J. San Fabián

Basis sets and active space in multiconfigurational self-consistent field calculations of nuclear magnetic resonance spin–spin coupling constants

The dependence of spin–spin nuclear magnetic resonance (NMR) coupling constants on the basis set and electron correlation has been investigated in methane using Hartree–Fock and multiconfigurational self-consistent field wave functions (HF-SCF and MCSCF). The effect of the size, contraction, and tight s functions of the basis sets is analyzed. Some suggestions about the contraction scheme are indicated. MCSCF wave functions with different numbers of active orbitals and different numbers of excited electrons were used. An approximation to determine spin–spin coupling constants at a high level of electron correlation from three calculations with a smaller level of correlation and reduced computational cost is investigated. The best calculated 1JCH and 2JHH couplings are 120.63 and −13.23 Hz, respectively, which are 0.24 and 1.24 Hz smaller than those experimentally obtained for the equilibrium geometry. The remaining error in these coupling constants can be attributed mainly to correlation and not to basis ...

MCSCF calculations of NMR spin–spin coupling constant of the HF molecule

The dependence of spin–spin NMR coupling constants on the basis set and electron correlation has been investigated for the hydrogen fluoride using Hartree–Fock (HF-SCF) and multiconfigurational self-consistent field (MCSCF) wave functions. The effect of the size, contraction, and tight s-type, augmented and polarization functions in the basis sets is analyzed. MCSCF wave functions with different number of active orbitals and excited electrons were used within the frozen-core approximation and with all-electron calculations. The correlation effect associated with the core electrons is not negligible. An approximation to determine spin–spin coupling constants at high level of electron correlation and reduced computational cost is applied satisfactorily. The best calculated and estimated 1JFH couplings are 544.20 and 536.63 Hz, respectively, with all electron correlation. Both values agree with the experimental one within the error bars (525±20 Hz).

Approximating correlation effects in multiconfigurational self-consistent field calculations of spin-spin coupling constants

The multiconfigurational self-consistent field (MCSCF) method in their approximations restricted and complete active spaces (RAS and CAS) provides a theoretically accurate description of the coupling constants of a wide range of molecules. To obtain accurate results, however, very large basis sets and large configuration spaces must be used. Nuclear magnetic resonance coupling constants for the equilibrium geometry have been calculated for a series of small molecules using approximated correlation contributions. The four contributions to the coupling constants (Fermi contact, spin dipolar, orbital paramagnetic, and orbital diamagnetic) have been calculated at the CAS and RAS MCSCF and second-order polarization propagator approximation levels using a large basis set. An additive model that considers the effect on the coupling constants from excitation of more than two electrons and from core-electron correlation is used to estimate the coupling constants. Compared with the experimental couplings, the best calculated values, which correspond to the MCSCF results, present a mean absolute error of 3.6 Hz and a maximum absolute deviation of 13.4 Hz. A detailed analysis of the different contributions and of the effects of the additive contributions on the coupling constants is carried out.

Vicinal proton–proton coupling constants: MCSCF ab initio calculations of ethane

Abstract Ab initio Hartree–Fock self consistent field and multiconfigurational self consistent field calculations have been carried out to study the dihedral angle dependence of the vicinal proton–proton coupling constant in an ethane molecule. The four contributions to 3 J HH , Fermi contact, spin dipolar, orbital paramagnetic and orbital diamagnetic, have been computed with five different basis sets, three of them rebuilt specifically to calculate coupling constants. The importance of the noncontact contributions is small and the correlation effect on these is practically null. The calculated Karplus equation reproduces the experimental equation for 3 J HH with a maximum deviation of 1.0 Hz when the proton–proton torsional angle is 180°. Our best average 〈 3 J HH 〉 coupling constant calculated using the experimental geometry (7.77 Hz) is in good agreement with the experimental value (8.02 Hz).

Computational NMR coupling constants: Shifting and scaling factors for evaluating 1JCH

Optimized shifting and/or scaling factors for calculating one‐bond carbon–hydrogen spin–spin coupling constants have been determined for 35 combinations of representative functionals (PBE, B3LYP, B3P86, B97‐2 and M06‐L) and basis sets (TZVP, HIII‐su3, EPR‐III, aug‐cc‐pVTZ‐J, ccJ‐pVDZ, ccJ‐pVTZ, ccJ‐pVQZ, pcJ‐2 and pcJ‐3) using 68 organic molecular systems with 88 1JCH couplings including different types of hybridized carbon atoms. Density functional theory assessment for the determination of 1JCH coupling constants is examined, comparing the computed and experimental values. The use of shifting constants for obtaining the calculated coupling improves substantially the results, and most models become qualitatively similar. Thus, for the whole set of couplings and for all approaches excluding those using the M06 functional, the root‐mean‐square deviations lie between 4.7 and 16.4 Hz and are reduced to 4–6.5 Hz when shifting constants are considered. Alternatively, when a specific rovibrational contribution of 5 Hz is subtracted from the experimental values, good results are obtained with PBE, B3P86 and B97‐2 functionals in combination with HIII‐su3, aug‐cc‐pVTZ‐J and pcJ‐2 basis sets. Copyright

Vicinal carbon-proton coupling constants. Angular dependence and fluorine substituent effects

Abstract Data sets of vicinal carbon-proton coupling constants 3JCH have been calculated for propane, 1-fluoropropane and 2-fluoropropane by means of SCF ab initio methods using various standard Gaussian-type basis sets and a double zeta basis set [ 4s2p1d 2s1p ] with additional tight s functions. The major contribution to 3JCH arises from the Fermi contact term. The remaining contributions, spin dipolar, orbital paramagnetic and orbital diamagnetic, are very small. A satisfactory agreement with experimental data is obtained after multiplying the best calculated values by a factor close to 0.8. The dependence of the calculated 3JCH couplings upon the torsion angles φ( 13 C α C β C γ H) , between the coupled nuclei, and φα(X13CαCβCγ), between a substituent X at Cα and the Cγ carbon, as well as the effect of a fluorine substituent bonded to the carbons Cα, Cβ, or Cγ, have been analysed using equations formulated from a substituent effect model. The two-dimensional angular dependence on φ and φα for the 3JCH coupling of propane is described by an equation including 11 terms with a r.m.s. deviation σ of 0.13 Hz. Likewise, the effect upon 3JCH of a fluorine attached to Cα depends on both angles φ and φα. This effect is described by an equation of five terms with a σ of 0.31 Hz. On the other hand, the effects upon 3JCH of a fluorine bonded to Cβ or Cγ depend mainly on the angle φ and are described by equations including, respectively, four and seven terms. The corresponding σ deviations for these equations are 0.13 and 0.28 Hz. The experimental effects upon 3JCH of a substituent OH are satisfactorily reproduced by these equations when the different electronegativity of oxygen and fluorine is taken into account.

Vicinal fluorine-proton coupling constants. Ab initio calculations of angular dependence and substituent effects

Abstract A data set of vicinal fluorine-proton coupling constants has been calculated by means of the SCF ab initio and semiempirical INDO/FPT methods. The angular dependence, the effect of individual substituents, and the effect of interaction between two substituents upon the 3 J FH couplings have been studied for the molecules CH 2 FCH 3 , CHF 2 CH 3 , CH 2 FCH 2 F, CF 3 CH 3 , and CHF 2 CH 2 F. The four contributions to 3 J FH ( J FC , J SD , J OD and J OP ) have been computed using the standard basis sets 6-31G, 6-31G ∗ , 6-31G ∗∗ and 6-311G ∗∗ and a double zeta basis set [4s2p1d/2s1p] with additional tight s functions on the H and F. The agreement with the experimental data is better for the last basis set but the trends of the angular dependence and substituent effects are also reproduced by the remaining basis sets. The major contribution arises from the FC term and the remaining contributions are much smaller being the OP the most important. The individual effect of an electronegative substituent depends on the carbon to which is bonded, being more important when the substituent is bonded to the carbon with the coupled hydrogen. The effect of interaction between two substituents seems to be not negligible, reaching values up to 6 Hz. The most important calculated interaction effects are the geminal δC 012 FF , δC 034 FF and δC 134 FF as well as the vicinal δC 213 FF and δC 214 FF .

Computational NMR coupling constants

Optimized shifting and/or scaling factors for calculating one‐bond carbon–hydrogen spin–spin coupling constants have been determined for 35 combinations of representative functionals (PBE, B3LYP, B3P86, B97‐2 and M06‐L) and basis sets (TZVP, HIII‐su3, EPR‐III, aug‐cc‐pVTZ‐J, ccJ‐pVDZ, ccJ‐pVTZ, ccJ‐pVQZ, pcJ‐2 and pcJ‐3) using 68 organic molecular systems with 88 1JCH couplings including different types of hybridized carbon atoms. Density functional theory assessment for the determination of 1JCH coupling constants is examined, comparing the computed and experimental values. The use of shifting constants for obtaining the calculated coupling improves substantially the results, and most models become qualitatively similar. Thus, for the whole set of couplings and for all approaches excluding those using the M06 functional, the root‐mean‐square deviations lie between 4.7 and 16.4 Hz and are reduced to 4–6.5 Hz when shifting constants are considered. Alternatively, when a specific rovibrational contribution of 5 Hz is subtracted from the experimental values, good results are obtained with PBE, B3P86 and B97‐2 functionals in combination with HIII‐su3, aug‐cc‐pVTZ‐J and pcJ‐2 basis sets. Copyright

Karplus Equation for (3)JHH Spin-Spin Couplings with Unusual (3)J(180°) < (3)J(0°) Relationship.

Vicinal (3)JHH coupling constants for monosubstituted ethane molecules present the unusual relationship (3)JHH (180°) < (3)JHH (0°) when the substituent contains bonding and antibonding orbitals with strong hyperconjugative interactions involving bond and antibond orbitals of the ethane fragment. This anomalous behavior is studied as a function of the substituent rotation for three model systems (propanal, thiopropanal, and 1-butene) at the B3LYP/TZVP level. The consistency of this level of theory to study this problem is previously established using different ab initio methods and larger basis sets. The origin of the unusual (3)JHH(180°) - (3)JHH(0°) relationship is attributed to simultaneous σ/π hyperconjugative interactions σCα-Hα → π*Cc═X, and σCα-Cβ → π*Cc═X. These interactions depend on the substituent rotation and their effects are different for (3)JHH(180°) than for (3)JHH(0°). The modelization carried out shows an increase of those effects as the substituent changes from weaker (CH═CH2) to stronger (CH═S) electron acceptor π*C═X.

Spin–spin coupling constants in ethylene: equilibrium values

Abstract The nuclear magnetic resonance spin–spin coupling constants for the ethylene have been calculated at the multiconfigurational self-consistent field (MCSCF) method using the restricted (RAS) and complete (CAS) active space approximations. An analysis of the calculated values and of the effects of different factors (active spaces, valence and core–electron correlation) is presented. The effect of increase the number of active orbitals and that of triple and quadruple excitations is important and opposite to the effect of core–electron correlation. The best calculated values for 1 J CC (68.83 Hz), 1 J CH (151.56), 2 J CH (−1.56 Hz), 2 J HH (1.07 Hz) 3 J HH (cis) (11.47 Hz), and 3 J HH (trans) (17.78 Hz) are in good agreement with the best calculated and experimental values.