An Ab Initio MO Study on Orbital Interaction and Charge Distribution in Alkali Metal Aqueous Solution: Li+, Na+, and K+

P1: GAD

josl2004.cls (05/08/2004 v1.1a LaTeX2e JOSL document class) pp1320-josl-493407 October 1, 2004 22:21

Journal of Solution Chemistry, Vol. 33, Nos. 6/7, June/July 2004 ( C© 2004)

An Ab Initio MO Study on Orbital Interactionand Charge Distribution in Alkali MetalAqueous Solution: Li+, Na+, and K+

Masato Tanaka1 and Misako Aida2,∗

Received January 5, 2004; revised May 24, 2004

The analysis of the orbital interaction between an alkali metal ion and the surroundingsolvent molecules is performed for aqueous solutions of Li+, Na+, and K+, by meansof the ab initio MO method with the aid of the quantum mechanical (QM)/molecularmechanics (MM) method. A total of 171 water molecules are included for each system.The effect of Li+ orbitals reaches as far as 6 A; 7 A for Na+; and 9 A for K+. This effectis caused by the orbital interactions between the valence orbitals of an alkali metal ionand of the surrounding water molecules. The electrostatic interaction and the orbitalinteraction must not be neglected. The difference in the effect between the alkali metalions originates from the difference in the valence orbital extensions of the alkali metalions.

KEY WORDS: Ionic aqueous solution; ab initio MO; hybrid QM/MM; hydrationshells; alkali metal ion.

1. INTRODUCTION

The hydration of ions is of fundamental importance in chemical and biolog-ical processes. Our chemical intuition suggests that water molecules should getpolarized by the central ion and the negative charge on water molecules would ori-ent towards the central ion, i.e., the charge distribution around the water moleculesgets distorted towards the central ion, thus reducing the formal charge of the cen-tral ion. Chemical intuition, however, does not give us any more detailed insight.How far does the influence of the central ion reach? Is there any difference in theinfluence between the different ions? If it is the case, then what is the origin of the

1Center for Quantum Life Sciences, Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan.

2Department of Chemistry, Graduate School of Science, Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan; e-mail: [email protected].

887

0095-9782/04/07-0887/0 C© 2004 Springer Science+Business Media, Inc.

P1: GAD


888 Tanaka and Aida

difference? The aim of the current study is to shed light on these questions as theypertain to aqueous alkali metal solutions.

There have been many experimental and theoretical investigations(1−3) of thehydration of ions. In most of the molecular dynamics (MD) and Monte Carlo(MC) studies, ions are treated with their formal charges, i.e., the charge of eachalkali metal ion is +1. There should be the electronic and orbital interactionsbetween the ion and the surrounding solvent molecules. A molecular mechanics(MM) treatment cannot deal with this phenomenon, since the charges of theconstituent atoms are usually fixed in the MM treatment. We should use thequantum mechanical (QM) method to investigate orbital interactions.

The current article is composed of three parts. First, the distribution of watermolecules around the alkali metal ion is shown for each Li+, Na+ and K+ ion. Itis shown that the water distribution in a local minimum configuration is similar tothe average distribution in the MC simulation. Secondly, using the local minimumconfiguration as a representative of the configurations, the orbital interactionsbetween the central alkali metal ion and the surrounding water molecules areanalyzed for each aqueous solution of Li+, Na+ and K+. Thirdly, we analyze thecharge distributions around the alkali metal ion for each aqueous solution of Li+,Na+ and K+.

2. METHOD

2.1. A Configuration of Solvent Molecules Around M+

In the current study, 171 water molecules around an alkali metal ion are in-cluded to mimic aqueous solutions of alkali metal ions. Since the aim of the currentstudy is to analyze the orbital interaction around an alkali metal ion in aqueoussolution, we deal with a configuration of the solvent molecules that is regarded asone of the local minima of the system. To obtain a local minimum of the solvent,we adopt the framework of the QM/MM-vib method as in our previous work.(4)

The level of HF/6-31G∗ is used for the QM subsystem (alkali metal ion) and theTIP3P parameter system is used for the MM subsystem (solvent molecules) withthe Lennard–Jones parameters listed in Table I. The geometry optimization of thesolvent molecules is performed after the simulated annealing process (in which allthe atoms are treated as MM). This procedure is repeated several times. The energygradients, both for the QM subsystem and for the MM subsystem, are calculatedanalytically. The program package of HONDO-2002(5) is used for this procedure.

2.2. Radial Distribution Function

The distribution of water molecules around an alkali metal ion in a configura-tion is given using the radial distribution function (RDF) of the distance between

P1: GAD


MO Study on Orbital Interaction and Charge Distribution in Li+, Na+, and K+ 889

Table I. Lennard-Jones Parameters Used in the QM/MM Calculations

Atom Q σ (A) ε [kcal-mol−1]

QMa Li+ 1.500 0.800Na+ 2.300 0.300K+b 3.360 0.136

O 3.600 0.150H 1.300 0.100

MMc O −0.834 3.151. 0.152H 0.417 0.000 0.000

aRef. (6).bRef. (7).cRef. (8).

the ion and an O atom of a water molecule. The RDF g(r ) is defined as

g(r ) = n(r )/�V (r )

N/V.

Here, r is the distance between the alkali metal ion and an O atom, n(r ) is thenumber of O atoms included in the range between r − �r/2 and r + r/2, and �Vis the volume of the spherical shell (�V ∼ 4πr2�r ). N is the total number of Oatoms and N/V is equal to the number density of O atoms.

2.3. Analysis of Overlap Populations Between M+ and Solvent

To analyze the orbital interaction between an alkali metal ion and the sur-rounding solvent water molecules, we divide the solvent molecules into severalshells and perform the overlap population analysis between the central ion and thewater molecules in various shells.

2.3.1. Division of Solvent Molecules into Hydration Shells

After we obtain a local minimum configuration of the M+-171W system,we partition the 171 solvent water molecules into five hydration shells (Fig. 1).The A shell contains the water molecules which are connected to M+ directly:these water molecules are located within a distance of 3.0 A from the central M+.The B shell contains the water molecules which are hydrogen bonded to the watermolecules in the A shell: these water molecules are located within a distance of5.0 A from the central M+. The C shell contains the water molecules which arehydrogen bonded to the water molecules in the B shell: these water molecules arelocated within a distance of 7.0 A from the central M+. The D shell contains thewater molecules which are hydrogen bonded to the water molecules in the C shell:these water molecules are located within a distance of 9.0 A from the central M+.The rest of the water molecules are defined as the E shell. Note that the E shell

P1: GAD


890 Tanaka and Aida

Fig. 1. A local minimum configuration of 171 MM water molecules around the Li+ (QM)cation and the schematic drawing of the definition of the hydration shells.

is not complete in the current calculations, because of the limited number of thewater molecules. The E shell contains the other water molecules which are notincluded in the A–D shells. The number of water molecules in the A, B, C, D,and E shells for the cases of Li+, Na+, and K+, respectively, are summarized inTable II.

2.3.2. Ab Initio MO Calculations with Various QM Hydration Shells

For each of the alkali metal cations, using the local minimum configurationof the M+-171W system as described in the section 2.1, five kinds of ab initioMO calculations are done with point charges assigned to MM atoms. First, onlythe M+ ion is treated as QM with the set of the point charges on the positions ofall the atoms for the MM water molecules in the A–E shells (case I). Secondly, thewater molecules in the A shell are treated as QM with the set of the point chargesfor the rest of the MM water molecules in the B–E shells (case II). Thirdly, thewater molecules in the A and B shells are treated as QM with the set of the pointcharges for the rest of the MM water molecules in the C–E shells (case III).Fourth, the water molecules in the A–C shells are treated as QM with the set of the

Table II. The Number of the Water Molecules in Each Shell

M+ A shell B shell C shell D shell Others (E shell)

Li+ 4 13 37 77 40Na+ 5 15 32 81 38K+ 6 13 36 75 41

P1: GAD



Fig. 2. The QM molecules in the five cases (cases I–V) of the system of Li+–171 water molecules.

point charges for the rest of the MM water molecules in the D–E shells (case IV).Finally, the water molecules in the A–D shells are treated as QM with the set of thepoint charges for the rest of the MM water molecules in the E shell (case V). TheQM molecules in these five cases are displayed in Fig. 2 for the Li+-171W system.Ab initio MO calculations are performed with the point charges which are same asthose used in TIP3P (listed in Table I). The program package of GAUSSIAN 98(9)

is used for these calculations with the levels of HF/6-31G∗ and HF/6-311G∗∗.

2.3.3. Average Overlap Populations

Overlap populations between the orbitals of the central metal (QM) and theorbitals of the QM solvent water molecules are calculated in the presence of

P1: GAD


892 Tanaka and Aida

the surrounding point charges in place of the MM atoms. We define the averageoverlap population, Wk(I ), as follows:

Wk(I ) = 1

NI

NI∑iwat

∑µ∈k

∑ν∈iwat

Qµν,

where k is an atomic orbital of the alkali metal ion, NI is the number of watermolecules in the layer I , and iwat is the i th water molecule in the layer I . Qµν isthe overlap population between the atomic orbitals µ and ν.(10)

Qµν = 2Pµν Sµν(µ �= ν)

Pµν = 2N/2∑

a

C∗µaCνa

Sµν =∫

φ∗µφν dr

In the above equations, Pµν and Sµν are the density matrix and the overlap matrixelements, respectively. The average overlap population, Wk(I ), gives the averagevalue of the overlap population between the atomic orbital, k, of the alkali metalion and all of the water molecules included in the layer I .

2.4. Charge Distribution

There are several commonly used methods for assigning a charge to anatom.(11) The Mulliken population analysis(12) has been used since the early stageof the molecular orbital theory, in which the wave function is partitioned in terms ofthe basis functions; the natural population analysis (NPA)(13) is preferred recently,whereby the one-electron density matrix is used for partitioning electron distribu-tion; the CHELPG method(14) is also used preferentially and is based on thefitting scheme. The atomic charges are calculated in the current study usingthe above three methods at the levels of HF/6-31G∗ and HF/6-311G∗∗ for each ofthe hydration shells (cases I–V). In the CHELPG scheme, the following valuesfor the van der Waals radii are used, H: 1.45, O: 1.70, Li: 1.50, Na: 2.00, and K:2.50 A.

2.5. Average Solvent Distribution

Using the local minimum configuration (Section 2.1) as an initial config-uration, the Monte Carlo (MC) method, which treats all molecules as MM, isapplied to obtain an average distribution of solvent molecules around an alkalimetal ion with 171 water molecules at 298 K. The radial distribution function ofthe ensemble is obtained as the average of the 171,000,000 MC steps for eachsystem.

P1: GAD



3. RESULTS AND DISCUSSION

3.1. Solvent Distribution Around Alkali Metal Cation

The radial distribution functions and the integration numbers for the M–Odistance are shown in Fig. 3. It is worthy of note that the radial distribution ofa local minimum solvent configuration is close to that of the MC simulation,and also close to the experimentally observed distribution.(1) Although the localminimum configuration is only one of numerous configurations, it represents thecharacteristics of the solvent distribution around an alkali metal ion. The positionof the first peak of the M–O distance obtained in the local minimum configurationis very close to that of the MC simulation and also to the X-ray analysis. Sinceit is impossible to take account of the numerous configurations in the orbitalanalysis, we deal with the local minimum configuration for further analysis shownbelow.

3.2. Overlap Populations Between M+ and Water Molecules

The radial distributions of solvent water molecules around Li+, Na+, and K+

ions are displayed in Fig. 3, for their optimized solvent configurations, respectively.The solvation layers are divided every 0.52 A (i.e., r = 0.52). The distributionsof the average overlap populations, Wn(r ), for the case V are displayed in Fig. 4,for the same layer division as in Fig. 3. Here, the solvation layer is defined asthe range between r − �r/2 and r + �r/2, and n is 2, 3, and 4 for Li+, Na+,and K+ aqueous solutions, respectively; i.e., n is the principal quantum numberof the valence orbitals of the alkali metal ion. The value of Wn(r ) includes thecontribution from both the s and p orbitals of the same principal quantum number,n. Since the values of Wk(r ) for the alkali metal core orbitals are very small, thoseare not plotted in Fig. 4. The basis set (6-31G∗), which we used in the currentstudy, includes the polarization functions for alkali metal ions; these functionsmimic the 3d orbitals of the alkali metal ions. It turned out that the contributionto the overlap population from those 3d orbitals is also small, for each of thecations.

Figure 4 shows that the average overlap population between the valenceorbitals of the cations and the solvent water molecules is the highest for the watermolecules in the A shell (directly solvated water molecules) for each of the cations;the order is Li+ > Na+ > K+. The average overlap population decreases as thedistance between the cation and the solvation layer increases. It reaches as far as6, 7, and 9 A, respectively, for Li+, Na+, and K+. As a general characteristic ofwave functions, the radial position of the highest probability of an electron movesfarther from the center as the principal quantum number of the electron increases,and the wave function of the electron reaches farther as the principal quantumnumber increases.

P1: GAD


894 Tanaka and Aida

Fig. 3. Radial distribution functions and integration numbers for M–O in alocal minimum configuration (bar graph and dashed line) and those in theMM/MM-MC simulation (solid lines).

P1: GAD



Fig. 4. Average overlap population between an ion and watermolecules in the layer at r for the case V (r = 0.52 A).

3.3. How Far Does the Effect of M+ Reach?

Figure 4 shows that the effect of alkali metal orbitals reaches as far as 6,7, and 9 A, for Li+, Na+, and K+, respectively. It should be stressed here thatthis effect is caused by orbital interactions. Not only the electrostatic interaction,

P1: GAD


896 Tanaka and Aida

which is usually taken into consideration, but also the orbital interaction mustnot be neglected. There have been many simulation studies dealing with aqueouscation solutions. In most of these studies, however, only a very limited number ofthe solvent water molecules are treated as QM and a periodic boundary conditionis applied with a rather small unit cell.(3) It should be noted that care must be takenin the assessment of those studies.

3.4. Charge Distribution Around the Alkali MetalCation by Using Several Methods

Various methods have been proposed to obtain the atomic charges in amolecule and the assessment of those methods is given by Breneman andWiberg.(14) Most of the assessment was done for the electron distribution in smallmolecules. In the current study, we are interested in the charge distribution ina large water cluster including an alkali metal cation. It is well known that theMulliken population analysis does not give necessarily a “correct” distribution ofthe electrons into atomic contributions in a molecule. It is not known, however, ifany method can be used to give a correct quantity for molecular clusters. Here weinvestigate the difference between the charge distributions based on the Mullikenpopulation analysis (Mulliken charge), the natural population analysis (Naturalcharge), and the CHELPG method (CHELPG charge).

The charges of M+ in the cases II–V are listed in Table III. The charge of M+

is +1 in the case I, since all of the solvent molecules are treated as MM. The netcharge of M+ decreases with the increasing number of the QM water moleculesfor each cation. This reflects the influence of the solvent water molecules on theelectronic structure of the central cation. The charge variation does not depend onthe basis set used (see Table III).

A deficiency is known in CHELPG; the electrostatic potential experiencedoutside a molecule is mainly determined by the atoms near the surface and con-sequently the charges on atoms buried within a molecule cannot be assigned withany great confidence.(11) Our current analysis confirms that the population analysisbased on the electrostatic potential, such as in the CHELPG method, should notbe applied to a cluster system. Using the CHELPG method, the average charge ofa water molecule in the D shell is shown to be negative in spite of the existence ofthe cationic center in the system (data not shown); this is apparently inadequate.

In the Mulliken scheme (Fig. 5a) for the aqueous Li+ solution, the charge ofthe central Li cation converges to +0.47 in case IV, in which the water moleculesare treated as QM in the A–C shells. In the aqueous Na+ solution, the Mullikencharge of the central Na cation almost converges to +0.42 in case IV. In theaqueous K+ solution, the Mulliken charge of the central K cation is +0.28 in caseV, in which the water molecules are treated as QM in the A–D shells, and it seemsthat convergence is not achieved yet. These results indicate that the solvent water

P1: GAD



Tabl

eII

I.V

aria

tion

ofC

harg

esof

M+

for

the

Cas

esII

–Va

Cas

eII

Cas

eII

IC

ase

IVC

ase

V

M+

Mul

liken

bN

atur

alc

CH

EL

PGd

Mul

liken

Nat

ural

CH

EL

PGM

ullik

enN

atur

alC

HE

LPG

Mul

liken

Nat

ural

CH

EL

PG

Li+

0.67

8e1.

135

0.88

00.

524

0.87

60.

938

0.46

60.

873

0.92

30.

466

0.87

40.

989

0.71

1f

0.91

31.

137

0.57

40.

902

0.90

00.

382

0.89

50.

908

0.37

80.

896

0.91

5N

a+0.

725e

1.06

60.

942

0.55

80.

930

0.94

60.

422

0.94

30.

791

0.40

80.

940

0.78

50.

764

f0.

947

1.06

80.

622

0.93

20.

995

0.48

50.

947

0.80

10.

270

0.94

40.

782

K+

0.74

1e1.

149

0.95

30.

597

0.93

61.

105

0.41

30.

951

0.94

50.

275

0.94

00.

989

0.77

3f

0.96

21.

156

0.65

70.

948

1.16

50.

499

0.94

90.

938

0.25

10.

940

0.98

5

aIn

the

case

I,th

ech

arge

ofM

+is

+1fo

ran

yof

the

met

hods

,sin

ceon

lyM

+is

trea

ted

asQ

M.

bM

ullik

ench

arge

.c N

atur

alch

arge

.dC

HE

LPG

char

ge.

e Inea

chM

+ ,th

enu

mbe

rsin

rom

anty

pear

eat

the

HF/

6-31

G∗ .

fIn

each

M+ ,

the

num

bers

inita

lics

are

atth

eH

F/6-

311G

∗∗.

P1: GAD


898 Tanaka and Aida

Fig. 5. The charges obtained with Mulliken (a, b, c) and Natural (d, e, f) population analyses.(a, d) The charge of M+ for the cases I–V; (b, e) the average charge of a solvent watermolecule in each hydration shell for the case V; (c, f) the average charge of a solvent watermolecule in the A shell for the cases II–V.

molecules within about 7 A should be treated as QM in the aqueous Li+ and Na+

solutions; the solvent water molecules farther than 9 A should be treated as QMin aqueous K+ solutions. On the other hand, Natural charges of all M+ appear toconverge already in case II (Fig. 5d): +0.88, +0.94, and +0.95 for Li+, Na+, andK+, respectively.

P1: GAD



In the Mulliken scheme, the negative charge penetrates into the central alkalimetal cation from the surrounding water molecules and the water molecules ofthe A shell become slightly cationic (Fig. 5b). In the NPA scheme, the chargeof alkali metal ion does not change much in the cases I–V (Fig. 5d); althoughthe negative charge penetrates into the central alkali metal cation from the sur-rounding water molecules, the water molecules of the A shell become slightlyanionic (Fig. 5e). It appears that the penetrated charge from the surrounding watermolecules distributes to the central cation and the A shell water molecules in theNPA scheme. This result may be contary to chemical institution. We would expectthat the water molecules surrounding an alkali metal ion would become slightlycationic. Although it is difficult to judge which method gives the correct scheme,we may say that the Natural charge does not necessarily give a correct chargedistribution in a molecular cluster.

It is interesting to note that the charge variation in the A shell in the Mullikenscheme (Fig. 5c) is similar to that in the NPA scheme (Fig. 5f). The charge variationin the A shell may reflect the orbital interactions between the central cation andthe surrounding water molecules. Although the Mulliken charges and the Naturalcharges are different quantitatively for the charge distribution in the hydrated alkalimetal cation, it is probable that both methods give a similar qualitative scheme:the charge distribution in the central alkali metal cation and the A shell watermolecules is influenced by the outer hydration shell.

3.5. Comparison with Experimental Observation

Some aqueous ions are noted as “structure makers” and others as “structurebreakers.”(15) The Li and Na cations are classified as the former and K cations asthe latter. Traditionally, it is believed that this classification may be related to thehydrogen-bond network around the central ion.(15) Recently, it was shown thatthe dominant effect of the ion on water configurations appears to be restricted tothe immediate vicinity of the ion, rather than being propagated into the surroundingliquid.(16) The experimental data indicated that the first hydration shell may actlike a chemically distinct species whose overall size controls the macroscopicviscosity.

We have shown in the current study that the influence of the central ionreaches as far as 6 A for Li+; 7 A for Na+; and 9 A for K+ (see Fig. 4). Thisresult indicates that at least this size of hydration must be included explicitly whena simulation is performed for ionic aqueous solutions. The actual effect of thecentral ion, however, is small for the outer sphere (see Fig. 5). Therefore, fromthe experimental point of view, macroscopic properties may be explained only bytaking the first hydration shell into account; on the other hand, from a theoreticalpoint of view, the first hydration shell is subjected to the influence of the outershells, which must be included explicitly in simulation studies.

P1: GAD


900 Tanaka and Aida

4. CONCLUSION

The charge of the alkali metal ion in aqueous solution is not +1. The orbitalinteractions between the central alkali metal cation and the surrounding watermolecules reach as far as 6, 7, and 9 A for Li+, Na+, and K+, respectively. It isimportant to take account of the orbital interaction as well as the electrostatic inter-action between the alkali metal ion and the surrounding solvent water molecules.

ACKNOWLEDGMENTS

The authors acknowledge valuable discussions with M. Dupuis. The calcu-lations were carried out in part at the Research Center for Computational Science,Okazaki National Research Institute. This work was supported in part by the Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports,Science and Technology of Japan, and by a Grant from Asahi Glass Foundation.

REFERENCES

1. H. Ohtaki and T. Radnai, Chem. Rev. 93, 1157 (1993).2. S. H. Lee and J. C. Rasaiah, J. Chem. Phys. 101, 6964 (1994); S. H. Lee and J. C. Rasaiah, J. Phys.

Chem. 100, 1420 (1996); S. Koneshan, J. C. Rasaiah, R. M. Lynden-Bell, and S. H. Lee, J. Phys.Chem. B 102, 4193 (1998).

3. (a) L. M. Ramaniah, M. Bernasconi, and M. Parrinello, J. Chem. Phys. 111, 1587 (1999); A. P.Lyubartsev, K. Laasonen, and A. Laaksonen, J. Chem. Phys. 114, 3120 (2001). (b) A. Tongraar,K. R. Liedl, and B. M. Rode, Chem. Phys. Lett. 286, 56 (1998); H. H. Loeffler and B. M. Rode,J. Chem. Phys. 117, 110 (2002); H. H. Loeffler, A. M. Mohammed, Y. Inada, and S. Funahashi,Chem. Phys. Lett. 379, 452 (2003); H. H. Loeffler, J. Comput. Chem. 24, 1232 (2003); A. Tongraar,K. R. Liedl, and B. M. Rode, J. Phys. Chem. A 102, 10340 (1998).

4. M. Aida, H. Yamataka, and M. Dupuis, Int. J. Quantum. Chem. 77, 199 (2000).5. M. Dupuis, A. Marquez, and E. R. Davidson, HONDO 2002, available from the Quantum chemistry

Program Exchange, Indiana University.6. M. Freindorf and J. Gao, J. Comp. Chem. 17, 386 (1996).7. K. Heinzinger, Physica B, C 131, 196 (1985).8. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys.

79, 926 (1983).9. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V.

G. Zakrzewski, J. A. Montgomery, Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam,A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B.Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K.Morokuma, N. Rega, P. Salvador, J. J. Dannenberg, D. K. Malick, A. D. Rabuck, K. Raghavachari,J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu, A. Liashenko,P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y.Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L.Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle, and J. A. Pople, Gaussian 98, RevisionA.11.3 (Gaussian, Inc., Pittsburgh, PA, 2002).

10. W. J. Hehre, L. Radom, P. V. R. Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory(Wiley, New York, 1986).

P1: GAD



11. F. Jensen, Introduction to Computational Chemistry (Wiley, Chichester, UK, 1999).12. R. S. Mulliken, J. Chem. Phys. 23, 1833 (1955).13. A. E. Reed and F. Weinhold, J. Chem. Phys. 78, 4066 (1983).14. C. M. Breneman and K. B. Wiberg, J. Comp. Chem. 11, 361 (1990).15. Y. Marcus, Ion solvation (Wiley, Chichester, UK, 1985).16. A. W. Omta, M. F. Kropman, S. Woutersen, and H. J. Bakker, Science 301, 347 (2003).

Documents

An Ab Initio MO Study on Orbital Interaction and Charge Distribution in Alkali Metal Aqueous Solution: Li+, Na+, and K+