Thermochemistry of arylselanyl radicals and the pertinent ions in acetonitrile

Article abstract of DOI:10.1021/ja0291787

Reduction and oxidation potentials of a series of parasubstituted phenylselanyl radicals, XC₆H₄Se^., have been measured using photomodulated voltammetry in acetonitrile. The thermodynamic significance of these data was subs

Full text of DOI:10.1021/ja0291787

Published on Web 02/01/2003
Thermochemistry of Arylselanyl Radicals and the Pertinent
Ions in Acetonitrile
Allan Hjarbæk Holm,† Laura Yusta,† Peter Carlqvist,‡ Tore Brinck,*,‡ and
Kim Daasbjerg*,†
Contribution from the Department of Chemistry, UniVersity of Aarhus, Langelandsgade 140,
DK-8000 Aarhus C, Denmark, and Physical Chemistry, Royal Institute of Technology,
SE-10044 Stockholm, Sweden
Received November 1, 2002 ; E-mail: kdaa@chem.au.dk
Abstract: Reduction and oxidation potentials of a series of parasubstituted phenylselanyl radicals,
XC6H4Se•, have been measured using photomodulated voltammetry in acetonitrile. The thermodynamic
significance of these data was substantiated through a study of the oxidation process of the pertinent
selenolates in linear sweep voltammetry. Both the reduction and the oxidation potentials correlate linearly
with the Hammett substituent coefficients σ and σ+ leading in the latter case to slopes, F+, of 2.5 and 3.8,
respectively. Through comparison of these slopes with those published previously for the O- and S-centered
analogues, it is revealed that the π-interaction becomes progressively smaller as the size of the radical
center increases in the order O, S, and Se. Solvation energies of the pertinent selenolates and selanylium
ions have been extracted from thermochemical cycles incorporating the measured electrode potentials for
XC6H4Se• as well as electron affinities and ionization potentials obtained from theoretical calculations at
the B3LYP/6-31+G(d) level. The extracted data show the expected overall substituent dependency for
both kinds of ions; that is, the absolute value of the solvation energy decreases as the charge becomes
more delocalized. The data have also been compared with solvation energies computed using the polarizable
continuum model (PCM). Interestingly, we find that, while the model seems to work well for selenolates, it
underestimates the solvation of selanylium ions in acetonitrile by as much as 25 kcal mol-1. These large
deviations are ascribed to the fact that the PCM method does not take specific solvent effects into account
as it treats the solvent as a continuum described solely by its dielectric constant. Gas-phase calculations
show that the arylselanylium ions can coordinate covalently to one or two molecules of acetonitrile in strong
Ritter-type adducts. When this strong interaction is included in the solvation energy calculations by means
of a combined supermolecule and PCM approach, the experimental data are reproduced within a few kcal
mol-1. Although the energy difference of the singlet and triplet spin states of the arylselanylium ions is
small for the gas-phase structures, the singlet cation is undoubtedly the dominating species in solution
because the triplet cation lacks the ability to form covalent bonds.
Introduction
In this paper, we wish to present our results concerning the
reduction and oxidation of a series of parasubstituted phenylse-
The important role of selenium compounds in both environ-
mental and biological systems has long been recognized.1,2 The
synthetic applicability of selenium compounds is also well
established and has been studied extensively over the past
15-20 years.3 However, despite intensive research, very little
is known about the redox properties of selenium compounds.
A few papers have been devoted to electrochemical investiga-
tions of diselenides,4,5 but no reports have appeared so far on
the reactive free radical and ionic species.
lanyl radicals (Scheme 1) in acetonitrile by employing the
photomodulated voltammetry (PMV) technique.6 Because the
standard potentials of the substituted phenylselanyl radicals can
be determined by linear sweep voltammetry (LSV) as well, it
will be possible to verify the reliability of the PMV measure-
ments. The extent of interaction between the π-system of the
aromatic ring and the orbitals of the adjacent atoms may be
evaluated through a comparison of slopes obtained in Hammett
plots of the potentials with those published previously for the
O- and S-centered analogues.
† University of Aarhus.
‡ Royal Institute of Technology.
Another point addressed by the present study is the solvation
energies of the ions formed upon reduction and oxidation of
the selanyl radicals. These solvation energies are extracted from
(1) Shamberger, R. J. Biochemistry of Selenium; Plenum: New York, 1983.
(2) Soda, K.; Tanaka, H.; Esaki, N. In The Chemistry of Organic Selenium
and Tellurium Compounds; Patai, S., Ed.; John Wiley: New York, 1987;
Vol. 2, Chapter 7.
(3) Organoselenium Chemistry: Modern DeVelopments in Organic Synthesis,
Top. Curr. Chem.; Wirth, T., Ed.; Springer-Verlag: Berlin, Heidelberg,
New York, 2000; Vol. 208 and references therein.
(4) Giles, G. I.; Tasker, K. M.; Johnson, R. J. K.; Jacob, C.; Peers, C.; Green,
K. N. Chem. Commun. 2001, 2490.
(5) Latypova, V. Z.; Chichirov, A. A.; Zhuikov, V. V.; Yakovleva, O. G.;
Vinokurova, R. I.; Ustyugova, I. A.; Kargin, Y. M. Zh. Obshch. Khim.
1989, 59, 1344.
(6) Wayner, D. D. M.; Griller, D. J. Am. Chem. Soc. 1985, 107, 7764.
9
2148
J. AM. CHEM. SOC. 2003, 125, 2148-2157
10.1021/ja0291787 CCC: $25.00 © 2003 American Chemical Society

Thermochemistry of Arylselanyl Radicals
A R T I C L E S
Scheme 1
from World Precision Instruments. In the linear sweep experiments, a
φ ) 1 mm glassy carbon (Sigradur G, HTW) disk was employed as
working electrode. The electrode surface was carefully polished before
each experiment with a 0.25 µm diamond suspension and rinsed in
ethanol. The counter electrode was a platinum coil melted into glass,
while a Ag wire in 0.1 M Bu4NBF4/acetonitrile separated from the
solution by a sintered glass tube served as quasi-reference electrode.
The ohmic drop in both the LSV and the PMV experiments was
compensated with a positive feedback system incorporated in the
homemade potentiostat.
thermochemical cycles incorporating the measured potentials
and electron affinities and ionization potentials obtained from
theoretical calculations. This provides the possibility of testing
one of the most successful solvation models, the polarizable
continuum model (PCM),7-10 on a series of relatively large ions.
So far, its success has mainly relied on the study of neutral
molecules and relatively small and localized ions.7-10 In recent
studies on carbanions,11 thiophenoxides,12 and arylsulfenium
ions,12 we have shown that, while the model can be applied
successfully for the anions, it underestimates the absolute value
of the solvation energy of the cations in acetonitrile. On the
basis of supermolecule calculations, this was attributed to a
strong specific solvation in terms of a Ritter-type adduct formed
between the sulfur atom of the sulfenylium ion and one molecule
of acetonitrile.12 For the selanylium ions, the possibility of
having similar interactions seems plausible, although the larger
size of Se as compared to S might lead to other effects as well.
Also it will be considered for both gas phase and solution if
the spin state of arylselanylium ions is a triplet or a singlet by
calculating the energy difference using high levels of theory.
Procedure. The method employed for generating the arylselanyl
radicals in the PMV experiments consisted of photolyzing the appropri-
ate diselenide as shown in eq 1.
(XC6H4Se-)2
9
hν8 2XC6H4Se•
(1)
The concentration of diselenide was typically 10 mM in a deaerated
solution of 0.1 M Bu4NBF4/acetonitrile. Samples were allowed to flow
through the cell at a rate of 2-3 mL min-1 to prevent depletion of
substrate and product accumulation. An output of 100 W from the lamp
was sufficient for photolyzing the different diselenides. Under these
conditions, the temperature near the electrode surface did not exceed
26 °C within an experiment as measured by a temperature sensitive
probe. The chopping frequency employed was 134 Hz. The sweep rate
was usually 0.1 V s-1. The voltammograms were corrected for the
background current recorded in the absence of substrate. All half-wave
potentials were referenced to SCE by measuring them relative to the
standard potential of the ferrocenium/ferrocene redox couple () 0.41
V versus SCE).19
The precursors used in the LSV studies, the substituted selenolates,
were generated in 1-2 mM concentration by a preparative two-electron
reduction of the pertinent diselenides in 0.1 M Bu4NBF4/acetonitrile
according to eq 2.
Experimental Section
Materials. Bis(4-chlorophenyl) and diphenyl diselenide were ob-
tained commercially from Aldrich and Lancaster, respectively, and used
as received. Bis(4-bromophenyl),13 bis(4-cyanophenyl),14 bis(4-di-
methylamino),15 bis(4-fluorophenyl),13 bis(4-methoxyphenyl),13 bis(4-
methylphenyl),13 and bis(4-nitrophenyl) diselenide14 were prepared
according to the references cited. The crude products contained varying
amounts (2-25%) of the corresponding monoselenide, which was
removed in a reductive purification procedure.16 Acetonitrile was
obtained from Lab-Scan and dried through a column of activated
alumina. The supporting electrolyte, tetrabutylammonium tetrafluo-
roborate (Bu4NBF4), was prepared and purified by standard procedures.
Apparatus. The instrumental setup used in the photomodulated
voltammetry technique has been described in detail recently.11,17,18 It
consisted of a 200 W Hg-Xe lamp (Photon Technology International)
for generating radicals photolytically, a water filter, a chopper (651,
EG&G Instruments), a lock-in amplifier (SR810 DSP, Stanford
Research Systems), and a home-built electrochemical flow-cell for
detecting the radicals. A net made of carbon fibers (transparency of at
least 50%) was used as working electrode. A small platinum rod
positioned in the outlet of the electrochemical cell served as counter
electrode. The reference electrode was a Flex-Ref electrode purchased
(XC6H4Se-)2 + 2e f 2XC6H4Se-
(2)
The sweep rates employed were in the range 0.2-20 V s-1. All
potentials were measured relative to the standard potential of anthracene
() -1.955 V versus SCE in 0.1 M Bu4NBF4/acetonitrile) and refer-
enced to SCE. Adsorption problems could be overcome by pretreating
the electrodes using multiscans.20 We did note, however, that the peak
potentials could vary by as much as 30 mV from one series of ex-
periments to another when employing different glassy carbon electrodes.
All solutions were carefully deaerated with argon before use.
Digital simulations were performed using the DigiSim version 3.03
software (Bioanalytical Systems, Inc.).21 In all simulations, the transfer
coefficient was set equal to 0.5. The diffusion coefficient was measured
for a number of selenolates and found to be (1.0 ( 0.1) × 10-5 cm-2
s-1 22
.
Solvation Energies. The formal relationships used for extracting
the two differential solvation energies, ∆∆G° (+•)exp and
sol
∆∆Gs°ol(-•)exp, from the experimentally obtained electrode potentials
are shown in eqs 3 and 4.23,24
(7) Tomasi, J.; Persico, M. Chem. ReV. 1994, 94, 2027 and references therein.
(8) Cossi, M.; Barone, V.; Cammi, R.; Tomasi, J. Chem. Phys. Lett. 1996,
255, 327.
(9) Menucci, B.; Tomasi, J. J. Chem. Phys. 1997, 106, 5151.
(10) Barone, V.; Cossi, M.; Tomasi, J. J. Chem. Phys. 1997, 107, 3210.
(11) Brinck, T.; Larsen, A. G.; Madsen, K. M.; Daasbjerg, K. J. Phys. Chem.
B 2000, 104, 9887.
(12) Brinck, T.; Carlqvist, P.; Holm, A. H.; Daasbjerg, K. J. Phys. Chem. A
2002, 106, 8827.
(13) Schmid, G. H.; Garratt, D. G. J. Org. Chem. 1983, 48, 4169.
(14) Syper, L.; Mlochowski, J. Tetrahedron 1988, 44, 6119.
(15) Bauer, H. Chem. Ber. 1913, 46, 92.
(16) Uneyama, K.; Maeda, K.; Tokunaga, Y. J. Org. Chem. 1995, 60, 370.
(17) Larsen, A. G.; Holm, A. H.; Roberson, M.; Daasbjerg, K. J. Am. Chem.
Soc. 2001, 123, 1723.
(18) Lund, T.; Wayner, D. D. M.; Jonsson, M.; Larsen, A. G.; Daasbjerg, K. J.
Am. Chem. Soc. 2001, 123, 12590.
∆∆G° (+•)exp ≡ ∆G° (+)exp - ∆G° (•)exp
)
sol
sol
sol
XC6H4Se+/XC6H4Se•
-IP + FE°
+ C (3)
(19) Daasbjerg, K.; Pedersen, S. U.; Lund, H. In General Aspects of the
Chemistry of Radicals; Alfassi, Z. B., Ed.; John Wiley: Chichester, 1999;
Chapter 12, p 410.
(20) Christensen, T. B.; Daasbjerg, K. Acta Chem. Scand. 1997, 51, 307.
(21) Rudolph, M.; Feldberg, S. W. DigiSim Version 3.03; Bioanalytical Systems,
Inc.
(22) Occhialini, D.; Pedersen, S. U.; Daasbjerg, K. J. Electroanal. Chem. 1994,
369, 39.
(23) Matsen, F. A. J. Chem. Phys. 1956, 24, 602.
(24) Peover, M. E. Trans. Faraday Soc. 1962, 58, 1656.
9
J. AM. CHEM. SOC. VOL. 125, NO. 8, 2003 2149

A R T I C L E S
Holm et al.
atoms except acidic hydrogens.31 The solvent parameters, including the
dielectric constant, were the same as those given for acetonitrile in the
program.
∆∆G° (-•)exp ≡ ∆G° (-)exp - ∆G° (•)exp
)
sol
sol
sol
XC6H4Se•/XC6H4Se-
EA - FE°
- C (4)
To investigate the importance of specific solute-solvent interactions,
we have included calculations of solvation energies for the cations using
a supermolecule approach. In this approach, we combine an explicit
treatment of one or two solvent molecules with the use of the PCM
method for estimating the remaining part of the solvation energy. We
have previously used similar methods successfully to study the catalytic
mechanism for hydrolysis of the methyl phosphate anion in aqueous
solution33 and to study the solvation of arylsulfenium ions and
thiophenoxides in acetonitrile.12 The expression for the solvation energy
of arylselanylium ions coordinated to one explicit acetonitrile molecule,
∆Gs°ol(+)sup, is given in eq 6.
The parameters ∆G° (+), ∆G° (-), and ∆G° (•) denote the solva-
sol
sol
sol
tion energies of the selenium-centered ions and radicals, while IP and
EA are the ionization potential and electron affinity of the arylselanyl
radicals, respectively. The two latter parameters are calculated using
the B3LYP/6-31+G(d) approach as described below. For the constant
C, a number of 109.3 kcal mol-1 is used, which originates from the
value of the absolute potential of the standard calomel electrode
() -4.74 V).25,26
In this context, it is also interesting to have a closer look at the
difference of ∆∆G° (+•)exp and ∆∆G° (-•) expressed as the param-
sol
sol
eter ∆∆G°sol(()exp in eq 5.
∆G° (+)sup ) ∆G1°fg(CH3CN) +
sol
∆∆G° (()exp ≡ ∆∆G° (+•)exp - ∆∆G° (-•)exp
)
∆G°(CH3CN + XC6H4Se+ f XC6H4Se+-NCCH3) +
sol
sol
sol
g
XC6H4Se+/XC6H4Se•
XC6H4Se•/XC6H4Se-
) + 2C (5)
-(IP + EA) + F(E°
+ E°
∆G° (XC6H4Se+-NCCH3)PCM (6)
sol
As the ∆∆G° (()exp parameter is independent of the radical species,
it should provide a good description of the solvation features of the
ions.
In this expression, ∆G1°fg(CH3CN) is the free energy required
to transfer one molecule of acetonitrile from the liquid phase to
the gas phase at a concentration of 1 mol dm-3. The value of
∆G°1fg(CH3CN) is estimated to be 3.91 kcal mol-1 from the vapor
pressure (25 mmHg)34 of acetonitrile at 298 K. The term
∆Gg°(CH3CN + XC6H4Se+ f XC6H4Se+-NCCH3) corresponds to
the free energy of binding one molecule of acetonitrile to
XC6H4Se+ in the gas phase at a concentration of 1 mol dm-3, and
∆Gs°ol(XC6H4Se+-NCCH3)PCM is the PCM computed solvation energy
of XC6H4Se+-NCCH3 at the same concentration. Formally, eq 6 is
derived from a thermochemical cycle where one acetonitrile molecule
is transferred to the gas phase, binds to XC6H4Se+ to form the adduct
XC6H4Se+-NCCH3, which then is transferred to the acetonitrile solution.
The corresponding expression for the coordination of two acetonitrile
molecules to XC6H4Se+ is shown in eq 7.
sol
Theoretical Approach. Optimized geometries and harmonic fre-
quencies for all molecules have been computed at the B3LYP/
6-31+G(d) level of theory. The B3LYP functional27 is a modification
of the three-parameter exchange-correlation functional of Becke.28 In
addition to the gradient-corrected exchange and correlation functionals
of Becke29 and Lee et al.,30 respectively, it includes a part of the
Hartree-Fock exchange-energy. Single point energies were computed
at the B3LYP/6-31+G(3df,2p) level of theory using the B3LYP/
6-31+G(d) optimized geometries. However, it was found that these
calculations gave results only marginally different from the B3LYP/
6-31+G(d) energies, and therefore we will only report the latter set of
data in this article. Zero point, enthalpy, and free energy corrections to
the electronic energies have been calculated on the basis of the unscaled
B3LYP/6-31+G(d) frequencies.
In this study, we have also calculated geometries and energies of
some molecular complexes at the MP2/6-31+G(d) level of theory. The
MP2 method is generally less reliable than the B3LYP method for
studying processes that involve breaking or formation of covalent bonds.
On the other hand, MP2 is more accurate than B3LYP for nonbonded
interactions, because it provides a proper description of the dispersion
component of the interaction energy.
∆Gs°ol(+)sup2 ) 2∆G°1fg(CH3CN) +
∆G°[2CH3CN + XC6H4Se+ f XC6H4Se+-(NCCH3)2] +
g
∆G° [XC6H4Se+-(NCCH3)2]PCM (7)
sol
To obtain solvation energies that are directly comparable with the
experimentally obtained ∆∆G° (+•)exp values, we have combined
sol
∆Gs°ol(+)sup and ∆G° (+)sup2 with ∆G° (•)PCM computed using the
sol
sol
PCM method according to eqs 8 and 9.
Solvation energies ∆G° (+)PCM, ∆G° (-)PCM, and ∆G° (•)PCM of
sol
sol
sol
the Se-centered ions and radicals have been calculated at the B3LYP/
6-31+G(d) level using the recent implementation of the polarizable
continuum model (PCM)8 in Gaussian 98.31 The solute cavities in these
calculations were made up of overlapping spheres centered at the atomic
nuclei. The radii of the spheres were taken as the van der Waals radii32
implemented in Gaussian 98 and scaled by a constant of 1.2 for all
∆∆G° (+•)sup ) ∆G° (+)sup - ∆G° (•)PCM
(8)
(9)
sol
sol
sol
∆∆G° (+•)sup2 ) ∆G° (+)sup2 - ∆G° (•)PCM
sol
sol
sol
It should be noted that eq 8 differs from the expression used to calculate
∆∆Gs°ol(+•)sup in our previous study on solvation of arylsulfenium
cations,12 where a supermolecule approach also was used for the
pertinent radical species. However, in this study, we choose to use a
pure PCM calculation, because supermolecule approaches can be less
accurate when the solute-solvent interaction in the first solvation shell
is very weak.
(25) Reiss, H.; Heller, A. J. Phys. Chem. 1985, 89, 4207.
(26) Lim, C.; Bashford, D.; Karplus, M. J. Phys. Chem. 1991, 95, 5610.
(27) Stephens, P. J.; Devlin, F. J.; Chablovski, C. F.; Frisch, M. J. J. Phys.
Chem. 1994, 98, 11623.
(28) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
(29) Becke, A. D. J. Chem. Phys. 1988, 96, 2155.
(30) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 33, 3098.
(31) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M.
A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann,
R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin,
K. N.; Strain, M. C.; Farkas, C. O.; Tomasi, J.; Barone, V.; Cossi, M.;
Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski,
J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.;
Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz,
J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.;
Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham,
M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.;
Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.;
Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.7;
Gaussian, Inc.: Pittsburgh, PA, 1998.
Results and Discussion
Half-Wave Potentials. a) PMV. Figure 1 shows the photo-
modulated voltammogram of C6H5Se• generated from photolysis
of diphenyl diselenide (see eq 1). The two characteristic steady-
state waves pertain to the generalized electrode processes shown
in eqs 10 and 11.
(33) Hu, C.-H.; Brinck, T. J. Phys. Chem. A 1999, 103, 5379.
(34) Weissberger, A.; Proskauer, E. S.; Riddik, J. A.; Toops, E. E. Organic
SolVents, 2nd ed.; Interscience Publishers: New York, 1955; p 224.
(32) Bondi, A. J. Phys. Chem. 1964, 68, 441.
9
2150 J. AM. CHEM. SOC. VOL. 125, NO. 8, 2003

Thermochemistry of Arylselanyl Radicals
A R T I C L E S
by carrying out a preparative reduction of the corresponding
diselenides in a two-electron process (see eq 2). Note that the
same methodology would not be applicable in the case of
selanylium ions due to their high reactivity on this time scale.
In Figure 2, linear sweep voltammograms are collected for
all substituted phenylselenolates with the characteristic irrevers-
ible one-electron oxidation wave appearing in the range of -0.41
V versus SCE for X ) N(CH3)2 to 0.09 V versus SCE for X )
CN at a sweep rate of 1 V s-1. The plot of the oxidation peak
potential, Eopx, versus the logarithm of the sweep rate, log ν,
depicted in Figure 3 in the case of X ) H shows that there
exists a linear relationship in the sweep rate range of 0.2-2 V
s-1 followed by distinct deviations when larger values of ν are
applied.
The slope of the linear section is close to 20 mV decade-1
which is consistent with a rapid heterogeneous electron transfer,
eq 12, followed by a fast dimerization reaction, eq 13, formally
described as an ErC2 mechanism.35
,
Figure 1. Background-corrected photomodulated voltammogram of the
phenylselanyl radical, C6H5Se•, generated by photolysis of 10 mM diphenyl
diselenide at a carbon fiber net in a 0.1 M Bu4NBF4/acetonitrile solution.
Sweep rate ) 0.1 V s-1
.
XC6H4Se+ + e h XC6H4Se•
(10)
(11)
XC6H4Se- - e h XC6H4Se•
(12)
(13)
XC6H4Se• + e h XC6H4Se-
kd
2XC6H4Se• 98 (XC6H4Se-)2
ox
1/2
red
1/2
In Table 1, the half-wave potentials, E and E , obtained for
In this region, the kinetic control is fully by the follow-up reac-
the series of parasubstituted phenylselanyl radicals are collected
along with the characteristic width of the waves, |E3/4 - E1/4|.
For a nernstian process unaffected by preceding or follow-up
chemistry, |E3/4 - E1/4| should be equal to 56.4 mV.35 The large
values of 85-155 mV observed experimentally for the present
systems would usually indicate that the charge-transfer kinetics
at the electrode surface are relatively slow.36 The consequence
tion, and Eopx is related to E°
through eq 14.37,38
XC6H4Se•/XC6H4Se-
2kdCo
RT RT
2RT
3F
Eopx ) E°
+ 0.902
-
ln
XC6H4Se•/XC6H4Se-
(
)
F
3F
ν
(14)
In the above expression, 2kd is the dimerization rate constant,
and Co is the bulk concentration of the arylselenolate. If a
reasonable estimate of 2kd can be provided, it is possible to
of such a quasi-reversible behavior would be that Eo1/x2 and Ered
are shifted in the positive and negative direction, respectively,
1/2
XC6H4Se+/XC6H4Se•
relative to the pertinent standard potentials E°
XC6H4Se•/XC6H4Se-
determine E°
. In this study, we assume that 109
XC6H4Se•/XC6H4Se-
and E°
. However, there could also be an effect
M-1 s-1 < 2kd < 4 × 1010 M-1 s-1 in line with the assessment
made by Andrieux et al. on arylthiyl radicals.39 The upper limit
is simply set as the diffusion-controlled rate constant in
acetonitrile. The lower limit is estimated on the basis of fast
cyclic voltammetry; even at sweep rates of 10 kV s-1 using a
0.6 mM selenolate concentration it was impossible to outrun
the dimerization reaction and detect the selanyl radical in terms
of a reduction wave on the reverse scan. Thus, a midpoint value
(on a logarithmic scale) of 2kd ) 6.3 × 109 M-1 s-1 is used
on the position of the waves from fast homogeneous reactions
involving XC6H4Se+ and XC6H4Se•.36 While XC6H4Se- has a
high stability in aprotic solvents, XC6H4Se• is expected to
dimerize in a fast process, and XC6H4Se+ would as a strong
electrophile react with any nucleophile present in the solution,
be it residual water or the solvent itself. Consequently, the values
ox
red
of E and E cannot a priori be set equal to the standard
1/2
1/2
XC6H4Se+/XC6H4Se•
potentials E°
XC6H4Se•/XC6H4Se-
and E° . In principle,
simulation of the voltammetric curves might provide some useful
information, but the combined effect of the homogeneous and
heterogeneous kinetics is a complicating factor that makes a
quantitative estimation of the difference between E1/2 and E°
difficult.36 Things are even further complicated by the fact that
the distribution of radicals will be nonhomogeneous due to the
variable light intensity along the absorption path and, especially,
by the shielding effect of the net used as working electrode.
b) LSV. Because of the uncertainties present in the inter-
pretation of the photomodulated voltammetry experiments, we
pursued another approach for judging the thermodynamic
significance of the measured half-wave potentials. This approach
consisted of studying the oxidation of the selenolates, that is,
the reverse of eq 11, taking advantage of the fact that stable
solutions of selenolates could easily be generated in acetonitrile
XC6H4Se•/XC6H4Se-
in the calculations of E°
, resulting in an un-
certainty on its determination of (0.03 V corresponding to
(0.7 kcal mol-1 when expressed in free energy terms. The
XC6H4Se•/XC6H4Se-
E°
values are collected in Table 1.
The curved section of the Eopx versus log ν plot in Figure 3
observed at sweep rates above 2 V s-1 is consistent with a
gradual shift in the kinetic control from the follow-up reaction
to the initial electron-transfer step.40-42 Under such conditions
of mixed kinetic control, it will be possible to estimate the het-
(37) Save´ant, J.-M.; Vianello, E. Electrochim. Acta 1967, 12, 1545.
(38) Andrieux, C. P.; Nadjo, L.; Save´ant, J.-M. J. Electroanal. Chem. 1973,
42, 223.
(39) Andrieux, C. P.; Hapiot, P.; Pinson, J.; Save´ant, J.-M. J. Am. Chem. Soc.
1993, 115, 7783.
(40) Nadjo, L.; Save´ant, J.-M. J. Electroanal. Chem. 1973, 48, 113.
(41) Save´ant, J.-M.; Vianello, E. C. R. Hebd. Seances Acad. Sci. 1963, 256,
2597.
(42) Andrieux, C. P.; Save´ant, J.-M. In InVestigations of Rates and Mechanisms
of Reactions, Techniques of Chemistry; Bernasconi, C. F., Ed.; Wiley: New
York, 1986; Vol. VI/4E, Part 2, pp 305-390.
(35) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals and
Applications; John Wiley: New York, 1980.
(36) Nagaoka, T.; Griller, D.; Wayner, D. D. M. J. Phys. Chem. 1991, 95, 6264.
9
J. AM. CHEM. SOC. VOL. 125, NO. 8, 2003 2151

A R T I C L E S
Holm et al.
ox
1/2
red
1/2
Table 1. Half-Wave Potentials E and E and Peak Widths |E3/4 - E1/4| Measured for XC6H4Se• by Means of Photomodulated
XC6H4Se•/XC6H4Se-
Voltammetry at a Carbon Fiber Net along with E°
Values Obtained from Linear Sweep Experiments at a Glassy Carbon
Electrode in 0.1 M Bu4NBF4/Acetonitrile; Computed Singlet and Triplet Ionization Potentials, IP(S) and IP(T), and Electron Affinities, EA, for
XC6H4Se•
ox
1/2
red
1/2
a,c
b
a,c
b
a,d
e
X
E
|E3/4 − E |
1/4
E
|E3/4 − E |
1/4
E°
• -
XC H Se /XC H Se
6 4 6 4
IP(S)e
IP(T)e
EA
N(CH3)2
OCH3
CH3
F
H
Cl
Br
CN
NO2
0.27
0.61
0.62
0.70
0.70
0.73
0.74
0.82
f
88
144
155
147
148
130
124
137
f
-0.28
-0.15
-0.13
-0.06
-0.06
-0.05
-0.02
0.05
117
114
116
128
131
110
111
99
-0.34
-0.14
-0.10
-0.03
-0.04
0.02
-0.01
0.17
0.16
6.88
7.57
8.16
8.34
8.33
8.27
8.20
8.78
9.03
7.17
7.75
7.97
8.29
8.19
8.24
8.18
8.58
8.76
1.92
2.06
2.16
2.36
2.25
2.47
2.50
2.93
3.20
0.09
85
a V versus SCE. b In mV. c Determined at a sweep rate of 0.1 V s-1 with an uncertainty of (30 mV; average of at least four determinations. d Uncertainty
is (30 mV. e In eV, calculated at the B3LYP/6-31+G(d) level using the Gaussian 98 suite of programs. f No reproducible oxidation wave was observable
in this case.
obtained previously for the thiophenoxides.39 With the finding
of rather large values for ko, it seems precluded that the
photomodulated voltammograms recorded at ν ) 0.1 V s-1
should be influenced by slow charge-transfer kinetics. In other
words, the relatively broad reduction waves with |E3/4 - E1/4
|
values of 85-131 mV cannot be related specifically to the
chemical system inasmuch as the experimental limitations of
the PMV technique discussed above. This conclusion is
reinforced by the fact that exactly the same tendency has been
observed in our previous studies on arylthiyl17 and R-hydroxy
alkyl radicals.18 Moreover, there is no correlation between the
ko and |E3/4 - E1/4| values.
In view of the above-mentioned limitations of the PMV tech-
nique, the question is how reliable the measured half-wave po-
tentials can be considered from a thermodynamic point of view?
Figure 2. Linear sweep voltammograms recorded for the oxidation of 1
A comparison of the two sets of Er1e/2d and E°
data
mM arylselenolate, XC6H4Se-, at a glassy carbon electrode in a 0.1 M
XC6H4Se•/XC6H4Se-
Bu4NBF4/acetonitrile solution. Sweep rate ) 1 V s-1
.
in Table 1 reveals that the agreement is actually quite good
with an absolute mean deviation of 50 mV. These observations
are consistent with those in our previous studies on arylthiyl17
and R-hydroxy alkyl radicals.18 There is no relationship between
|E3/4 - E1/4| and the differences observed in the potentials. For
instance, the reduction wave pertaining to X ) CN is relatively
sharp with |E3/4 - E1/4| ) 99 mV, but still Er1e/2d is smaller than
XC6H4Se•/XC6H4Se-
E°
by 120 mV. In contrast to this stands the
red
agreement within 20 mV between E and E°
1/2
XC6H4Se•/XC6H4Se-
for X ) H, even if |E3/4 - E1/4| is as large as 131 mV.
red
1/2
In view of the overall good agreement between E and
XC6H4Se•/XC6H4Se-
E°
and the fact that all other photomodulated
waves have similar widths ranging between 88 and 155
ox
1/2
red
1/2
mV, we conclude that the measured E and E values
listed in Table 1 are within 50 mV of the corresponding
E° and E° values.
Figure 3. Plot of Eopx versus log ν for the oxidation of 1 mM phenylse-
lenolate. Sweep rates of 0.2-20 V s-1 are applied, but only the four points
pertaining to the 0.2-2 V s-1 range are included in the linear regression.
XC6H4Se+/XC6H4Se•
XC6H4Se•/XC6H4Se-
ox
Hammett Plots. In Figures 4 and 5, the values of E and
1/2
Er1e/d2 are plotted against the Hammett substituent coefficient σ+.
We correlate to σ+ rather than σ or σ- to be able to compare
directly with previous correlations reported for the reduction
potentials of substituted phenylthiyl radicals in aprotic sol-
vents17,39,43,44 and water45 and phenoxyl radicals in acetonitrile46
erogeneous rate constant, ko, through simulation of the experi-
mental voltammograms using the DigiSim software.21 In the
XC6H4Se•/XC6H4Se-
simulations, we choose to keep the E°
values
determined from the linear section of the Eopx versus log ν plot
fixed as this seemed to give the most consistent results. Still, it
and water.47 Actually, the correlations with σ are equally good
ox
1/2
with the following relationships ensuing: E ) 0.36σ + 0.65
XC6H4Se•/XC6H4Se-
should be emphasized that the variation in E°
(43) Bordwell, F. G.; Zhang, X.-M.; Satish, A. V.; Cheng, J.-P. J. Am. Chem.
Soc. 1994, 116, 6605.
never exceeded 20 mV even if it was treated as a variable in
the program.
(44) Venimadhavan, S.; Amarnath, K.; Harvey, N. G.; Cheng, J.-P.; Arnett, E.
M. J. Am. Chem. Soc. 1992, 114, 221.
The extracted values of ko are all close to 0.1 cm s-1
,
(45) Armstrong, D. A.; Sun, Q.; Schuler, R. H. J. Phys. Chem. 1996, 100, 9892.
(46) Hapiot, P.; Pinson, J.; Yousfi, N. New J. Chem. 1992, 16, 877.
independent of the substituent, and quite similar to those
9
2152 J. AM. CHEM. SOC. VOL. 125, NO. 8, 2003

Thermochemistry of Arylselanyl Radicals
A R T I C L E S
Table 2. Hammett Slopes, F+, Obtained for the Reduction and
Oxidation Potentials of Substituted Phenylselanyl, Phenylthiyl, and
Phenoxyl Radicals in Different Solvents
redox couple
F+
solvent
reference
ArSe•ArSe- a
ArS•/ArS- c
ArS•/ArS- c
ArS•/ArS- d
ArS•/ArS- a
ArS•/ArS- e
ArO•/ArO- d
ArO•/ArO- e
ArSe+/ArSe• a
ArS+/ArS• a
2.5b acetonitrile
this study
6.6
6.7
5.4
6.4
3.7
10.1
7.0
3.8
4.7
sulfolane/3-methylsulfolane (5%) 44
dimethyl sulfoxide
acetonitrile
acetonitrile
water
acetonitrile
water
43
39
17
45
46
47
this study
17
acetonitrile
acetonitrile
a
Half-wave potentials measured by means of photomodulated voltam-
metry. b The F+ value is 3.4 if E°
parameter rather than E
is used as the correlation
XC6H4Se•/XC6H4Se-
ox
Figure 4. Plot of E versus σ+.
red
1/2
c Irreversible oxidation potentials of the anions
1/2
.
measured by means of linear sweep voltammetry. d Standard potentials
measured by means of fast cyclic voltammetry. e Standard potentials
measured by means of pulse radiolysis.
substituent effect on the stabilization of phenoxyl radicals due
to spin delocalization by analyzing the spin density distribution
on the oxygen.50 It was found that the strongest stabilizing effect
was exerted by resonance-donating substituents and that this
could explain the observed linear correlation between the O-H
bond dissociation energy of phenols and σ+. This also explains
why σ+ can be the better correlation parameter for Er1e/d2 in the
case of phenoxyl radicals but not so in the case of arylthiyl and
arylselenyl radicals.
Table 2 presents all relevant slopes F+ obtained from the
Hammett plots (based on equilibrium constants) for the substi-
tuted phenylselanyl radicals in the present study and for the
substituted phenylthiyl and phenoxyl radicals in previous
studies.17,39,43-47 At least a few points are worth noting. First,
the values of F+ are positive for both the reduction and the
oxidation processes. This agrees with the expectation that
electron-donating substituents should make it harder to reduce
both the phenylselanyl radicals and the phenylselanylium ions.
Another apparent result is the order of F+ values: F+(XC6H4O•)
> F+(XC6H4S•) > F+(XC6H4Se•) and F+(XC6H4S+) >
F+(XC6H4Se+). This illustrates that the substituent effect
becomes larger as the π-interaction between the chalcogen center
and the aromatic system increases going from Se to S and O.
The fact that the slopes F+(XC6H4O•) and F+(XC6H4S•) are
smaller for aqueous than for aprotic solutions can be attributed
to the strong solvation of anions in water in terms of hydrogen
bonding. Finally, it should be noted in the case of the arylselanyl
radicals that F+ is larger for the oxidation process (F+ ) 3.8)
than for the reduction process (F+ ) 2.5), which is opposite to
the order seen for the S-centered analogues.17
Spin States. Before discussing the solvation features of
arylselanylium ions, it is important to consider their spin state.
At the B3LYP/6-31+G(d) level, the singlet and triplet states
of the phenylselanylium ion are very similar in energy. The
triplet state is favored over the singlet state by only 3.6 kcal
mol-1 at 0 K. This can be compared to the singlet-triplet
splitting for the phenylsulfenium ion which was computed to
be -0.02 kcal mol-1 at the same level.12 At the generally more
accurate CBS-QB3 level, the singlet state of the phenylsulfenium
ion was found to be favored over the triplet state by 1.53 kcal
red
1/2
Figure 5. Plot of E versus σ+.
Scheme 2
(r2 ) 0.90) and E1re/d2 ) 0.23σ - 0.09 (r2 ) 0.98). On the other
hand, σ- provides without comparison the poorest correlation
(even for Er1e/d2) due to large deviations of the points pertaining
to the electron-donating groups, in particular, N(CH3)2. The
reason that σ should be a relatively better correlation parameter
in the case of Se as compared to S and O is related to the extent
of orbital overlap with the aromatic ring that becomes progres-
sively smaller with size in the order O, S, and Se. In fact, while
the bonding between the chalcogen radical center and the
aromatic ring has been described essentially as a single bond
for phenylthiyl and phenylselanyl radicals, there is double bond
character in the case of phenoxyl radicals.48,49 The latter feature
can be attributed to spin delocalization of the odd electron in
the radical as illustrated by the resonance structures drawn in
Scheme 2 (Z ) O, S, or Se).
Note also that the electron-withdrawing ability of the CdZ
dipole is much larger for O with an electronegativity of 3.5
than it would be for S and Se with electronegativities of 2.5
and 2.4, respectively. In an earlier study, we investigated the
(47) Lind, J.; Shen, X.; Eriksen, T. E.; Mere´nyi, G. J. Am. Chem. Soc. 1990,
112, 479.
(48) Tripathi, G. N. R.; Sun, Q.; Armstrong, D. A.; Chipman, D. M.; Schuler,
R. H. J. Phys. Chem. 1992, 96, 5344.
(49) Kimura, S.; Bill, E.; Bothe, E.; Weyhermu¨ller, T.; Wieghardt, K. J. Am.
Chem. Soc. 2001, 123, 6025.
(50) Brinck, T.; Haeberlein, M.; Jonsson, M. J. Am. Chem. Soc. 1997, 119,
4239.
9
J. AM. CHEM. SOC. VOL. 125, NO. 8, 2003 2153

A R T I C L E S
Holm et al.
Scheme 3
IP and EA. The B3LYP/6-31+G(d) computed values of the
singlet and triplet IPs of the phenylselanyl radical, IP(S) and
IP(T), are 8.33 and 8.19 eV, respectively. The EA at the same
level is 2.25 eV. To our knowledge, no experimental data are
available for the phenylselanyl radical. To estimate the reliability
of our computations, we can look at the results for the
phenylthiyl radical. In this case, IP(S) and EA were computed
to 8.43 and 2.27 eV, respectively.12 The corresponding values
obtained at the CBS-QB3 level of theory were 8.48 and 2.41
eV. These results are in relatively good agreement with the
experimental determinations of IP ) 8.6 ( 0.1 eV and EA )
2.26 ( 0.10 eV.55 On this basis, we expect the B3LYP/
6-31+G(d) computed values for the IPs of arylselanyl radicals
to be slightly underestimated but still accurate to within 0.2 eV
corresponding to 4.6 kcal mol-1 when expressed in free energy
units. The computed EAs for arylselanyl radicals are presumably
more accurate than the IPs.
mol-1 12
. We were not able to compute the singlet-triplet split-
ting of the phenylselanylium ion using the CBS-QB3 method,
because this method has not been implemented for compounds
containing third row atoms in Gaussian 98. However, if we
assume that the error in the B3LYP/6-31+G(d) calculated
singlet-triplet splitting is similar for the phenylsulfenium and
the phenylselanylium ions, we can estimate the triplet state to
be favored over the singlet state by around 2 kcal mol-1 in the
latter. Without comparison, the energy difference is much more
pronounced for alkylselanylium ions. For instance, the singlet-
triplet splitting in the methylselanylium ion is 29.7 kcal mol-1
according to computations performed at the B3LYP/6-31+G(d)
level. Similar results have been obtained in experimental and
theoretical studies on alkylsulfenium ions.51-53 Thus, it is clear
that the aromatic ring in the phenylselanylium ion leads to a
significant stabilization of the singlet state, which is comparable
to that seen in the phenylsulfenium ion. This stabilization can
be attributed to charge delocalization due to a favorable
resonance interaction between the positive selenium atom and
the aromatic ring as illustrated in Scheme 3.
The importance of this resonance interaction can be under-
stood from the computed geometry of the singlet phenylsela-
nylium ion (1) depicted in Figure 6. The carbon-carbon bonds
in the aromatic ring are strongly alternating in length, and the
carbon-selenium bond (1.784 Å) is considerably shorter than
a normal single bond (1.94 Å) as predicted from the covalent
radii of selenium and carbon.54 The charge of the selenium atom,
which is calculated to be 0.32 au using Mulliken population
analysis, is also consistent with the presence of a strong
resonance interaction.
The resonance interaction in the triplet state of the phenylse-
lanylium ion (2) differs in character from that in the singlet
state. In the triplet state, the two lone pair electrons of selenium
are divided upon two p-orbitals, and the resonance interaction
between the p-orbital perpendicular to the plane of the aromatic
ring and the π-system leads to spin delocalization rather than
charge delocalization as illustrated in Scheme 4.
A spin density analysis indicates that approximately one-half
of an unpaired electron is delocalized over the aromatic system
in the triplet state with the highest spin density found over the
ortho and para positions. However, the spin delocalization of
the triplet state is not expected to lead to as large of a
stabilization as the corresponding charge delocalization of the
singlet state. The weaker resonance interaction of the triplet state
as compared to that of the singlet state is confirmed by less
strongly alternating C-C bond lengths and a longer C-Se bond
(see Figure 6). There is also a higher charge on selenium in the
triplet state (0.44 au) than in the singlet state (0.32 au). As we
shall see, the magnitude and sign of the singlet-triplet splitting
are affected by substituents, which can be explained by
considering the substituent effects on the resonance interactions.
In Table 1, the values of IP(S), IP(T), and EA are listed for
the different arylselanyl radicals. The electron affinity of the
arylselanyl radical is strongly affected by the presence of
resonance-withdrawing substituents such as NO2 and CN. This
can be explained by a strong through-resonance interaction
between the negatively charged selenium and the substituents
at the aromatic ring. Consequently, we also find a good
correlation between EA and σ- following the equation: EA )
0.74σ- + 2.25, r2 ) 0.93. This correlation is better than that
between EA and σ: EA ) 0.80σ + 2.37, r2 ) 0.90. At first it
may seem surprising that EA correlates better with σ- than with
σ when the opposite is true for Er1e/2d. However, it should be
red
1/2
recalled that E is a solvent parameter and while solvation
diminishes the substituent effect on the stabilization of anions
it leaves the stabilization of radicals largely unaffected.
The computed values of IP(S) show that the resonance-
donating substituents, N(CH3)2 and OCH3, have a strongly
stabilizing effect on the arylselanylium ion. There is also a good
linear correlation between IP(S) and σ+ following the equa-
tion: IP(S) ) 0.83σ+ + 8.28, r2 ) 0.97. This agrees with
expectations because there is through-resonance interaction
between the positively charged selenium and a resonance-
donating substituent. For triplet state cations such an interaction
would be predicted to be weaker and indeed the slope obtained
for the correlation of IP(T) with σ+ is smaller: IP(T) ) 0.61σ+
+ 8.20, r2 ) 0.98 Note that there is a significant substituent
effect on the singlet-triplet splitting. While IP(T) is larger than
IP(S) by 4-7 kcal mol-1 for resonance-donating substituents
such as N(CH3)2 and OCH3, the opposite is true for the electron-
withdrawing NO2 and CN groups. This trend is not surprising
considering that the through-resonance charge delocalization is
expected to be larger for the singlet state than for the triplet
state. In addition, resonance-withdrawing substituents are known
to mediate spin delocalization, which can explain their stabiliz-
ing effect on triplet cations.56-58
Solvation Energies. To obtain a better understanding of the
thermochemistry of selenium-centered anions and cations, we
turned our attention toward a calculation of the solvation
energies of the two sets of ions on the basis of the electrode
potentials measured and the computed ionization potentials and
(51) Rodriquez, C. F.; Hopkinson, A. C. J. Mol. Struct. (THEOCHEM) 1987,
152, 55.
(52) Pople, J. A.; Curtiss, L. A. J. Phys. Chem. 1987, 91, 3637.
(53) Curtiss, L. A.; Nobes, R. H.; Pople, J. A.; Radom, L. J. Chem. Phys. 1992,
97, 6766.
(54) Cotton, F. A.; Wilkinson, G.; Gauss, P. L. Basic Inorganic Chemistry, 2nd
ed.; John Wiley & Sons: New York, 1987; p 92.
(55) NIST Standard Reference Database No. 69.
(56) Walter, R. I. J. Am. Chem. Soc. 1966, 88, 1923.
(57) Wayner, D. D. M.; Arnold, D. R. Can. J. Chem. 1984, 62, 1164.
(58) Jiang, X.-K. Acc. Chem. Res. 1997, 30, 283.
9
2154 J. AM. CHEM. SOC. VOL. 125, NO. 8, 2003

Thermochemistry of Arylselanyl Radicals
A R T I C L E S
Figure 6. B3LYP/6-31+G(d) optimized structures of the singlet phenylselanylium ion (1), the triplet phenylselanylium ion (2), the singlet phenylselanylium
ion-acetonitrile 1:1 adduct (3), and the singlet phenylselanylium ion-acetonitrile 1:2 adduct (4).
Scheme 4
are largely determined by the degree of charge delocalization
in the system.
The ∆∆G° (-•)exp values vary from -58 kcal mol-1 in the
sol
cases of X ) N(CH3)2 and OCH3 to -38 kcal mol-1 for X )
NO2. Accordingly, we also find a linear correlation between
∆∆G° (-•)exp and σ-: ∆∆G° (-•)exp ) 12.7σ- - 54.7, r2 )
electron affinities (see eqs 3 and 4). In the calculations of
sol
sol
∆∆G° (-•)exp, we used the values of Ered rather than
0.97. The variation of ∆∆G° (-•)exp for the arylselenolates is
sol
sol
XC6H4Se•/XC6H4Se-
1/2
very similar to that found for the sulfur analogues:12
E°
to be consistent with the corresponding
∆∆G° (Se,-•)exp ) 1.15 ∆∆G° (S,-•)exp + 13.6 (r2 ) 0.98).
ox
1/2
sol
sol
∆∆G° (+•)exp values that were based solely on E data. In
sol
In contrast to the nice consistency in the anion data sets stand
any case, the effect on ∆∆G° (-•)exp is small and within 1-2
sol
red
1/2
kcal mol-1 because of the small difference between E and
the large deviations observed for ∆∆G° (+•); the experimen-
sol
tal values (column 7) are found to be not only considerably
larger in magnitude than the corresponding computed values
(column 6) - in many cases by more than 20 kcal mol-1 - but
also they exhibit a much larger substituent effect as clearly
illustrated by the plot of the two data sets in Figure 7.
XC6H4Se•/XC6H4Se-
E°
. With IP data available for both the singlet
and the triplet states of the arylselanylium ions, two sets of
∆∆G° (+•)exp values might be extracted, in principle, but for
reasons that will become clear below, we limited the calculations
to include the singlet state only.
sol
The decrease in ∆∆G° (+•)exp amounts to 31 kcal mol-1 as
The experimentally based solvation data are collected in
sol
the degree of charge localization in the cations increases going
Table 3 together with the solvation energies ∆G° (+)PCM
,
sol
from X ) N(CH3)2 to CN. The following correlation with σ+
∆G° (-)PCM
,
∆G° (•)PCM
,
∆∆G° (-•)PCM
,
and
sol
sol
sol
is obtained: ∆∆G° (+•)exp ) -13.3σ+ - 65.1, r2 ) 0.91. In
∆∆G° (+•)PCM computed by the PCM method. For the
sol
sol
general, the absolute values of ∆∆G° (+•)exp are larger than
cations, we have listed values of ∆G° (S+)PCM and
sol
sol
those of ∆∆G° (-•)exp, indicating that the solvation of the
∆G° (T+)PCM for both the singlet and the triplet states.
sol
sol
cations is stronger than that of the anions. The variation in
However, in the further calculation of ∆∆G° (+•)PCM, the
sol
∆∆G° (()exp listed in the last column of Table 3 is from -31
singlet state data were the only ones used in agreement
with the procedure employed for extracting the corresponding
sol
kcal mol-1 for X ) CN to 16 kcal mol-1 for X ) N(CH3)2. In
the case of the phenylselanylium ion with a calculated
Mulliken charge of only 0.32 au on the selenium atom, the
∆∆G° (+•)exp data set. In any case, the difference in the
sol
∆G° (S+)PCM and ∆G° (T+)PCM values is relatively small,
sol
sol
∆∆G° (+•)exp value of -67 kcal mol-1 is even close to the
although the substituent effect is distinct in the sense that the
solvation of the singlet state is more favorable than that of the
triplet state for the two most electron-donating groups, OCH3
and N(CH3)2, whereas the opposite is true for electron-
withdrawing groups such as CN and NO2. The calculations of
sol
-71 kcal mol-1 found for the completely localized and much
smaller potassium ion in acetonitrile.59
The ∆∆G° (+•)exp data set for the arylselenylium ions
sol
is almost equal to that for the sulfur analogues, indepen-
dent of the substituent.12 Actually, there exists a linear re-
∆G° (•)PCM show that the solvation of the neutral XC6H4Se•
sol
species as expected is relatively weak; all values are between
2.8 and 5.6 kcal mol-1. Thus, the substituent effects on
∆∆G° (+•)PCM and ∆∆G° (-•)PCM are very similar to those
lation with a slope close to unity: ∆∆G° (Se,+•)exp
)
sol
0.98 ∆∆G° (S,+•)exp - 2.47 (r2 ) 0.95). In the case of the
sol
arylsulfenium ions, we demonstrated that both the large
sol
sol
on ∆G° (+)PCM and ∆G° (-)PCM, respectively.
magnitude of ∆∆G° (+•)exp as well as the significant sub-
sol
sol
sol
As for a comparison of the computed and experimental
solvation data, there is relatively good agreement between the
stituent effect could be explained on the basis of a supermolecule
approach by considering the formation of strong covalent 1:1
adducts between the ions and acetonitrile.12 Thus, we decided
to investigate if similar covalent adducts could be formed for
the arylselanylium ions.
The optimized molecular geometry of the singlet phenylse-
lanylium ion-acetonitrile adduct (3) is shown in Figure 6. At
the B3LYP/6-31+G(d) level, the computed gas-phase binding
∆∆G° (-•) values listed in columns 8 and 9, respectively.
sol
The most deviating behaviors are seen for the strongly electron-
withdrawing and electron-donating groups with X ) N(CH3)2
exhibiting the largest difference of 8 kcal mol-1. This is also
illustrated in Figure 7, where the computed solvation energies,
∆∆G° (-•)PCM, are plotted against the experimental counter-
sol
parts, ∆∆G° (-•)exp. The fact that the PCM method works
sol
quite well for the anions indicates that the solvation energies
(59) Marcus, Y. Ion SolVation; John Wiley: Chichester, 1985.
9
J. AM. CHEM. SOC. VOL. 125, NO. 8, 2003 2155

A R T I C L E S
Holm et al.
Table 3. Computed Solvation Energies ∆G° (S+)PCM, ∆G° (T+)PCM, ∆G° (-)PCM, ∆G° (•)PCM, ∆∆G° (+•)PCM, and ∆∆G° (-•)PCM and
sol
sol
sol
sol
sol
Solvation Energies ∆∆G° (+•)exp, ∆∆G° (-•)exp, and ∆∆Gs°ol (()exp Calculated from Experimental Solution Data and Computed Gas-Phase
sol
sol
sol
Dataa
b
b
b
b
b,c
d
b
e
f
X
∆Gs°ol(S+)PCM
∆G° (T+)PCM
∆G° (−)PCM
∆G° (•)PCM
∆∆G° (+•)PCM
∆∆G° (+•)exp
∆∆G° (−•)PCM
∆∆G° (−•)exp
∆∆G° (±)exp
sol
sol
sol
sol
sol
sol
sol
sol
N(CH3)2
OCH3
CH3
F
H
Cl
Br
CN
NO2
-35.1
-37.1
-37.7
-42.0
-41.5
-40.2
-39.5
-45.2
-46.5
-32.6
-36.3
-37.9
-42.6
-41.8
-41.3
-40.4
-47.9
-49.5
-47.0
-51.3
-50.5
-49.3
-51.4
-46.9
-46.7
-43.0
-40.2
3.3
4.2
5.6
4.8
4.4
4.8
4.5
2.8
3.4
-38.4
-41.3
-43.3
-46.8
-45.9
-45.0
-44.0
-48.0
-49.9
-43
-51
-65
-67
-67
-65
-63
-74
-50.3
-55.7
-56.1
-54.1
-55.9
-51.7
-51.2
-45.8
-43.6
-58
-58
-57
-54
-56
-51
-51
-43
-38
16
7
-8
-13
-11
-13
-12
-31
a All values are in kcal mol-1 b Calculated at the PCM-B3LYP/6-31+G(d) level. c Calculated for the singlet state cation. d From eq 3 using the values
.
of IP(S) for the singlet state cation. e From eq 4. f From eq 5.
character of the bond is also confirmed by the strong substituent
effect on the binding enthalpy; the enthalpy increases from
-43.6 to -25.8 kcal mol-1 when going from the CN substituent
to OCH3. As we shall see, this can explain the strong substituent
effect on ∆∆G° (+•)exp
.
sol
The phenylselanylium ion-acetonitrile adduct is very similar
in character and geometry to the previously reported phenyl-
sulfenium ion-acetonitrile adduct.12 However, the B3LYP/
6-31+G(d) calculated binding enthalpy of -41.1 kcal mol-1
for the former is considerably smaller than the -28.5 kcal mol-1
found for the latter. We can only speculate on the reasons for
this difference, but one factor could be that the larger size of
the p-orbital on selenium as compared to sulfur leads to a better
overlap with the lone pair orbital on acetonitrile. It is also likely
that the resonance interaction is weaker in the phenylsel-
anylium ion than in the phenylsulfenium ion, and consequently
the loss of the interaction upon forming the bond is energetically
less costly in the former.
Figure 7. Computed solvation energies obtained at the PCM-B3LYP/
6-31+G(d) level versus experimental solvation energies obtained from eqs
3 and 4. The solid line corresponds to a 1:1 relationship between computed
and experimental values. Substituents: (a) N(CH3)2; (b) OCH3; (c) CH3;
(d) F; (e) H; (f) Cl; (g) Br; (h) CN; (i) NO2.
In our previous study, we noted that the singlet phenylsulfe-
nium ion is not able to bind two acetonitrile molecules
covalently.12 Instead, it was found that the second acetonitrile
molecule binds to the phenylsulfenium ion-acetonitrile adduct
noncovalently with a binding enthalpy of -9.9 kcal mol-1 at
the B3LYP/6-31+G(d) level. However, for the singlet phen-
ylselanylium ion, we have been able to locate a favorable
structure with two molecules of acetonitrile covalently bonded.
This structure is shown as 4 in Figure 6. Calculations at the
B3LYP/6-31+G(d) level on the 1:1 adduct 3 show that the
binding enthalpy of a second acetonitrile molecule is equal to
-21.1 kcal mol-1. Thus, the total binding enthalpy for the two
enthalpy and free energy of binding are -41.1 and -31.1 kcal
mol-1, respectively. The covalent character of the adduct is
confirmed by the fact that the Se-N bond length of 1.874 Å is
in agreement with the 1.87 Å predicted for a typical Se-N single
bond from the covalent radii of selenium and nitrogen.54 A MP2/
6-31+G(d) calculation gave a similar geometry with a Se-N
bond length of 1.872 Å, and a slightly more negative binding
enthalpy of -44.2 kcal mol-1. The Se-N bond lies in a plane
perpendicular to the aromatic ring at an angle of 99°. Further-
more, in contrast to the finding for the isolated singlet
phenylselanylium ion (1), the aromatic C-C bonds in 3 are
almost identical in length. At the same time, the C-Se bond of
3 (1.900 Å) is longer than that of 1 (1.784 Å), and almost as
long as a single bond (1.94 Å) as calculated from the covalent
radii of carbon and selenium.
These factors together indicate that the resonance interaction
between the aromatic π-system and the selenium atom is to a
great extent lost in 3. On the other hand, the geometry of the
acetonitrile moiety of 3 is almost identical to that of the free
acetonitrile molecule. We can therefore conclude that the Se-N
bond can be characterized as a σ-bond arising from the
interaction of an empty p-orbital on selenium, which lies
perpendicular to the plane of the aromatic ring, and the nitrogen
lone-pair orbital of acetonitrile. However, according to the
Mulliken population analysis, this is a relatively polar bond,
because only 0.47 of an electron has been transferred from the
acetonitrile moiety to the phenylselanylium ion. The polar
acetonitrile molecules becomes equal to -62.2 kcal mol-1
,
corresponding to -31.1 kcal mol-1 for each of the molecules
in the symmetrical 4. The length of the Se-N bonds in 4 is
2.130 Å, which is considerably larger than the 1.874 Å
calculated for the Se-N bond in 3 with the single acetonitrile
molecule. We were also able to locate a similar type of complex
at the MP2/6-31+G(d) level. The formation of the 1:2 adduct
is thus favored as compared to the 1:1 adduct with respect to
the binding enthalpy, but as it will be shown below, this does
not hold when the free energy of solvation is considered.
For the triplet phenylsulfenium ion, we found that it was
unable to form a covalent bond to acetonitrile.12 Rather, the
interaction could be described as a strong van der Waals
complex with a S-N bond length of 2.65 Å and a complexation
enthalpy of -9.4 kcal mol-1. This behavior of the triplet state
was attributed to its lack of an empty p-orbital that could form
9
2156 J. AM. CHEM. SOC. VOL. 125, NO. 8, 2003

Thermochemistry of Arylselanyl Radicals
A R T I C L E S
Table 4. Computed Solvation Energies ∆G° (+)sup and
contribution is overshadowed by the free energy contributions
due to loss of translational and rotational entropy and nonspecific
solvation. Still, we have to emphasize that the free energy
difference is not sufficiently large to make a definite conclusion
regarding the coordination number of the phenylselanylium ion.
sol
∆∆G° (+•)sup Using a Combined Supermolecular and PCM
sol
Approach for Singlet State Arylselanylium Ion-Acetonitrile 1:1
Adducts and Experimentally Based Solvation Energies
a
∆∆G° (+•)exp
sol
X
∆Gs°ol(+)sup
∆∆G° (+•)sup
∆∆G° (+•)exp
sol
sol
OCH3
H
CN
-45.5
-67.5
-73.8
-49.7
-71.9
-76.6
-51
-67
-74
Conclusions
red
1/2
ox
1/2
Reduction and oxidation potentials, E and E , of a series
a All values are in kcal mol-1
.
of parasubstituted phenylselanyl radicals, XC6H4Se•, have been
measured using photomodulated voltammetry in acetonitrile.
The data obtained for the reduction process were supported by
a covalent bond with the nitrogen lone-pair orbital. Also, the
phenylselanylium ion forms a weaker bond with acetonitrile in
the triplet state than in the singlet state, although the difference
is less pronounced. With a complexation enthalpy of -19.2 kcal
mol-1 and a Se-N bond length of 2.52 Å computed at the
B3LYP/6-31+G(d) level, the bonding is intermediate between
a covalent and a van der Waals bond. Thus, it may be concluded
that the singlet phenylselanylium ion should be completely
dominating in solution. This result also provides the explanation
why we only extracted experimental solvation energies for the
singlet ion.
XC6H4Se•/XC6H4Se-
the measurement of the standard potentials, E°
,
in linear sweep voltammetry. The absolute mean deviation of
the two sets is 50 mV. Both the reduction and the oxidation
potentials correlate linearly with the Hammett substituent
coefficients σ or σ+, giving in the latter case slopes F+ of 2.5
and 3.8, respectively. This indicates that the substituent effect
ox
1/2
red
1/2
is larger on E than E . A comparison with literature re-
sults obtained for corresponding series of the other chalcogens
reveals that F+(XC6H4O•) > F+(XC6H4S•) > F+(XC6H4Se•) and
F+(XC6H4S+) > F+(XC6H4Se+), illustrating that the π-interac-
tion becomes progressively smaller as the size of the central
atom increases in the order O, S, and Se.
To estimate if the experimental solvation energies of the
cations indeed can be explained by the formation of covalent
arylselanylium ion-acetonitrile adducts, we decided to calculate
∆G° (+) using the combined supermolecular and PCM ap-
proach described in the Theoretical Approach section (see eqs
sol
Computed electron affinities and ionization energies have
been combined with the experimental reduction and oxidation
potentials to obtain solvation energies for the anions and cations.
These values have been compared with solvation energies
calculated using the PCM approach. For the anions, there is a
relatively good agreement both in absolute and in relative terms
between the two sets of values. The substituent effect on the
solvation energy is found to be determined by the degree of
charge separation in the system as manifested by a linear
6 and 7). The ∆G° (+)sup value calculated in the case of the
sol
1:1 adduct 3 is -67.5 kcal mol-1. Thus, the computed solvation
energy is lowered by 26 kcal mol-1 when compared with the
PCM value calculated without an explicit solvent molecule
[∆G° (+)PCM ) -41.5 kcal mol-1]. A ∆∆G° (+•)sup value of
sol
sol
-71.9 kcal mol-1 is obtained when ∆G° (•)PCM of the phen-
sol
ylselanyl radical is subtracted from the ∆G° (+)sup value, eq
sol
8. This value is in reasonable agreement with ∆∆G° (+•)exp
)
sol
relationship between ∆∆G° (-•)exp and the Hammett sub-
sol
-67 kcal mol-1. We also considered the substituent effect on
∆G° (+)sup and ∆∆G° (+•)sup by carrying out computations
stituent coefficient σ-. The numerical values of ∆∆G° (+•)exp
sol
sol
sol
as well as the substituent effect on ∆∆G° (+•)exp are con-
sol
for X ) CN and OCH3. For ∆∆G° (+•)sup, values of -76.6
sol
siderably larger than those observed for the corresponding
and -49.7 kcal mol-1 were obtained, respectively, agreeing with
the corresponding experimental values of -74 and -51 kcal
mol-1. On this basis, we conclude that the large substituent
effects on the solvation energies observed experimentally can
be explained by the formation of strong 1:1 ion-solvent adducts.
In Table 4, all of the above data are collected.
∆∆G° (-•)exp set. The large solvation effects for the cations
sol
are not reflected in the computed PCM solvation energies.
However, gas-phase calculations show that the singlet arylse-
lanylium ions can form strong Ritter-type adducts with aceto-
nitrile that are similar in character yet stronger than those
previously found for the arylsulfenium ions. When this covalent
interaction is included in the solvation energy calculations by
means of a combined supermolecule and PCM approach, the
experimental data are reproduced within a few kcal mol-1. It
should be emphasized that all of the above results pertain
specifically to the use of acetonitrile as solvent. In a current
project, we intend to study the effect of using other solvents as
well.
At this point, one should also consider the possibility of
having the 1:2 adduct in solution. Calculations of
∆∆G° (+)sup2 and ∆∆G° (+•)sup2 in the case of 4 give values
sol
sol
of -65.5 and -69.9 kcal mol-1, respectively. These values are
slightly larger than those for the 1:1 adduct. Hence, the
calculations predict that it is more favorable for the phenylse-
lanylium ion to bind one acetonitrile molecule than two in
solution, despite the favorable enthalpy for binding the second
molecule as mentioned above. In other words, the latter
JA0291787
9
J. AM. CHEM. SOC. VOL. 125, NO. 8, 2003 2157