Michał Stachów

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 (N(2), CO, CO(2), NH(3), CH(4), C(2)H(2), C(2)H(4), C(2)H(6), and C(6)H(6)) were calculated using the dedicated Jensen pcJ-n 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)J(XH) SSCCs and (3)J(HH60) and (2)J(HH(gem)) in ethane. Similarly, the functionals HSEh1PBE, HSE2PBE, wB97XD, wB97, and wB97X predicted accurately (1)J(CC), and B98, B97-1, B97-2, PBE1PBE, B1LYP, and O3LYP provided accurate (1)J(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.

From CCSD(T)/aug-cc-pVTZ-J to CCSD(T) complete basis set limit isotropic nuclear magnetic shieldings via affordable DFT/CBS calculations

It is shown that a linear correlation exists between nuclear shielding constants for nine small inorganic and organic molecules (N2, CO, CO2, NH3, CH4, C2H2, C2H4, C2H6 and C6H6) calculated with 47 methods (42 DFT methods, RHF, MP2, SOPPA, SOPPA(CCSD), CCSD(T)) and the aug‐cc‐pVTZ‐J basis set and corresponding complete basis set results, estimated from calculations with the family of polarization‐consistent pcS‐n basis sets. This implies that the remaining basis set error of the aug‐cc‐pVTZ‐J basis set is very similar in DFT and CCSD(T) calculations. As the aug‐cc‐pVTZ‐J basis set is significantly smaller, CCSD(T)/aug‐cc‐pVTZ‐J calculations allow in combination with affordable DFT/pcS‐n complete basis set calculations the prediction of nuclear shieldings at the CCSD(T) level of nearly similar accuracy as those, obtained by fitting results obtained from computationally demanding pcS‐n calculations at the CCSD(T) limit. A significant saving of computational efforts can thus be achieved by scaling inexpensive CCSD(T)/aug‐cc‐pVTZ‐J calculations of nuclear isotropic shieldings with affordable DFT complete basis set limit corrections. Copyright

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 ab initio 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-3Gel, STO-3Gmag), 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 (13)C nuclear isotropic shieldings, calculated with STO-3Gmag and Jensens polarization consistent pcS-2 basis sets, were also identical. The STO-3Gmag basis sets, being half the size of the latter one, are promising alternative for studying (13)C nuclear magnetic shieldings in larger size CNTs and fullerenes.

3He NMR: from free gas to its encapsulation in fullerene

The 3He nuclear magnetic shieldings were calculated for single helium atom, its dimer, simple models of fullerene cages (He@Cn), and single wall carbon nanotubes. The performances of several levels of theory (HF, MP2, DFT‐VSXC, CCSD, CCSD(T), and CCSDT) were tested. Two sets of polarization‐consistent basis sets were used (pcS‐n and aug‐pcS‐n), and an estimate of 3He nuclear magnetic shieldings in the complete basis set limit using a two‐parameter fit was established. Theoretical 3He results reproduced accurately previously reported theoretical values for helium gas, dimer, and helium probe inside several fullerene cages. Excellent agreement with experimental values was achieved. 3He nuclear magnetic shieldings of single helium atom approaching various points of benzene ring were tested, and an impact of 3He confinement within fullerene cages of different size on the 3He chemical shift was determined. Copyright

Theoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis-, and trans-1,2-difluoroethylenes

A theoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis- and trans-1,2-difluoroethylenes is reported. The results obtained using density functional theory (DFT) combined with large basis sets and gauge-independent atomic orbital calculations were critically compared with experiment and conventional, higher level correlated electronic structure methods. Accurate structural, vibrational, and NMR parameters of difluoroethylenes were obtained using several density functionals combined with dedicated basis sets. B3LYP/6-311++G(3df,2pd) optimized structures of difluoroethylenes closely reproduced experimental geometries and earlier reported benchmark coupled cluster results, while BLYP/6-311++G(3df,2pd) produced accurate harmonic vibrational frequencies. The most accurate vibrations were obtained using B3LYP/6-311++G(3df,2pd) with correction for anharmonicity. Becke half and half (BHandH) density functional predicted more accurate (19)F isotropic shieldings and van Voorhis and Scuserias τ-dependent gradient-corrected correlation functional yielded better carbon shieldings than B3LYP. A surprisingly good performance of Hartree-Fock (HF) method in predicting nuclear shieldings in these molecules was observed. Inclusion of zero-point vibrational correction markedly improved agreement with experiment for nuclear shieldings calculated by HF, MP2, CCSD, and CCSD(T) methods but worsened the DFT results. The threefold improvement in accuracy when predicting (2)J(FF) in 1,1-difluoroethylene for BHandH density functional compared to B3LYP was observed (the deviations from experiment were -46 vs. -115 Hz).

Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations

A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH2O, H2O, HF, F2, HCN, SiH4 and H2S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T)), with affordable pcS‐2 basis set and corresponding complete basis set results, estimated from calculations with the family of polarization‐consistent pcS‐n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and shieldings obtained with the significantly smaller basis sets pcS‐2 and aug‐cc‐pVTZ‐J for the selected set of 37 calculation methods. It was possible to formulate a practical approach of estimating the values of isotropic nuclear magnetic shielding constants at the CCSD(T)/CBS and MP2/CBS levels from affordable CCSD(T)/pcS‐2, MP2/pcS‐2 and DFT/CBS calculations with pcS‐n basis sets. The proposed method leads to a fairly accurate estimation of nuclear magnetic shieldings and considerable saving of computational efforts. Copyright

DFT calculation of structures and NMR chemical shifts of simple models of small diameter zigzag single wall carbon nanotubes (SWCNTs)

Linearly conjugated benzene rings (acenes), belt‐shape molecules (cyclic acenes) and model single wall carbon nanotubes (SWCNTs) were fully optimized at the unrestricted level of density functional theory (UB3LYP/6‐31G*). The models of SWCNTs were selected to get some insight into the potential changes of NMR chemical shift upon systematic increase of the molecular size. The theoretical NMR chemical shifts were calculated at the B3LYP/pcS‐2 level of theory using benzene as reference. In addition, the change of radial breathing mode (RBM), empirically correlated with SWCNT diameter, was directly related with the radius of cyclic acenes. Both geometrical and NMR parameters were extrapolated to infinity upon increase in the studied systems size using a simple two‐parameter mathematical formula. Very good agreement between calculated and available experimental CC bond lengths of acenes was observed (RMS of 0.0173 Å). The saturation of changes in CC bond lengths and 1H and 13C NMR parameters for linear and cyclic acenes, starting from 7–8 conjugated benzene rings, was observed. The 13C NMR parameters of individual carbon atoms from the middle of ultra‐thin (4,0) SWCNT formed from 10 conjugated cyclic acenes differ by about 130 ppm from the corresponding open end carbon nuclei. Copyright

DFT calculations of structures, 13C NMR chemical shifts, and Raman RBM mode of simple models of small‐diameter zigzag (4,0) carboxylated single‐walled carbon nanotubes

Linearly conjugated benzene rings (acenes), belt‐shaped molecules (cyclic acenes), and models of single‐walled carbon nanotubes (SWCNTs) with one carboxylic group at the open end were fully optimized at the B3LYP/6‐31G* level of theory. These models were selected to obtain some insight into the nuclear isotropic changes resulting from systematically increasing the basic building units of open‐tip‐monocarboxylated SWCNTs. In addition, the position of radial breathing mode (RBM), empirically correlated with the SWCNT diameter, was directly related with the radius of model cyclic acene rings. A regular convergence of selected structural, NMR, and Raman parameters with the molecular system size increase was observed, and a simple two‐parameter mathematical formula enabled their estimation in infinity. The predicted 13C NMR chemical shifts of carbon atoms close to the substituted rim of carboxylated models of zigzag (4,0) SWCNTs differed significantly from the pristine nanotubes. Copyright

From small to medium and beyond: a pragmatic approach in predicting properties of Ne containing structures

In this study, we outlined a pragmatic approach for structural studies leading to better understanding of polycarbon structures using 21Ne as a nuclear magnetic resonance (NMR) probe. 21Ne NMR parameters of a single neon atom and its dimer were predicted at the CCSD(T) level in combination with large basis sets. At a lower level of theory, an interaction of neon atom with 1,3-cyclopentadiene ring and with five- and six-membered rings in carbazole was studied using the restricted Hartree–Fock (RHF) and density functional theory (DFT) combined with smaller basis sets. The RHF and DFT modelling of neon interaction with nanosized objects were performed on cyclacenes and selected fullerenes.

DFT study of zigzag (n, 0) single-walled carbon nanotubes: 13C NMR chemical shifts

(13)C NMR chemical shifts of selected finite-size models of pristine zigzag single walled carbon nanotubes (SWCNTs) with a diameter of ∼0.4-0.8nm and length up to 2.2nm were studied theoretically. Results for finite SWCNTs models containing 1, 4 and 10 adjacent bamboo-type units were compared with data obtained for infinite tubes in order to estimate the reliability of small finite models in predicting magnetic properties of real-size nanotubes and to assess their tube-length dependence. SWCNTs were fully optimized using unrestricted density functional theory (DFT-UB3LYP/6-31G*). Cyclacenes, as the shortest models of open-ended zigzag SWCNTs, with systematically varying diameter were calculated as well. GIAO NMR calculations on the SWCNT and cyclacene models were performed using the BHandH density functional combined with relatively small STO-3Gmag basis set, developed by Leszczyński and coworkers for accurate description of magnetic properties. Regular changes of carbon (13)C chemical shifts along the tube axis of real size (6, 0) and (9, 0) zigzag carbon nanotubes were shown. The (13)C NMR shifts according to increasing diameter calculated for zigzag (n, 0, n=5-10) cyclacenes followed the trends observed for zigzag (n, 0) SWCNTs. The results for 4-units long SWCNTs match reasonably well with the data obtained for infinite zigzag (n, 0) SWCNTs, especially to those with bigger diameter (n=8-15). The presence of rim hydrogens obviously affects theoretical (13)C chemical shieldings and shifts in cyclacenes and thus cyclacenes can provide only approximate estimation of (13)C NMR parameters of real-size SWCNTs. The NMR properties predicted for the longest 10-units long models of SWCNTs reliably correspond to results obtained for infinite nanotubes. They were thus able to accurately predict also recently reported experimental chemical shift of chiral (6, 5) SWCNT.