Nuclear magnetic shielding in molecules. The application of GIAO's in LCAO-X α-calculations

Abstract

A nonempirical method for the calculation of nuclear magnetic shielding based on the four current density functional formalism is presented. Using SCF-LCAO-X=-calculations with application of GIAO's effective one particle equations are solved. The results for nuclear magnetic shielding in diatomic molecules are of good quality, compared with other theoretical and experimental data. 31.20.J; 33.25; 76.60.C One of the most important second-order effects in molecules is the nuclear magnetic shielding. For its calculation the perturbed Hartree-Fock scheme (coupled HFmethod -CHF) is usually applied, see e.g. [1]. PACS:A significant improvement in the calculation of nuclear magnetic shielding could be achieved by the GIAO (gauge invariant atomic orbital) approach from Ditchfied [2]. This CHF-GIAO method was used for example by Fukui et al. [3]. Schindler and Kutzelnigg formulated a CHF-mcthod with individual gauge for localized orbitals (IGLO) [4] and applied it to more complicated molecules [5,6]. The application of special gauge factors is one way to minimize the gauge problem. On the other hand, in the last years density functional methods were used for calculations of N M R shielding in molecules, for example -Bieger et al. [7] with an UCP-X=-method -Freier et al. [8] with SW-X~-calculations of 13C-chemical shifts and - Malkin and Zhidomirov [9] studied the N M R shielding of small molecules with DV-X~-calculations. Our studies are based on the four current density functional formalism. Bieger et al. [7] have developed a method to calculate chemical shifts, allowing the use of a LCAO-X~-scheme [10] in computations of magnetic properties of molecules. The present paper deals with the application of GIAO's in the LCAO-X~-scheme.The nuclear magnetic shielding of a nucleus in a molecule can be calculated from the electronic current density J(r), which is induced by an external magnetic field Rajagopal and Callaway [-11] formulated a theorem for the total ground state energy of a many particle system in an external field as a unique functional of the four current density dU. One particle equations, as a generalization of the usual Kohn-Sham equations [12], can be derived from this theorem [13]. In the non-relativistic limit and vanishing spin density these equations are:(2) Neff = NH dp gx C .~_ Next -VB is the Hartree potential, Vxc is the exchange correlation potential and V~x t stands for the potential from the nucleus. For the vector potential a similar decomposition is possibleAef f = a -~ axc + Aext.The current density J(r) can be expressed by the wavefunctions from (2)Linear combination of atomic orbitals Z~, are used for the one-particle functions:

Probing the Origin of Adaptive Aromaticity in 16‐Valence‐Electron Metallapentalenes

“…Nucleus-independent chemical shifts (NICS) [36] and gauge-including magnetically induced currents (GIMIC) [37] calculations were performed using the gauge invariant atomic orbitals (GIAO). [38] NICS(1) zz values were obtained by placing ghost atoms at 1 above/below the ring centers at the (U)B3LYP/def2-TZVP//(U)PBE0-D3BJ/6-31G(d)~LanL2DZ level of theory ( Figure S3). Electron density of delocalized bonds (EDDB) [39] analyses based on density matrices within the natural atomic orbital (NAO) representation were carried out using the RunEDDB script program.…”

The Role of C–H···H–B Interactions in Establishing Rotamer Configurations in Metallabis(dicarbollide) Systems

“…[37] Topological Bader analysis [34] was performed using Xaim [48] software on the BP86/TZ2P(+) total electron densities. Magnetic shieldings were computed for the geometry optimized rotamers at BP86/TZ2P(+) level employing DFT-GIAO [49] method with a "Statistical Average of Orbital dependent model Potential" (SAOP) implemented in ADF [50,51] using TZ2P(+) basis set. 11 B-NMR chemical shifts were calculated relative to B 2 H 6 and converted into the usual BF 3 ·OEt 2 scale by using the experimental value of B 2 H 6 of 16.6 ppm.…”

Benchmarking quantum mechanical calculations with experimental NMR chemical shifts of 2-HADNT

“…The gauge that includes atomic orbital (GIAO) was first implemented with X-a approximation of the exchange-correlation functional (DFT) [12,13]. The second-order property shielding tensor has also been described using other methods such as the individual gauge for localized orbitals (IGLO) [14,15], the individual gauge for local origin (LORG) [16], the continuous set of gauge transformations (CSGT) [17], and the individual gauges for atoms in molecules (IGAIM) [18].…”

“…Accurate prediction of chemical shifts can be achieved through calculations using the coupled-cluster singles and doubles (CCSD) model augmented by perturbative correction for triple excitation (CCSD(T)) method [9][10][11], with a deviation of 1 ppm between the experimental chemical shifts and the calculated results for C-13. The accuracy can be further improved by the inclusion of zero-point vibrational correction in the Hartree-Fock (HF), MP2, CCSD, and CCSD(T) calculations of the chemical shifts except for the DFT calculations [11].The gauge that includes atomic orbital (GIAO) was first implemented with X-a approximation of the exchange-correlation functional (DFT) [12,13]. The second-order property shielding tensor has also been described using other methods such as the individual gauge for localized orbitals (IGLO) [14,15], the individual gauge for local origin (LORG) [16], the continuous set of gauge transformations (CSGT) [17], and the individual gauges for atoms in molecules (IGAIM) [18].…”