Published on Web 01/30/2003

HSAB Principle Applied to the Time Evolution of Chemical

Reactions†
Pratim Kumar Chattaraj* and Buddhadev Maiti
Contribution from the Department of Chemistry, Indian Institute of Technology,
Kharagpur 721302, India
Received July 9, 2002 ; E-mail: pkc@chem.iitkgp.ernet.in

Abstract: Time evolution of various reactivity parameters such as electronegativity, hardness, and
polarizability associated with a collision process between a proton and an X- atom/ion (X ) He, Li+, Be2+,
B3+, C4+) in its ground (1S) and excited(1P,1D,1F) electronic states as well as various complexions of a
two-state ensemble is studied using time-dependent and excited-state density functional theory. This collision
process may be considered to be a model mimicking the actual chemical reaction between an X-atom/ion
and a proton to give rise to an XH+ molecule. A favorable dynamical process is characterized by maximum
hardness and minimum polarizability values according to the dynamical variants of the principles of maximum
hardness and minimum polarizability. An electronic excitation or an increase in the excited-state contribution
in a two-state ensemble makes the system softer and more polarizable, and the proton, being a hard acid,
gradually prefers less to interact with X as has been discerned through the drop in maximum hardness
value and the increase in the minimum polarizability value when the actual chemical process occurs. Among
the noble gas elements, Xe is the most reactive. During the reaction: H2 + H+ f H3+ hardness maximizes
and polarizability minimizes and H2 is more reactive in its excited state. Regioselectivity of proton attack in
the O-site of CO is clearly delineated wherein HOC+ may eventually rearrange itself to go to the
thermodynamically more stable HCO+.

Introduction has been proposed which states that, “the natural direction of
evolution of any system is toward a state of minimum
Pearson1-3 introduced the concept of hardness through his
polarizability”.
famous hard-soft acid-base (HSAB) principle which states
Density functional theory (DFT)3,11 has been quite successful
that,1-4 “hard acids prefer to coordinate with hard bases and
in providing solid theoretical footing for the qualitative popular
soft acids prefer to coordinate with soft bases for both their
indices of chemical reactivity like electronegativity and hardness.
thermodynamic and kinetic properties”. Another important
Electronegativity (ø)12 and hardness(η)4 are respectively defined
related hardness principle also proposed by Pearson5 is the
for an N-electron system with energy E, as the following first
maximum hardness principle (MHP)1,6,7 which states that,6
and second-order derivatives
“there seems to be a rule of nature that molecules arrange
themselves so as to be as hard as possible”. The validity of ∂E
HSAB principle has been shown8 to somehow demand that of
the MHP. Owing to the inverse relationship9 between hardness
ø ) -µ ) - (∂N ) V(r)
(1)

and polarizability a minimum polarizability principle (MPP)10 and

( ) ()
† Dedicated to Professor Walter Kohn, the father of the Density
Functional Theory, on his 80th birthday. 1 ∂2E 1 ∂µ
(1) Pearson, R. G. Chemical Hardness: Application from Molecules to Solid;
η) ) (2)
2 ∂N2 V(r) 2 ∂N V(r)
Wiley-VCH: Weinheim, 1997.
(2) Sen, K. D.; Mingos, D. M. P. Chemical Hardness: Structure and Bonding;
Springer: Berlin, 1993; Vol. 80.
(3) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules;
where µ and V(r) are chemical potential (Lagrange multiplier
Oxford University Press: Oxford, 1989. associated with normalization constraint of DFT) and external
(4) (a) Pearson, R. G. Hard and Soft Acids and Bases; Dowden, Hutchinson potential, respectively. Equivalently, hardness can be expressed
& Ross: Stroudsberg, PA, 1973. (b) Parr, P. G.; Pearson, R. G. J. Am.
Chem. Soc. 1983, 105, 7512.
(5) Pearson, R. G. J. Chem. Edu. 1987, 64, 561. Pearson, R. G. Acc. Chem. (9) (a) Pearson, R. G. in 2. (b) Politzer, P. J. Chem. Phys. 1987, 86, 1072. (c)
Res. 1993, 26, 250. Ghanty, T. K.; Ghosh, S. K. J. Phys. Chem. 1993, 97, 4951. (c) Fuentealba,
(6) (a) Parr, R. G.; Chattaraj, P. K. J. Am. Chem. Soc. 1991, 113, 1854. (b) P.; Reyes, O. J. Mol. Struct. (THEOCHEM) 1993, 282, 65. (d) Fuentealba,
Chattaraj, P. K.; Liu, G. H.; Parr, R. G. Chem. Phys. Lett. 1995, 237, 171. P.; Simon-Manso, Y. J. Phys. Chem. A 1998, 102, 2029.
(c) Ayers, P. W.; Parr, R. G. J. Am. Chem. Soc. 2000, 122, 2010. (10) (a) Chattaraj, P. K.; Sengupta, S. J. Phys. Chem. 1996, 100, 16 126. (b)
(7) Chattaraj, P. K. Proc. Ind. Natl. Sci. Acad. Part. A 1996, 62, 513. Ghanty, T. K.; Ghosh, S. K. J. Phys. Chem. 1996, 100, 12 295.
(8) (a) Chattaraj, P. K.; Lee, H.; Parr, R. G. J. Am. Chem. Soc. 1991, 113, (11) (a) Hohenberg, P.; Kohn, W. Phys. ReV. B 1964, 136, 864. (b) Kohn, W.;
1855. (b) Chattaraj, P. K.; Schleyer, P. v. R. J. Am. Chem. Soc. 1994, 116, Sham, L. J. Phys. ReV. A 1965, 140, 1133.
1067. (c) Cedillo, A.; Chattaraj, P. K.; Parr. R. G. Int. J. Quantum Chem. (12) Parr, R. G.; Donnelly, D. A.; Levy, M.; Palke, W. E. J. Chem. Phys. 1978,
M. Zerner Spl. Issue 2000, 77, 403. 68, 3801.
10.1021/ja0276063 CCC: $25.00 © 2003 American Chemical Society J. AM. CHEM. SOC. 2003, 125, 2705-2710 9 2705
ARTICLES Chattaraj and Maiti

as13 to bind those systems which are in their ground states where
they are the hardest and the affinity of binding would keep on
η)
1
N
∫∫η(r,r′)f(r′)F(r)drdr′ (3) decreasing with electronic excitations or with an increase in
the excited-state contribution in a two-state ensemble. Here, we
verify this prognosis using TDDFT and excited-state DFT.
where f(r)is the Fukui function14 and the hardness kernel is given
To test the efficacy of the present method on the reactivity
by
behavior along a given group of the periodic table we also study
2 the protonation of He, Ne, Ar, Kr, and Xe. The chemical
1 δ F[F]
η(r,r′) ) (4) reactions H2 + H+ f H3+ and CO + H+ f HOC+ + HCO+
2 δF(r)δF(r′) are also studied. For the former reaction H2 is considered in
in terms of the Hohenberg-Kohn-Sham universal functional both the ground and the excited states. The other reaction is
of DFT.11 The wave function of an N-particle system is chosen to specifically test the regioselectivity in the reaction
completely characterized by N and V(r). Although ø and η involving a multiple-site molecule.
measure the response of the system when N changes at fixed Computational Details
V(r), polarizability(R) plays the same role for varying V(r) at
Dynamical profiles of various reactivity parameters associated with
constant N. the collision process between a proton and several helium isoelectronic
So far the studies on HSAB principle has been restricted to systems (X ) He, Li+, Be2+, B3+, C4+) and their two-state ensembles
ground states and for time-independent situations. In the present are generated by solving a generalized nonlinear Schrödinger equation
work, we analyze this principle in the light of the principles of within a quantum fluid density functional framework23,24 for the TD
maximum hardness and minimum polarizability by making use charge and current densities required for the calculation of any reactivity
of two important aspects of DFT, viz., time-dependent (TD) index in a given instant. Various functionals used for this purpose and
DFT15 and excited-state DFT.16 To our knowledge, this is for the numerical details are available elsewhere.24 This procedure stems
the first time these electronic structure principles are studied in from the TDDFT.1,5,7 This initial boundary value problem has been
a dynamical system involving excited electronic states. It may, solved by a leap-frog type finite difference scheme.24 Initial (t ) 0)
near Hartree-Fock wave functions in 1S, 1P, 1D, and 1F electronic states
however, be noted that there is no general excited-state DFT17
for different helium isoelectronic systems are taken from Clementi and
but for some special cases such as in states which are of lowest
Roetti25 and Mukherjee et al.26 for the ground and excited electronic
energy for a given symmetry class18 or in an ensemble of states19 states, respectively. In case of the two-state ensemble the density is
and these are the cases considered in the present work. chosen as
Because a system is generally more reactive in its excited
state it is expected from the MHP and the MPP that a system Fensemble ) (1 - ω)Fgs + ωFes (5)
would become softer and more polarizable on electronic
excitation. This idea has been confirmed in the cases of atoms,20 where Fgs and Fes are ground state25 and excited state26 (11P, 1s2p
ions20 and molecules21 for the lowest energy state of a particular configuration) densities, respectively, and ω is a real number19,27 that
symmetry and different complexions of a two -state ensemble. measures the relative weights of various electronic states present in
In the present work, we study the time evolution of various the ensemble.
reactivity parameters such as electronegativity, hardness and While the near Hartree-Fock ground-state wave functions of He,
Ne, Ar, Kr, Xe are taken from Clementi and Roetti,25 the 4-31G double-
polarizability associated with a collision process between a
Zeta ground states of H2 and CO as well as the excited state of H2 are
proton and various helium isoelectronic systems (X ) He, Li+,
taken from Snyder and Basch.28 Owing to the cylindrical symmetry of
Be2+, B3+, C4+)in their ground and excited electronic states as the diatomics, we have used cylindrical polar coordinates (F̃,φ,z) in
well as in a two-state ensemble. This collision process may be our calculations. The internuclear axis is taken along the z direction
considered to be a model mimicking the actual chemical reaction and the F̃ - z plane as the molecular plane. Because of the cylindrical
between an X atom and a proton to give rise to an XH + molecule symmetry all local quantities are evaluated at the (F̃-z) points.
as is the standard practice in chemical kinetics to visulalize Electronegativity is calculated by extending Gordy’s work29 to a TD
chemical reactions as collision processes.22 According to HSAB situation. The TD chemical potential becomes equal to the total
principle, the proton, being a hard acid, is expected to prefer electrostatic potential10,24 at a point rµ, i.e.

F(r,t) Z1 Z2
∫|r
(13) (a) Berkowitz, M.; Ghosh, S. K.; Parr, R. G. J. Am. Chem. Soc. 1985, 107,
6811. (b) Ghosh, S. K.; Berkowitz, M. J. Chem. Phys. 1985, 83, 2976. -ø(t) ) µ(t) ) dr - - (6)
(14) Parr, R. G.; Yang. W. J. Am. Chem. Soc. 1984, 106, 2976. µ - r| |R 1 - r µ | |R2 - r µ|
(15) (a) Runge, E.; Gross, E. K. U. Phys. ReV. Lett. 1984, 52, 997. (b) Dhara,
A. K.; Ghosh, S. K. Phys. ReV. A 1987, 35, 442.
(16) Singh, R.; Deb, B. M. Phys. Rep. 1999, 311, 47. where rµ is the point at which the sum of functional derivatives of the
(17) Kohn, W., Private discussion. total kinetic and exchange-correlation energies vanishes at that time
(18) (a) Gunnarson, O.; Lundqvist, B. I. Phys. ReV. B 1976, 13, 4274. (b) Ziegler, step. This process is a TD extension of the method proposed by Politzer
T.; Rauk, A.; Baerends, E. J. Theor. Chim. Acta 1977, 43, 261. (c) von
Barth, U. Phys. ReV. A 1979, 20, 1693.
(19) (a) Theophilou, A. J. Phys. C 1979, 12, 5419. (b) Hadjisavvas, N.; (23) Deb, B. M.; Chattaraj, P. K. Phys. ReV. A 1989, 39, 1696.
Theophilou, A. Phys. ReV. A 1985, 32, 720. (c) Kohn, W. Phys. ReV. A (24) Chattaraj, P. K.; Sengupta, S. J. Phys. Chem. A 1997, 101, 7893.
1986, 34, 5419. (d) Gross, E. K. U.; Oliveira, L. N.; Kohn, W. Phys. ReV. (25) Clementi, E.; Roetti, C. At. Data Nucl. Data Tables 1974, 14, 174.
A 1988, 37, 2805-2809. (e) Oliveira, L. N.; Gross, E. K. U.; Kohn, W. (26) Mukherjee, P. K.; Sengupta, S.; Mukherji, A. Int. J. Quantum Chem. 1970,
Phys. ReV. A 1988, 37, 2821. 4, 139.
(20) Chattaraj, P. K.; Poddar, A. J. Phys. Chem. A 1998, 102, 9944; Chattaraj, (27) (a) Nagy, A. Phys. ReV. A 1990, 42, 4388; Nagy, A. Phys. ReV. A 1994,
P. K.; Poddar, A. J. Phys. Chem. A 1999, 103, 1274. 49, 3074. (b) Levy, M. Phys. ReV. A 1995, 52, 4313. (c) Chattaraj, P. K.;
(21) (a) Chattaraj, P. K.; Poddar. A. J. Phys. Chem. A 1999, 103, 8691. (b) Ghosh, S. K.; Liu, S.; Parr, R. G. Int. J. Quantum Chem. 1996, 60, 535.
Fuentealba, P.; Simon-Manso, Y.; Chattaraj, P. K. J. Phys. Chem. A 2000, (28) Snyder, L. C.; Basch, H. Molecular WaVe Functions and Properties:
122, 348. Tabulated From SCF Calculations In A Gaussian Basis Set; John Wiley
(22) Laidler, K. J. Chemical Kinetics; Harper and Row: New York, 1987, & Sons: New York, 1972; pp T-2 to T-3 and pp T-40 to T-41.
Chapter 4. (29) Gordy, W. Phys. ReV. 1964, 69, 604.

2706 J. AM. CHEM. SOC. 9 VOL. 125, NO. 9, 2003

HSAB Principle ARTICLES

Figure 2. Time evolution of hardness (η, au) during a collision process

between an X - atom/ion (X ) He, Li+, Be2+, B3+, C4+) in various
electronic states (1S, 1P, 1D, 1F) and a proton. (black line) 1S; (red line) 1P;
(green line) 1D; (blue line) 1F.
Figure 1. Time evolution of chemical potential (µ, au) during a collision
process between an X-atom/ion (X ) He, Li+, Be2+, B3+, C4+) in its ground
state and a proton.

et al.30 to calculate the covalent radii of atoms using electronegativity

equalization principle.31 This definition of the TD chemical potential
is akin to the functional derivative of a TD energy quantity.32 Electronic
chemical potential has also been calculated using free energy density
functionals in recent years which helps in ab initio molecular dynamics
simulations within a grand canonical ensemble.33 In eq 6, R1, R2, and
Z1, Z2 are radius vectors and atomic numbers of the target (X-atom/
ion) and the projectile (H+) nuclei, respectively. The origin of the
coordinate system is fixed on the target nucleus and the position of the
projectile is determined by a Coulomb trajectory.34 A linear trajectory
provides qualitatively similar results.35
While TD hardness is calculated from eq 3, the TD polarizability
is calculated as follows
Z
R(t) ) |Dind (t)|/|GZ(t)| (7)
Z Figure 3. Time evolution of polarizability (R, au) during a collision process
where Dind (t) is the electronic part of the induced dipole moment and between an X-atom/ion and a proton. See the caption of Figure 2 for details.
GZ(t) is the component of the external Coulomb field along the Z-axis
mimicking the weak electric field generally used in defining the to rapid charge oscillations. These time steps bracket the
dynamic polarizability. encounter regime where the electron density is shared by both
Results and Discussion
the nuclei. In the departure regime, µ again changes drastically
to reach a stable value more or less the same as that obtained
Ground and Excited States Reactivity Dynamics of Pro- in the approach regime. Because the qualitative features of the
tonation of He-Isoelectronic Systems. Figure 1 depicts the time dynamic µ-profiles for the excited states and two-state ensembles
evolution of chemical potential associated with the collision are quite similar we refrain from presenting them here.
process between a proton and an X-atom/ion (X ≡ He, Li+, Dynamic profiles of η and R for the ground (1S) and various
Be2+, B3+, C4+) in its ground-state mimicking the corresponding excited states (1P, 1D, 1F; for C, only 1S and 1P densities are
chemical reaction. available) of He isoelectronic atom/ions colliding with a proton
Three distinct zones are discernible for the whole collision are presented in Figures 2 and 3, respectively. In all cases,
process: approach, encounter and departure. Neither rµ nor µ hardness gets maximized and polarizability gets minimized in
is calculable in the encounter regime because the condition the encounter regime signifying a favorable dynamical process
mentioned above is not satisfied anywhere in space. After the vis a vis the dynamical variants of the MHP and MPP. Very
initial transients die out, µ becomes more or less stable in the large hardness and small polarizability values stem from the
approach regime. Toward the end of this regime and the fact that the electron density is shared by both the nuclei in the
beginning of the departure regime, µ changes drastically due encounter regime unlike the isolated atom/ion case where the
electron distribution is spherical due to the central nature of
(30) Polizer, P.; Parr, R. G.; Murphy, D. R. J. Chem. Phys. 1983, 79, 3859.
(31) Sanderson, R. T. Science 1951, 114, 670. Sanderson, R. T. Science 1955, the Coulomb potential originating from a single nucleus. It is
121, 207. Sanderson, R. T. J. Chem. Educ 1954, 34, 238. known20,21 that any system becomes softer and more polarizable
(32) Bartolotti, L. J. Phys. ReV. A 1982, 26, 2243. Deb, B. M.; Ghosh, S. K. J.
Chem. Phys. 1982, 31, 238. with electronic excitation i.e., for any given species η1S〉η1P〉η1D〉η1F
(33) Vuilleumier, R.; Sprik, M.; Alavi, A. J. Mol. Struct. (THEOCHEM), 2000,
506, 343; Tavernelli, I.; Vuilleumier, R.; Sprik, M. Phys. ReV. Lett. 2002,
and R1S〈R1P〈R1D〈R1F vindicating the MHP and MPP. Now, proton
88, 213 002-1; being a hard acid would prefer to bind with X (X ≡ He, Li+,
(34) Kulander, K. C.; Sandhya Devi, K. R.; Koonin, S. E. Phys. ReV. A 1982, Be2+, B3+, C4+) in the order 1S〉1P〉1D〉1F, and hence, the
25, 2968.
(35) Chattaraj, P. K.; Maiti, B., unpublished work. maximum η value would decrease and the minimum R value

J. AM. CHEM. SOC. 9 VOL. 125, NO. 9, 2003 2707

ARTICLES Chattaraj and Maiti

Figure 4. Time evolution of hardness (η, au) during a collision process Figure 7. Time variation of polarizability (R, au) of He, Ne, Ar, Kr, Xe
between an X - atom/ion (X ) He, Li+, Be2+, B3+, C4+) in different during protonation.
complexions of a two - state ensemble (ω ) 0, 0.25, 0.5) and a proton.
(black line) ω ) 0; (cyan line) ω ) 0.25; (violet line) ω ) 0.5.

Figure 8. Time evolution of hardness (η, au) during a collision process

between a hydrogen molecule in its ground state and a proton.

hardness and polarizability of He, Ne, Ar, Kr, Xe during

protonation. The actual chemical reaction may be envisaged as
follows

Figure 5. Time evolution of polarizability (R, au) during a collision process He + H+ (0 e t e 9.075)
between an X-atom/ion and a proton. See the caption of Figure 4 for details.
f HeH+ (9.075 < t < 10.025)

f distorted Li+ (t = 10.025 au)

f HeH+ (10.025 < t < 10.975)

f He + H+ (t g 10.975)
Hardness attains a maximum value and polarizability attains a
minimum value in the encounter regime, as expected. The
hardness maximum decreases and the polarizability minimum
Figure 6. Time variation of hardness (η, au) of He, Ne, Ar, Kr, Xe during increases as we proceed in the sequence He f Ne f Ar f Kr
protonation. f Xe. It is a clear-cut signature of increasing reactivity in that
would increase in the order 1Sf1Pf1Df1F, which is precisely sequence corroborating the fact that Xe is the most reactive
the case providing the validity of the HSAB principle in a according to the MHP and MPP which has been the reason
dynamical context. behind the fact that the first attempt of compound formation of
Figures 4 and 5 depict respectively the time dependence of noble gas elements was tried on Xe.
η and R for various complexions of a two-state ensemble (ω ) Dynamic Reactivity Profiles of the Chemical Reaction:
0, 0.25 and 0.5) of X (X ) He, Li+, Be2+, B3+, C4+) colliding H2 + H+ f H3+. The density profile of the H2 molecule in its
with a proton. In the encounter regime η maximizes and R ground (1∑g+) state is symmetric at both nuclei (See figure
minimizes in all cases as would have been predicted by the provided in the Supporting Information). It is expected that
MHP and the MPP for a favorable chemical reaction. As during protonation the hardness would get maximized and the
expected from a dynamical variant of the HSAB principle vis polarizability would get minimized in the neighborhood of the
a vis the validity of the MHP and the MPP the maximum η nuclei since the density attains its maximum values at those
value decreases and the minimum R value increases with an points and they would be symmetric which is what precisely
increase in the excited-state contribution in a two-state ensemble. obtained in the present work. The hardness profile is depicted
Reactivity Dynamics of Protonation of Noble Gas Systems. in Figure 8 and the polarizability profile is provided in the
Figures 6 and 7, respectively, depict the time variation of Supporting Information. We also calculate the corresponding
2708 J. AM. CHEM. SOC. 9 VOL. 125, NO. 9, 2003
HSAB Principle ARTICLES

carbon and oxygen sides which are consistent. According to

these figures, vis a vis the MHP and MPP the O-site is
kinetically more favored for protonation. This explains the
laboratory synthesis36 of isoformyl cation HOC+ as well as its
presence in the dense interstellar cloud37 such as in the source
Sagittarius B2. Proton being a hard acid would prefer to attack
at the harder O-end. It may be noted that in the formation of
metal carbonyls CO often attacks through the softer C-site to
the soft metal atoms in their low oxidation states. Moreover,
when CO acts as an electrophile, attack is predominantly via
the C-site (due to the low energy π* LUMO with high amplitude
Figure 9. Time evolution of hardness (η, au) during a collision process on the carbon atom), and hence, the O-site has relatively more
between a hydrogen molecule in its first excited state and a proton. nucleophilic character and accordingly larger affinity toward
H+. Condensed local softness of C is much larger than that of
O in CO as has been revealed by both ab initio SCF and DFT
calculations.38 Formation of HOC+ is thus suggested by both
HSAB principle as well as Klopman’s theory39 of charge-
controlled hard-hard interactions. Once HOC+ is formed it may
rearrange itself to go over to the thermodynamically more
stable40 formyl cation HCO+.
Thus, the HSAB principle manifests itself in a dynamical
context as well. Now, chemical processes can be understood
and analyzed better, from start to finish, with the help of HSAB
principle.
Concluding Remarks
To understand the dynamical behavior of chemical reactivity
Figure 10. Dynamic hardness (η, au) profile for protonation of CO
considering the attack from both the carbon and oxygen sides. indices during a chemical reaction involving ground and excited
electronic states, a model collision process between an X-atom/
ion (X ≡ He, Li+, Be2+, B3+, C4+) and a proton is studied within
a quantum fluid density functional framework. The whole
collision process can be divided into three distinct regimes, viz.,
approach, encounter and departure in terms of the time-
dependent electronegativity profile. In the encounter regime
where the actual chemical process takes place, hardness
maximizes and polarizability minimizes as expected from the
principles of maximum hardness and minimum polarizability.
A system becomes softer and more polarizable with electronic
excitation as well as where the excited-state contribution in a
two-state ensemble increases. The maximum hardness value
decreases and the minimum polarizability value increases in the
encounter regime for these situations. Because proton is a hard
acid this fact is a clear-cut signature of the HSAB principle in
a dynamical situation.
Reactivity of noble gas elements toward protonation increases
in the sequence He f Ne f Ar f Kr f Xe. In the reaction:
Figure 11. Dynamic polarizability (R, au) profile for protonation of CO
considering the attack from both the carbon and oxygen sides. H2 + H+ f H3+ hardness maximizes and polarizability
minimizes in the neighborhood of the two nuclei. Excited-state
profiles for the first excited state of H2. As in the ground state, H2 is more reactive than the ground-state H2. Regioselectivity
the hardness profile is presented in Figure 9, whereas supporting of protonation is toward the O-end of CO which in turn can
material contains the polarizability plot. Being softer and more reorganize to HCO+.
polarizable this state exhibits lower ηmax and higher Rmin values
Acknowledgment. We are grateful to Professor W. Kohn for
when compared to the corresponding values for the ground state.
helpful discussions and CSIR, New Delhi for financial as-
Regioselectivity of the Chemical Reaction. CO + H+ f
HCO+ + HOC+. The density profile of CO in its ground state (36) Gudeman, S. C.; Woods, R. C. Phys. ReV. Lett. 1982, 48, 1344.
is presented in the Supporting Information. Electron density is (37) Woods, R. C.; Gudeman, C. S.; Dickman, R. L.; Goldsmith, P. F.; Huguenin,
G. R.; Irvine, W. M.; Hjalmarson, A.; Nyman, L. A.; Olofsson, H.
centered around the C and O nuclei with the latter having larger Astrophys. J. 1983, 270, 583.
contribution as also discerned28 by the corresponding Mulliken (38) Oláh, J.; Alsenoy, C. V.; Sannigrahi, A. B. J. Phys. Chem. A 2002, 106,
3885.
charges of respectively 5.7991 and 8.2009. Figures 10 and 11 (39) Klopman, G. J. Am. Chem. Soc. 1968, 90, 223; Chattaraj, P. K. J. Phys.
respectively depict the dynamical hardness and polarizability Chem. A 2002, 105, 511.
(40) Dixon, D. A.; Komornicki, A.; Kraemer, W. P. J. Chem. Phys. 1984, 81,
profiles for protonation considering the attack from both the 3603.

J. AM. CHEM. SOC. 9 VOL. 125, NO. 9, 2003 2709

ARTICLES Chattaraj and Maiti

sistance. We would like to thank the anonymous reviewers and symmetric at both nuclei, the polarizability profiles in the ground
Professor Donald G. Truhlar, Associate Editor of J. Am. Chem. and the first excited states, and the density profile of CO in its
Soc. for very constructive criticisms. ground state. This material is available free of charge via the
Internet at http://pubs.acs.org.
Supporting Information Available: Figure showing the
electron density of the H2 molecule in its ground (1∑g+) state, JA0276063

2710 J. AM. CHEM. SOC. 9 VOL. 125, NO. 9, 2003