and Density Functional Complete Basis-Set-Predicted NMR Parameters

The molecular and spectroscopic parameters calculated using the hybrid density functional B3PW91 are reported for a model set of compounds composed of H2, N2, NH3, CH4, C2H4, HCN, CH3CN, and H2O. An estimation of the DFT and Hartree−Fock complete basis-set limit (CBS) energy and NMR parameters from the 2- (3-) point exact fit versus least-squares fit (NLLSQ) was obtained with the cc-pVxZ and aug-cc-pVxZ basis sets (x = D, T, Q, 5, 6). A marginally faster convergence of the fitted parameters obtained with core-valence basis sets cc-pCVxZ and aug-cc-pCVxZ was noticed. The Hartree−Fock-predicted CBS heavy-atom isotropic shieldings of the model molecules, as compared with those of DFT, were closer to experiment. It was also shown that GIAO MP2-predicted NMR parameters yield the best agreement with those obtained from experiment and benchmark calculations. As support for experimental studies, the CBS approach of calculating accurate nuclear shieldings of larger molecules is proposed

On the convergence of zero-point vibrational corrections to nuclear shieldings and shielding anisotropies towards the complete basis set limit in water

<p>The method and basis set dependence of zero-point vibrational corrections (ZPVCs) to nuclear magnetic resonance shielding constants and anisotropies has been investigated using water as a test system. A systematic comparison has been made using the Hartree–Fock, second-order Møller–Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) and Kohn–Sham density functional theory with the B3LYP exchange-correlation functional methods in combination with the second-order vibrational perturbation theory (VPT2) approach for the vibrational corrections. As basis sets, the correlation consistent basis sets cc-pVXZ, aug-cc-pVXZ, cc-pCVXZ and aug-cc-pCVXZ with <i>X</i> = D, T, Q, 5, 6 and the polarisation consistent basis sets aug-pc-n and aug-pcS-n with <i>n</i> = 1, 2, 3, 4 were employed. Our results show that basis set convergence of the vibrational corrections is not monotonic and that very large basis sets are needed before a reasonable extrapolation to the basis set limit can be performed. Furthermore, our results suggest that coupled cluster methods and a decent basis set are required before the error of the electronic structure approach is lower than the inherent error of the VPT2 approximation.</p> <p></p

Convergence of Nuclear Magnetic Shieldings in the Kohn−Sham Limit for Several Small Molecules

Convergence patterns and limiting values of isotropic nuclear magnetic shieldings were studied for several small molecules (N2, CO, CO2, NH3, CH4, C2H2, C2H4, C2H6, and C6H6) in the Kohn−Sham limit. Individual results of calculations using dedicated families of Jensen’s basis sets (pcS-n and pcJ-n) were fitted toward the complete basis set limit (CBS) using a simple two-parameter formula. Several density functionals were used; calculated vibrational corrections (ZPV) applied; and, for comparison purposes, similar calculations performed using RHF, MP2, SOPPA, SOPPA(CCSD), and CCSD(T) methods and additionally, the aug-cc-pVTZ-J basis set. Finally, the CBS estimated results were critically compared with earlier reported literature data and experimental results. Among 42 studied DFT methods, the KTn and “pure” functionals produced the most accurate heavy atom isotropic nuclear shieldings

Efficient Modeling of NMR Parameters in Carbon Nanosystems

Rapid growth of nanoscience and nanotechnology requires new and more powerful modeling tools. Efficient theoretical modeling of large molecular systems at the <i>ab initio</i> and Density Functional Theory (DFT) levels of theory depends critically on the size and completeness of the basis set used. The recently designed variants of STO-3G basis set (STO-3G_el, STO-3G_mag), modified to correctly predict electronic and magnetic properties were tested on simple models of pristine and functionalized carbon nanotube (CNT) systems and fullerenes using the B3LYP and VSXC density functionals. Predicted geometries, vibrational properties, and HOMO/LUMO gaps of the model systems, calculated with typical 6-31G* and modified STO-3G basis sets, were comparable. The ¹³C nuclear isotropic shieldings, calculated with STO-3G_mag and Jensen’s polarization consistent pcS-2 basis sets, were also identical. The STO-3G_mag basis sets, being half the size of the latter one, are promising alternative for studying ¹³C nuclear magnetic shieldings in larger size CNTs and fullerenes

Basis Set Convergence of Indirect Spin–Spin Coupling Constants in the Kohn–Sham Limit for Several Small Molecules

The performance of more than 40 density functionals in predicting indirect spin–spin coupling constants (SSCCs) in the Kohn–Sham basis set limit was tested. For comparison, similar calculations were performed using the RHF, SOPPA, SOPPA­(CC2), and SOPPA­(CCSD) methods, and the results were estimated toward the complete basis set (CBS) limit. The SSCCs of nine small molecules (N₂, CO, CO₂, NH₃, CH₄, C₂H₂, C₂H₄, C₂H₆, and C₆H₆) were calculated using the dedicated Jensen pcJ-<i>n</i> polarization-consistent basis sets and used for the CBS limit estimations within the Kohn–Sham limit. These CBS results were compared with calculations using the aug-cc-pVTZ-J basis set. Among the 41 studied DFT methods, the tHCTHhyb, HSEh1PBE, HSE2PBE, wB97XD, wB97, and wB97X functionals reproduced accurately the experimental ¹<i>J</i>(XH) SSCCs and ³<i>J</i>(HH60) and ²<i>J</i>(HH_<i>gem</i>) in ethane. Similarly, the functionals HSEh1PBE, HSE2PBE, wB97XD, wB97, and wB97X predicted accurately ¹<i>J</i>(CC), and B98, B97-1, B97-2, PBE1PBE, B1LYP, and O3LYP provided accurate ¹<i>J</i>(CO) results in the CO molecule. A very good performance for the calculation of the SSCCs based on the use of the relatively small basis set aug-cc-pVTZ-J was observed

Host−Guest Complex Dependent Regioselectivity in Substitution Reactions of Chlorocyclotriphosphazene-Containing PNP-Crowns with Alkylenediamines

Host−Guest Complex Dependent Regioselectivity in Substitution Reactions of Chlorocyclotriphosphazene-Containing PNP-Crowns with Alkylenediamine

Thermodynamic <i>vs</i> Supramolecular Effects in the Regiocontrol of the Formation of New Cyclotriphosphazene-Containing Chiral Ligands with 1,1‘-Binaphthyl Units: Spiro <i>vs</i> Ansa Substitution at the N₃P₃ Ring

Synthesis of new cyclophosphazene-containing chiral ligands (6−9) with 1,1‘-binaphthyl units has been achieved by stepwise dicyclosubstitution of hexachlorocyclotriphosphazene (1), with two sodium cation paired dinucleophiles derived from bis-β-naphthol (2) and tetraethylene glycol (3). The structures of the disubstitution products have been found to be addition order-dependent. In particular, the substitution pattern of the 1,1‘-binaphthalene-2,2‘-dioxy substituent in the N3P3 ring [spiro (4 → 6, 7) or ansa (8, 9)] was related to whether or not the crown substituent had been incorporated into 1 beforehand. Addition of the phase transfer catalyst reagent, tetrabutylammonium bromide, to the reaction mixture of 5 + 2-Na2 led to the parallel formation of both the spiro 6 and ansa 8 isomers. Spiro vs ansa regioisomerism of the binaphthalenedioxy derivatives formed is discussed in terms of the contributions of the respective thermodynamic and supramolecular effects to the regiocontrol of substitution in the N3P3 ring. It is found that there are two main factors determining the orientation of the binaphthalenedioxy substitutent incoming to the N3P3 ring:  the thermodynamic stability of seven-membered spirocycles at the P-atoms and the crown-related cation assistance of the ansa substitution at the macrocycle bearing P-atoms; the regiocontrol resulting from the supramolecular effects predominates, whenever possible. The structures of compounds 7−9 were proven by X-ray crystallography. The metal cation complexing properties of compounds 6−9 were compared by a simple TLC method. The results show that the complexing properties of the chiral binaphthalenedioxy-containing PNP-crown ligands 6−9 toward alkali metal and silver cations are either similar (spiro-ansa derivative 6) or enhanced (bis-ansa derivatives 7−9) with respect to the parent tetrachloro PNP-crown 5

A Regioselective Route to New Polytopic Receptors by Diaminolysis of Chlorocyclotriphosphazatriene-Containing Crown Ethers

A general strategy is reported for the facile preparation of diamino-derivatized PNP-crowns, giving access to a large range of new host molecules of different sizes, shapes, and topology. Reactions of the tetrachloro-PNP-crown precursor 1 with polymethylene-diamines 2a−h (n = 2−6, 8, 10, 12) proceed rapidly and regioselectively via substitution reactions of Cl at the PNP-crown-forming P-atoms; the reaction is assisted by the macrocyclic 1,3-oxy(tetraethylenoxy) substituent at the N3P3 ring which provides a site for the hydrogen-bond-driven assembly of reagents 1 and 2. The products belong to three different classes of polytopic receptors:  lateral macrobicycles (ansa, 5a−h), bola-amphiphilic tritopic bis-crowns (bino, 6a−h), and tetratopic cylindrical macrotricycles (bis-bino, 8a−h). The structures of 5, 6, 8, and 10b were established by MS and 31P NMR spectroscopy, and an X-ray crystal structure was obtained for the bis-bino 1,3-diaminopropane PNP-crown derivative 8b. Preliminary screening by a simple TLC test of the metal−cation complexing properties of the series of compounds 5, 6, and 8 revealed their capacity to bind both harder (alkali and alkaline earth) and softer (transition) metal cations, with significant affinity being displayed toward potassium and silver cations by many of the ligands studied