Use of locally dense basis sets for nuclear magnetic resonance shielding calculations

The locally dense basis set approach to the calculation of nuclear magnetic resonance shieldings is one in which a sufficiently large or dense set of basis functions is used for an atom or molecular fragment containing the resonant nucleus or nuclei of interest and fewer or attenuated sets of basis functions employed elsewhere. Provided the dense set is of sufficient size, this approach is capable of determining chemical shieldings nearly as well as a calculation with a balanced basis set of quality equal to the locally dense set, but with considerable savings of CPU time. Detailed comparisons are provided of locally dense and balanced calculations in the gauge including atomic orbital (GIAO) method for the individual principal values, the isotropic shieldings, and the tensor orientations for hydrogen, carbon, nitrogen, oxygen, fluorine, and phosphorus nuclei. It is seen that chemical functional groups can often define the appropriate molecular fragment to be taken locally dense. While the present test cases are for the most part small molecules, the value of the method is that it will allow calculations on systems that would otherwise presently be computationally expensive or inaccessible. © John Wiley & Sons, Inc.     

Theoretical investigation on 1H and 13C NMR chemical shifts of small alkanes and chloroalkanes

Using density functional theory (DFT) with the B3LYP, PBE, and PBE0 exchange-correlation functionals as well as the Moller-Plesset second-order perturbation theory (MP2) combined with a series of rather extended basis sets, 1H and 13C chemical shifts of small alkanes and chloroalkanes (with different numbers of chlorine atoms on specific positions) have been simulated and compared to experimental data. For the 1H chemical shifts, theory tends to reproduce experiment within the limits of the experimental errors. In the case of 13C chemical shift, the differences between theory and experiment increase monotonically with the number of chlorine atoms and exhibit a deviation from additivity. This behavior is related to the saturation of the experimental 13C chemical shifts with the number of chlorine atoms, whereas the evolution is mostly linear at both DFT and MP2 levels of approximation. This difference has been traced back to the relativistic spin-orbit coupling effects, which are exalted as a result of the enhancement of the s character of the C atom when increasing the number of linked Cl atoms. Thus, it was demonstrated that not only electron correlation but also relativistic effects have to be considered for estimating the 13C chemical shifts when several Cl atoms are directly attached to the C atom. Linear (theory/experiment) regressions have then been performed for the different types of C atoms, i.e., bearing one, two, and three Cl atoms, with excellent correlation coefficients. The linear correlation relationships so obtained can then serve to predict and facilitate the interpretation of the nuclear magnetic resonance spectra of more complex compounds. Furthermore, by investigating the basis set effects, the correlation between the chemical shifts calculated using the 6-311 + G(2d,p) basis set and the more extended 6-311 + G(2df,p) and aug-cc-pvtz basis sets is excellent, demonstrating that the choice of the 6-311 + G(2d,p) basis set for calculating the 1H and 13C chemical shifts is relevant.     

固体酪氨酸^1^3C核磁屏蔽张量的实验与理论研究

应用最近发展的三回波二维慢速魔角旋转(Triple-Echo 2D MAT)实验方法测得了酪氨酸中各不等价碳的化学位移各向异性(CSA)张量主值。由从头计算获得的结果与实验值符合较好, 说明对于具有复杂结构的多原子体系, 对杂原子使用较小的基函数, 而对所关心的碳原子使用较大的基函数以提高计算精度, 这样可以达到既节省计算机空间与计算时间而不影响计算精度的目的。     

Combined bond-polarization basis sets for accurate determination of dissociation energies. II. Basis set superposition error as a function of the parent basis set

The effect of the parent basis set on the basis set superposition error caused by bond functions is investigated systematically. An important difference between BSSE at the SCF and correlated levels is pointed out. Three new basis sets are defined, denoted 6-311 + G(d,p)B, 6-311 + G(2d,p)B, and 6-311 + G(2df,p)B. BSSE for the first-row hydrides seems to increase uniformly with increasing atomic number of the central atom. Expansion of the valence part of the basis set from 6-31G to 6-311G, as well as adding f functions, has a significant effect on the BSSE. Additional BSSEs incurred by bond functions are less than or equal to 1 kcal/mol for the 6-311 + G(2df,p)B basis set. For the dissociation energies of the first-row hydride species, agreement with experiment within only a few kcal/mol can be obtained even without resorting to isogyric reaction cycles. For high-quality calculations, adding bond functions seems to have definite advantages over expanding the polarization space beyond the [2d1f] level.     

An efficient methodology to study cyclodextrin clusters: application to α-CD hydrated monomer, dimer, trimer and tetramer

The hydrated α-cyclodextrin (α-CD) clusters resulting from the following process: nα-CD + n(H₂O)₆ → α-CD_n · 6nH₂O, with n = 1, 2, 3, 4, have been investigated using semiempirical (PM3), ab initio Hartree-Fock and Density Functional Theory (BLYP functional) levels of theory. The largest structure containing 576 atoms and 5,760 contracted basis functions (6-31G(d,p) basis set) poses as a considerable hard task for quantum chemical calculations. As the number of basis function increases rapidly with the cluster size, an alternative procedure to make the calculations feasible is certainly welcome, in order to perform BLYP calculations with an adequate basis set. Through the aid of a computer program that we developed, it became of practical use the selection of atom by atom basis sets, using the common chemical sense, enabling quantum mechanical calculations to be performed for very large molecular interacting systems (inclusion complexes), at an affordable computational cost. In this article we show how an appropriate selection of basis functions, leaving the CH_n groups with a minimal basis set and the oxygen atoms (and OH groups) with a better quality basis set, lower considerably the computational cost with no significant loss in the calculated interaction energies. A regular pattern is observed for α-CD hydrated monomer, dimer, trimer and tetramer, therefore adding support to the use of this procedure when studying larger hydrogen bonded clusters where electron correlation effects are important. We show that the procedure reported here enables DFT calculations for hydrated cyclodextrin using basis set up to the 6-311++G(3df,3pd) triple zeta quality .     

Approximate STO functions for the first-row transition metal atoms

Slater type orbital (STO) basis sets for the atoms Sc-Zn have been derived using a technique based on the distance between subspaces. The accuracy for several properties of these basis sets has been tested. Basis sets studied are of both single- and double-zeta sizes, although this technique can be generalized for any size. Uniform quality criteria through the series of atoms Sc-Zn are difficulty to establish due to the varying number of d electrons. A comparative study at the atomic level of the quality of STO basis sets (both the two new basis sets and Clementi's basis sets) for the first-row transition elements has been carried out. Results show that the new basis sets provide better simulation for several properties. Molecular calculations on compounds with these atoms using a Gaussian expansion fitted according to the new values of optimized STOs are also included. The results obtained are similar to those reported when STO-3G basis set is used.     

Quantum-chemical calculations of NMR chemical shifts of organic molecules: XV. Relativistic calculations of <Superscript>29</Superscript>Si NMR chemical shifts of silanes

Calculations of ²⁹Si NMR chemical shifts of 68 silanes possessing various substituents, in particular, with heavy halogens attached to silicon atom, were carried out applying an efficient calculation scheme of locally dense basis set in the framework of the electron density functional theory utilizing the Keal–Tozer functional combined with relativistic Dyall basis sets on a four-component relativistic level. The main factors of calculation accuracy of silicon chemical shifts were analyzed including the relativistic effects, environmental impact, and vibrational corrections. The mean absolute calculation error for the studied compounds series accounting for all mentioned factors was 14.0 ppm for the nonrelativistic calculation and 6.7 ppm for the four-component relativistic calculation at the range of silicon chemical shifts variation of ~250 ppm.     

Orbitals expanded in slater functions with single-exponent by shell and by subshell

Slater-type orbitals (STO s) with a single-exponent by shell or by subshell have been constructed to reduce the number of integrals evaluated in the electronic calculations. The expansion of orbitals in these new basis sets has been carried out in detail for the ground state of the Ne atom. We have carried out a study of STO basis sets with a different size for this atom that could help to propose empirical rules for the selection of these basis sets for other atoms. The usefulness of STO s with single-exponent by shell and subshell and the splitting of s and p functions are discussed. © 1994 John Wiley & Sons, Inc.     

A fully relativistic method for calculation of nuclear magnetic shielding tensors with a restricted magnetically balanced basis in the framework of the matrix Dirac-Kohn-Sham equation

A new relativistic four-component density functional approach for calculations of NMR shielding tensors has been developed and implemented. It is founded on the matrix formulation of the Dirac-Kohn-Sham (DKS) method. Initially, unperturbed equations are solved with the use of a restricted kinetically balanced basis set for the small component. The second-order coupled perturbed DKS method is then based on the use of restricted magnetically balanced basis sets for the small component. Benchmark relativistic calculations have been carried out for the (1)H and heavy-atom nuclear shielding tensors of the HX series (X=F,Cl,Br,I), where spin-orbit effects are known to be very pronounced. The restricted magnetically balanced basis set allows us to avoid additional approximations and/or strong basis set dependence which arises in some related approaches. The method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians for relativistic calculations of chemical shifts and spin-spin coupling constants of heavy-atom systems. In particular, no picture-change effects arise in property calculations.     

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Summary Generally contracted basis sets for second row atoms have been constructed using the Atomic Natural Orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over several atomic states, positive and negative ions, and atoms in an external electric field. The contracted basis sets give virtually identical results as the corresponding uncontracted sets for the atomic properties, which they have been designed to reproduce. The design objective has been to describe the ionization potential, the electron affinity, and the polarizability as accurately as possible. The result is a set of well balanced basis sets for molecular calculations. The starting primitive sets are 17s12p5d4f for the second row atoms Na-Ar. Corresponding ANO basis sets for first row atoms have recently been published.     

Long-range relativistic heavy atom effect on 1H NMR chemical shifts of selenium- and tellurium-containing compounds

Previously unknown manifestation of heavy atom effect on the NMR chemical shifts of β- and γ-protons initiated by the relativistic effects of the tellurium and selenium atoms has been investigated in the representative series of selenium- and tellurium-containing compounds. To approve the four-component density functional approach to be the appropriate tool for the investigation of the heavy atom on light atom effect (HALA), the benchmark calculations of the proton chemical shifts have been performed at the CCSD level using comprehensively chosen locally dense basis set with taking into account solvent, vibrational, and relativistic corrections. A good agreement with the experimental data was achieved. The magnitudes of the relativistic HALA corrections to β- and γ-proton chemical shifts were found to vary in a wide range, namely from −3.08 ppm for the γ-proton of methyltelluraldehyde to 14.51 ppm for β-proton in benzotelluraldehyde.     

Basis set error estimation for DFT calculations of electronic g‐tensors for transition metal complexes

We present a detailed study of the basis set dependence of electronic g‐tensors for transition metal complexes calculated using Kohn–Sham density functional theory. Focus is on the use of locally dense basis set schemes where the metal is treated using either the same or a more flexible basis set than used for the ligand sphere. The performance of all basis set schemes is compared to the extrapolated complete basis set limit results. Furthermore, we test the performance of the aug‐cc‐pVTZ‐J basis set developed for calculations of NMR spin‐spin and electron paramagnetic resonance hyperfine coupling constants. Our results show that reasonable results can be obtain when using small basis sets for the ligand sphere, and very accurate results are obtained when an aug‐cc‐pVTZ basis set or similar is used for all atoms in the complex. © 2014 Wiley Periodicals, Inc.     

Ab initio prediction of 15N-NMR chemical shift in α-boron nitride based on an analysis of connectivities

Hydrogen-saturated cut-outs of hexagonal boron nitride have been used to model the solid state. Model compounds have been geometry optimized by means of density functional theory, whereas chemical shift calculations have been carried out at the coupled-perturbed Hartree–Fock level of theory employing gauge-including atomic orbital (GIAO) basis sets. The reliability of results has been tested against experimental values for chemical shifts in stable molecules with similar structural elements. With increasing cluster size, viz. a vanishing influence of the saturating hydrogens on the innermost nitrogen atoms, we find a convergence of ¹⁵N chemical shifts. A classification scheme for the chemical environment of a nitrogen atom has been set up according to its bonding graph including the second coordination sphere. For a given connectivity, chemical shifts vary within a few parts per million, thus enabling us to predict a ¹⁵N-NMR chemical shift of −285 ± 5 ppm for solid α-boron nitride. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 716–725, 1998     

An SCF study of 10-vertex and 12-vertex boranes and heteroboranes

For symmetry-constrained boranes B₁₀H, B₁₂H, and their valence isoelectronic analogues containing a single hetero atom, completely optimized geometries were obtained using Hartree–Fock SCF calculations with the 3-21G and 6-31G* basis sets. For the anionic and dianionic species, the geometry optimization was also carried out using the 6-31 + G* basis set. Harmonic vibrational frequencies were obtained at HF/3-21G level. The results compare well with experiment where available.     

Modified MINDO/3 13C chemical shift calculations for simple hydrocarbons

Calculations of ¹³C chemical shifts in some simple hydrocarbons have been carried out using the GIAO approach in the MINDO/3 semiempirical formalism. In order to achieve reasonable agreement with experiment it is necessary to modify (increase) the vacant orbital energies in the MINDO/3 calculation in order to reduce the magnitude of the paramagnetic contribution, and to also modify this dominant term by generally reducing it as a function of the number of hydrogen and carbon atoms bonded to the resonant nucleus in question. For a set of 34 resonant nuclei of the simpler hydrocarbons, agreement with experiment of the order of 7.8 ppm is attained; however, pathological cases such as cyclopropane and some simple allenes continue to cause problems, increasing the standard deviation of the full set to 12.5 ppm. Our results indicate that the MINDO/3 approach is as viable for ¹³C chemical shift calculations as other semiempirical approaches, all of which seem currently to be limited to a standard deviation of the order of 10 ppm.     

Reliability of atomic natural orbital basis sets in calculations involving pseudopotentials

The performance of Atomic Natural Orbital (ANO) basis sets for calculations involving nonempirical core pseudopotentials has been studied by comparing the results for atomic and molecular nitrogen obtained using contracted ANO basis sets with those obtained using both the primitive set and a segmented one. The primitive set has been optimized at the SCF level for atomic N treated as a five-electron pseudo-atom, and consists of 7s and 7p primitive GTOs supplemented by 2d and 1f GTOs optimized at the CI level. From this primitive set three contracted [3s 3p 2d 1f] sets have been obtained. The first one has been derived from the ANOs of the neutral atom, the second has been obtained from an averaged density matrix and the third one is a segmented set. For the atom, the segmented set gives a zero contraction error at the SCF level as it must be in valence-only calculations. The ANO basis sets show some small contraction error at the SCF level but perform better in CI calculations. However, for the diatomic N₂ molecule the ANO basis sets exhibit a rather large contraction error in the calculated SCF energy. A detailed analysis of the origin of this error is reported, which shows that the conventional strategy used to derive ANO basis sets does not work very well when pseudopotentials are involved.     

Additivity model for calculations of UHF spin densities in some aza-aromatic radical anions

The concept of a universal basis set for electronic structure calculation is illustrated by presenting results obtained when basis sets are transferred from one atom to another. A single Slater-orbital basis set, consisting of nine 1s and six 2p functions, produces Hartree-Fock total energies and orbital energies in good agreement with the most accurate calculations of these energies obtained using different basis sets individually optimized for each atom. Transferability of integrals is a natural consequence of the use of the same basis set for each atom in a molecule.