Anharmonic vibrational frequency calculations for solvated molecules in the B3LYP Kohn–Sham basis set limit
Abstract The solvent dependence of harmonic and anharmonic vibrational wavenumbers of water, formaldehyde and formamide was studied using the B3LYP method. The results obtained with the hierarchy of Jensen's polarization-consistent basis sets were fitted with two-parameter formula toward the B3LYP Kohn–Sham complete basis set (CBS) limit. Anharmonic corrections have been obtained by a second order perturbation treatment (VPT2) and vibrational configuration interaction (VCI) method. The solvent environment was treated according to the self-consistent reaction field polarizable continuum model (SCRF PCM) approach.
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…
DFT study of zigzag (n, 0) single-walled carbon nanotubes: 13C NMR chemical shifts
Abstract 13 C NMR chemical shifts of selected finite-size models of pristine zigzag single walled carbon nanotubes (SWCNTs) with a diameter of ∼0.4–0.8 nm and length up to 2.2 nm 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 w…
3 He NMR: from free gas to its encapsulation in fullerene
The (3)He 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 (3)He nuclear magnetic shieldings in the complete basis set limit using a two-parameter fit was established. Theoretical (3)He 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. (3)H…
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 com…
DFT studies on armchair (5, 5) SWCNT functionalization. Modification of selected structural and spectroscopic parameters upon two-atom molecule attachment
Abstract Density functional theory (DFT) studies on adsorption of several gaseous homo- and hetero-diatomic molecules (AB) including H2, O2, N2, NO and CO on external surface of H-capped pristine armchair (5, 5) single-walled carbon nanotube (SWCNT) were conducted. Structures of C70H10 and the corresponding C70H10–AB adducts were fully optimized at the B3LYP/6-311G* level of theory. Calculated HOMO/LUMO energy gaps (Eg), 13C NMR chemical shifts and IR/Raman parameters were analyzed and critically compared with available experimental data. Significant changes of carbon NMR atom chemical shifts (up to −100 ppm) and shielding anisotropies (up to −180 ppm) at sites of addition were observed. Fu…
Phosphorus mononitride: A difficult case for theory
Phosphorus nitride (PN) is the simplest molecule formed solely by phosphorus and nitrogen. It represents an interesting model for materials, where phosphorus is directly attached to nitrogen. Nevertheless, both theoretical and experimental studies often provide an incomplete picture on the structural, electronic, and spectral properties of PN. Theoretical predictions often suffer from insufficient level of theory, incomplete basis set, or from neglecting several effects, for example, zero‐point vibrational correction (ZPVC). Therefore, we performed an extensive benchmark study on structural, electronic, and spectral properties of PN at the Hartree‐Fock, density functional theory (DFT), or e…
Calculation of Raman parameters of real-size zigzag (n, 0) single-walled carbon nanotubes using finite-size models
Structural and selected Raman features of pristine single-walled carbon nanotubes (SWCTNs) with diameters from 0.4 to 1.2 nm and total lengths up to 2.15 nm were studied using the density functional theory (DFT) at the UB3LYP/6-31G* level. Models of different lengths (1, 4, 6 and 10 adjacent bamboo-units) of zigzag (n, 0) SWCNTs, for n ranging from 5 to 15, were studied. Highly systematic changes of individual CC bond lengths and angles along the nanotube axis were observed and described for the longest models. Predicted Raman active radial breathing mode (RBM) vibrational frequencies regularly decreased upon increasing the nanotube diameter and only a negligible effect of the tube length w…
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 com…
Modeling21Ne NMR parameters for carbon nanosystems
The potential of nuclear magnetic resonance (NMR) technique in probing the structure of porous systems including carbon nanostructures filled with inert gases is analysed theoretically using accurate calculations of neon ((21) Ne) nuclear magnetic shieldings. The CBS estimates of (21) Ne NMR parameters were performed for single atom, its dimer and neon interacting with acetylene, ethylene and 1,3-cyclopentadiene. Several levels of theory including restricted Hartree-Fock (RHF), Moller-Plesset perturbation theory to the second order (MP2), density functional theory (DFT) with van Voorhis and Scuseria's t-dependent gradient-corrected correlation functional (VSXC), coupled cluster with single …
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 o…
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 4…
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.