7
7
1
Se– H spin–spin coupling constants of 2-substituted selenophenes
of Dunning,[10] namely, cc-pVXZ (X = D, T) and aug-cc-pVTZ,
together with the former two with decontracted s-functions and
augmented with two tight s-functions (ξ1 = 63865962.54 and
ξ2 = 426498512.2 for selenium), cc-pVXZ-su2 (X = D, T) and also
the basis set aug-cc-pVTZ-J originally proposed by Enevoldsen,
Oddershede and Sauer for calculation of spin–spin coupling
constants and extended in the present paper for selenium. The
rest of the atoms (uncoupled) were specified with Dunning’s
cc-pVDZ in all the cases.
removed the contraction completely. Stepwise addition of up to
four additional tight s-type functions with exponents obtained
as even-tempered series from the ratio (6.678025278) between
the two largest s-type functions in the original basis set showed
that convergence is already obtained with two additional s-type
functionswithexponents63865962.54and426498512.2. Addition
of up to three tight p-type or four tight d-type functions with
exponents obtained analog to the s-type functions did not change
the result any further. The final uncontracted basis set therefore
consisted of 23 sets of s-type, 14 sets of p-type, 10 sets of d-type
and 2 sets of f-type functions (23s14p10d2f). Using the molecular
orbital coefficients of H2 Se in this basis set, it was contracted
to [12s9p6d2f] in a 14-14-14-1-1-1-1-1-1-1-1-1/13-13-13-1-1-1-1-
1-1/8-1-1-1-1-1/1-1 scheme. The final basis set aug-cc-pVTZ-J for
selenium is given in Table 1.
[
6]
It is well known that standard energy optimized basis sets
are in general not flexible enough to represent the operators
involved in the calculation of indirect nuclear spin–spin coupling
constants correctly.[
11–14]
Consequently, several attempts have
recently been made to develop basis sets suitable for high-
accuracy calculations of spin–spin coupling constants.[6,15–22]
They are all modifications of standard basis sets and are based
on the fact that the Fermi contact (FC) operator contains a delta
function and measures the electron density at the position of
the nucleus and that standard basis sets do not give a good
description of this part of the wavefunction. In the basis sets by
For fourth row atoms like Se, one can expect that relativistic
effects play some role (for reviews, see Ref. [26]). A fully relativistic
theory of spin–spin coupling constants, i.e. based on the Dirac
equation, has already been presented some time ago,[ but the
number of applications is still very small and, more important, no
implementation based on correlated wavefunction methods as
27]
[
21,22]
Jensen and coworkers,
tight p- and d-type functions are also
added in order to give a better description of the paramagnetic
spin orbit (PSO) and spin-dipolar (SD) terms for the cases where
these contributions are of the same order of magnitude as that of
used in the present work is yet available apart from a recent four-
component Dirac–Kohn–Sham implementation.[
28]
Relativistic
[
29]
and electron correlation effects are, however, not additive, and
calculations of spin–spin coupling constants at the uncorrelated
HF-SCF level are often qualitatively wrong. The predictive power of
the recent Dirac–Hartree–Fock calculation of the one-bond Se–H
7
7
1
the FC term. However, this is not the case for any of the Se– H
spin–spin coupling constants investigated here; therefore, we
concentrate only on the FC term.
One of these optimized basis sets is called ‘aug-cc-pVTZ-J’[6,15,16]
and is based on the correlation consistent aug-cc-pVTZ basis sets
coupling in H2 Se is therefore uncertain. Alternatively, one can
[30]
include relativistic effects also via perturbation theory or two-
[
10]
[26,31,32]
by Dunning and coworkers.
The original basis sets were then
component approaches.
Recent correlated calculations of
this type on H2 Se or GeH4[ indicate the relativistic corrections
to one-bond X–H couplings for atoms X, like Ge or Se, are in the
order of 10%.
32]
modified in three ways: (i) The contraction of all basis functions
was completely removed. (ii) Four s-type functions with very large
exponents were added in the case of all atoms and three sets of
d-type functions with large exponents were added to the third
row atoms Al, Si, P, S and Cl. The exponents of the additional
functions were obtained in an even-tempered fashion from the
ratio between the two largest exponents in the original basis
set. (iii) The additional ‘aug’ diffuse second polarization function
In a comparison with experimental coupling constants mea-
sured in liquids, one should also consider the effect of nuclear
motion, i.e. vibrational corrections, and the solvent shift. Although
vibrational corrections of one-bond X–H coupling constants can
amount up to 5%,[ for two- or three-bond couplings, they are
33]
(
d-type for H and f-type for all other atoms) was removed. The
typically less than 1 Hz as shown in recent calculations on Pyrrole,
[
15]
[34]
resulting basis sets, called ‘aug-cc-pVTZ-Juc’, are rather large. In
order to reduce the size, one could either employ a locally dense
basis set scheme[ or recontract the basis set again. Geertsen
or Guilleme and San Fabi a´ n have e.g. recontracted their basis
sets with the SCF molecular orbital coefficients of the molecule
in question. However, this would require a basis set optimization
for each new molecule studied, which is rather inconvenient. In
the aug-cc-pVTZ-J basis sets, this idea was therefore generalized
and the SCF molecular orbital coefficients of the simplest
hydride of each atom in question were used as contraction
coefficients.[
developed for correlated wavefunction calculations at the level
of the SOPPA or SOPPA(CCDS) method,
also shown to perform very well in density functional theory (DFT)
calculations,[
based on the correlation consistent cc-pCV5Z basis set.
However, an aug-cc-pVTZ-J basis set for selenium has so far
not been published. Following the scheme described above, we
have therefore generated a corresponding basis set for Se. All
the calculations during the basis set optimization were performed
on H2 Se and at the SOPPA level. For hydrogen, the aug-cc-
pVTZ-J basis set was employed in all the steps. For Se, we
started with the aug-cc-pVTZ basis set by Wilson et al.[ and
Furan and Thiophene.
shifts for two- or three-bond couplings are typically very small.
Similarly, it is known that the solvent
[
35]
23]
[14]
2
3
Results of the benchmark calculations of J(Se,H-2) and J(Se,H-
3) in selenophene (1) carried out at different levels of theory
taking into account all four coupling contributions to the total
coupling, J: Fermi contact, JFC, spin-dipolar, JSD, diamagnetic spin-
orbital, JDSO, and paramagnetic spin-orbital, JPSO, are compiled
in Table 2. It follows that generally the wavefunction methods
SOPPA and SOPPA(CCSD) perform much better as compared to
the density functional method DFT-B3LYP for both couplings. This
[
18]
15,16]
77
1
The aug-cc-pVTZ-J basis sets were originally
is especially obvious in the case of geminal Se– H coupling,
which is essentially overestimated within the DFT framework. On
the other hand, computationally more demanding SOPPA(CCSD)
does not show any noticeable advantages as compared to the
parent SOPPA method. Among six basis sets under consideration,
contracted Sauer’s aug-cc-pVTZ-J and decontracted Dunning’s
cc-pVTZ-su2 with two tight s-functions are apparently the best.
Keeping this in mind, we performed our further calculations of all
[
4,5,6]
but were afterward
19,24]
e.g. in comparison with a much larger basis set
[
19]
7
7
1
Se– H coupling constants in the whole series of 2-substituted
selenophenes 1–7 at the SOPPA level with two most efficient basis
sets, namely, aug-cc-pVTZ-J (Table 3) and cc-pVTZ-su2 (Table 4).
Before discussing these data, it should be noted that, in
contrast to compounds 1–3 possessing no rotational conformers,
25]
Magn. Reson. Chem. 2010, 48, 44–52
Copyright ꢀc 2009 John Wiley & Sons, Ltd.
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