article density functional theory study on mechanism of

CHINESE JOURNAL OF CHEMICAL PHYSICS VOLUME 26, NUMBER 1 FEBRUARY 27, 2013

ARTICLE

Density Functional Theory Study on Mechanism of Forming Spiro-Ge-heterocyclic Ring Compound from Me2Ge=Ge: and Acetaldehyde

Xiu-hui Lu∗, Yong-qing Li, Wei-jie Bao, Dong-ting Liu

School of Chemistry and Chemical Engineering, University of Ji’nan, Ji’nan 250022, China

(Dated: Received on November 12, 2012; Accepted on December 10, 2012)

The H2Ge=Ge:, as well as and its derivatives (X2Ge=Ge:, X=H, Me, F, Cl, Br, Ph, Ar, . . .)is a kind of new species. Its cycloaddition reactions is a new area for the study of germy-lene chemistry. The mechanism of the cycloaddition reaction between singlet Me2Ge=Ge:and acetaldehyde was investigated with the B3LYP/6-31G∗ method in this work. Fromthe potential energy profile, it could be predicted that the reaction has one dominant re-action pathway. The reaction rule is that the two reactants firstly form a four-memberedGe-heterocyclic ring germylene through the [2+2] cycloaddition reaction. Because of the4p unoccupied orbital of Ge: atom in the four-membered Ge-heterocyclic ring germyleneand the π orbital of acetaldehyde forming a π→p donor-acceptor bond, the four-memberedGe-heterocyclic ring germylene further combines with acetaldehyde to form an intermedi-ate. Because the Ge atom in intermediate happens sp3 hybridization after transition state,then, intermediate isomerizes to a spiro-Ge-heterocyclic ring compound via a transition state.The research result indicates the laws of cycloaddition reaction between Me2Ge=Ge: and ac-etaldehyde, and lays the theory foundation of the cycloaddition reaction between H2Ge=Ge:and its derivatives (X2Ge=Ge:, X=H, Me, F, Cl, Br, Ph, Ar, . . .) and asymmetric π-bondedcompounds, which are significant for the synthesis of small-ring and spiro-Ge-heterocyclicring compounds.

Key words: Me2Ge=Ge:, Four-membered Ge-heterocyclic ring germylene, Spiro-Ge-heterocyclic compound, Potential energy profile

I. INTRODUCTION

Unsaturated germylenes is a kind of quite unstableactive intermediates. In 1997, Clouthier et al. ob-served the first unsaturated germylene−−germylidene(H2C=Ge:) [1], which was produced by striking anelectric discharge in a high-pressure argon pulse usingthe tetramethylgermane (TMG) vapor as the precur-sor. At the same time, ab initio calculations madepredictions of its molecular structure, electronic spec-trum, and oscillatory fluorescence decay of jet-cooledgermylidene (H2C=Ge:) [2], the ground state struc-ture of H2C=Ge: and D2C=Ge: [3] and the stimu-lated emission pumping (SEP) spectroscopy of the firstexcited singlet state of germylidene [4]. Stogner andGrev have done a lot of ab initio calculations on bothgermylidene and the trans-bent germyne HC≡GeH iso-mer [5]. They found that germylidene was the globalminimum on the H2C=Ge: potential energy surface,with germyne some 43 kcal/mol higher in energy. Thebarrier to germyne isomerization was predicted to be

∗Author to whom correspondence should be addressed. E-mail:[email protected]

only 7 kcal/mol and no stable linear germyne structurescould be found. With regard to the cycloadditon reac-tion of the unsaturated germylene, we have done someelementary discussion [6−9]. But these studies are lim-ited to the cycloaddition reaction of H2C=Ge: and itsderivatives (X2C=Ge:, X=H, Me, F, Cl, Br, Ph, Ar,. . .). There are no reports on the cycloaddition reac-tion of H2Ge=Ge: and its derivatives (X2C=Si:, X=H,Me, F, Cl, Br, Ph, Ar, . . .) until now, it is a new branchof unsaturated germylene’s cycloaddition reaction. Itis quite difficult to investigate mechanisms of cycload-dition reaction directly by experimental methods dueto the high activity of unsaturated germylene, there-fore, the theoretical study is more practical. To explorethe rules of cycloaddition reaction between H2Ge=Ge:(include its derivatives) and the asymmetric π-bondedcompounds, Me2Ge=Ge: and acetaldehyde were se-lected as model molecules, the cycloaddition reactionmechanism (considering the H and Me transfer simul-taneously) was investigated and analyzed theoretically.The results show that the cycloaddition reaction con-sists of four possible pathways, as follows:

DOI:10.1063/1674-0068/26/01/43-50 43 c©2013 Chinese Physical Society

44 Chin. J. Chem. Phys., Vol. 26, No. 1 Xiu-hui Lu et al.

II. COMPUTATIONAL METHODS

B3LYP/6-31G∗ implemented in the Gaussian 03package [10] is employed to locate all the stationarypoints along the reaction pathways. Full optimizationand vibrational analysis are done for the stationarypoints on the reaction profile. Zero point energy (ZPE)corrections are included for the energy calculations. Inorder to explicitly establish the relevant species, the in-trinsic reaction coordinate (IRC) [11, 12] is also cal-culated for all the transition states appearing on thecycloaddition energy surface profile. Density functionaltheory (DFT) has become one of the most importanttheories in the computational chemistry field due tomoderate amount of calculation and high calculationaccuracy. B3LYP method is the most widely used DFTmethod. Compared with other methods, B3LYP notonly has higher calculation accuracy of the molecularground state, but also considers the interrelation be-tween the electronic effect, thus, the energy is more ac-curate. Now, B3LYP is the most commonly used cal-culation method of quantum chemistry. In addition,B3LYP is quite accurate when dealing with clusters of

small molecular systems, and has got general recogni-tion of the chemists. This is also the reason that weselect B3LYP method in this work.

III. RESULTS AND DISCUSSION

A. Reaction (1): channels of forming the four-memberedGe-heterocyclic ring germylene (P1), Me-transferProducts (P1.1 and P1.2), and H-transfer products (P1.3)

Theoretical researchs show that the ground state ofMe2Ge=Ge: is a singlet state. The geometrical param-eters of the intermediate (INT1), transition states (TS1,TS1.1, TS1.2, and TS1.3), and products (P1, P1.1,P1.2, and P1.3) which appear in reaction (1) betweenMe2Ge=Ge: and acetaldehyde are given in Fig.1, theenergies are listed in Table I, and the potential energyprofile for the cycloaddition reaction is shown in Fig.2.According to Fig.2, it can be seen that the reaction (1)consists of five steps: the first one is that the two re-actants (R1, R2) form an intermediate (INT1), whichis a barrier-free exothermic reaction of 77.3 kJ/mol;

DOI:10.1063/1674-0068/26/01/43-50 c©2013 Chinese Physical Society

Chin. J. Chem. Phys., Vol. 26, No. 1 Spiro-Ge-heterocyclic Ring Compound 45

1.95184.1

71.4103.179.9

113.171.9112.6

74.0

87.4108.6128.3

89.7125.2 120.3

Ge1Ge2OC1=51.6

C3

2.290

106.669.5

82.51.353

1.984105.469.3

C4

C3C3

C3

C3

C3

C3C3

C3

C3

C4

C4

C4C4C4

C4

C4C4

C4

C1C1

C1

C1

C1

C1

C1C1C1

C2

C1C2

C2

C2

C2C2C2

C2C2C2

Ge1

Ge1

Ge2Ge2Ge2

Ge2

Ge2

Ge2

Ge2

Ge2Ge2Ge2

Ge1Ge1

Ge1

Ge1Ge1

Ge1Ge1

Ge1

R1

O

O

OOO

OO

OOO

1.829

1.257

2.0911.241

2.0771.224

2.512

2.178

1.251

2.512

1.246

2.205

2.534

1.351

2.5072.409

1.814

1.416

1.8971.458

R2 Ge1Ge2OC1=64.4

Ge1Ge2OC1=2.6

Ge1Ge2OC1=-0.2

Ge1Ge2OC1=19.3

Ge1Ge2OC1=-44.7

Ge1Ge2OC1=5.5

Ge1Ge2OC1=46.3

Ge1Ge2OC1=-3.6

2.316 2.330

2.5102.496

70.2

INT1 TS1

P1 TS1.1 P1.1 TS1.2

P1.2 TS1.3 P1.3

Ge1

FIG. 1 Optimized B3LYP/6-31G∗ geometrical parameters and the atomic numbering for the species in cycloaddition reaction(1). Bond lengths are in A, bond angles and dihedral angles are in (◦).

the second step is INT1 isomerizes to a four-memberedGe-heterocyclic ring germylene (P1) through transitionstate (TS1) with an energy barrier of 6.1 kJ/mol; thethird, fourth, and fifth steps are that the P1 undergoesMe and H transfer via transition states TS1.1, TS1.2,and TS1.3 with energy barriers of 118.8, 180.9, and116.2 kJ/mol, respectively, resulting in the formationof products P1.1, P1.2, and P1.3. Because the energiesof P1.1, P1.2, and P1.3 are 55.6, 56.2, and 38.5 kJ/molhigher than that of P1, so the reactions of P1→P1.1,P1→P1.2, and P1→P1.3 are prohibited in thermody-namics at the normal temperature and pressure, reac-tion (1) will end in product P1.

B. Reaction (2): channel of forming a spiro-Ge-hetero-cyclic ring compound (P2)

In reaction (2), the four-membered Ge-heterocyclicring germylene (P1) further reacts with acetaldehyde(R2) to form a spiro-Ge-heterocyclic ring compound(P2). The geometrical parameters of intermediate(INT2), transition state (TS2) and product (P2) which

appear in reaction (2) are given in Fig.3. The energiesare listed in Table I, and the potential energy profile forthe cycloaddition reaction is shown in Fig.2.

According to Fig.2, it can be seen that the processof reaction (2) as follows: on the basis of P1 formedfrom the reaction (1) between R1 and R2, the P1 fur-ther reacts with acetaldehyde to form an intermedi-ate (INT2), which is a barrier-free exothermic reac-tion of 58.0 kJ/mol; next, the intermediate (INT2) iso-merizes to a spiro-Ge-heterocyclic ring compound (P2)via a transition state (TS2) with an energy barrier of23.8 kJ/mol. The reaction of INT2→P2 is endother-mic reaction, because the energie of P2 is 10.3 kJ/molhigher than that of INT2.

C. Reaction (3): channels of forming four-memberedGe-heterocyclic ring germylene (INT3), Me-transferproducts (P3 and P3.1), H-transfer product (P3.2)

The geometrical parameters of four-membered Ge-heterocyclic ring germylene (INT3), transition states(TS3, TS3.1, and TS3.2) and products (P3, P3.1, and



R1+R

2 0

.0

P1+R

2 0

.0TS

1.2 -0

.4IN

T3+R

2

0.0

P2

-47.7

TS1.1

-62.5

INT4

-88.

9

P1

-181

.3

TS1

-71.2

INT1

-77.3

TS3

.1 -

70.3

TS3

-92.2

TS3.2

-116

.2 IN

T3-1

27.2

E / (kJ/mol)

P1.1

-125

.7

-61.5

TS1

.3

P3.1

-139

.8

P3

-125

.8 P3.2

-161

.2

TS2

-34.2

INT2

-58.0

P1.2

-125

.1

P1.3

-142

.8

TS4

-49.

2

0

-50

-100

-150

-200

R FIG

. 2 T

he po

tentia

l ene

rgy p

rofil

e for

the c

yclo

addi

tion r

eacti

ons b

etwee

n Me

Ge=G

e: an

d MeH

C=O

with

B3L

YP/6

-31G

.

-250

2 *

P4

-93.8



TABLE I Zero point energy (ZPE), total energies (ET) and relative energies (ER) for the species from B3LYP/6-31G∗

method.

Reaction Species ZPE/a.u ETa/a.u ER

b/(kJ/mol)

Reaction (1) R1+R2 0.12994 −4383.47311 0.0

INT1 0.13212 −4383.50254 −77.3

TS1 (INT1-P1) 0.13174 −4383.50023 −71.2

P1 0.13404 −4383.54216 −181.3

TS1.1 (P1-P1.1) 0.13129 −4383.49692 −62.5

P1.1 0.13319 −4383.52098 −125.7

TS1.2 (P1-P1.2) 0.13062 −4383.47328 −0.4

P1.2 0.12971 −4383.52076 −125.1

TS1.3 (P1-P1.3) 0.12842 −4383.49791 −65.1

P1.3 0.12832 −4383.52750 −142.8

Reaction (2) P1+R2 0.18985 −4537.31647 0.0

INT2 0.19202 −4537.33857 −58.0

TS2 (INT2-P2) 0.19112 −4537.32951 −34.2

P2 0.19318 −4537.33462 −47.7

Reaction (3) R1+R2 0.12994 −4383.47311 0.0

INT3 0.13269 −4383.52155 −127.2

TS3 (INT3-P3) 0.13224 −4383.50821 −92.2

P3 0.13317 −4383.52101 −125.8

TS3.1 (INT3-P3.1) 0.13060 −4383.49987 −70.3

P3.1 0.13066 −4383.52637 −139.8

TS3.2 (INT3-P3.2) 0.12789 −4383.51738 −116.2

P3.2 0.12801 −4383.53451 −161.2

Reaction (4) INT3+R2 0.18849 −4537.29588 0.0

INT4 0.19156 −4537.32975 −88.9

TS4 (INT4-P4) 0.19001 −4537.31462 −49.2

P4 0.19246 −4537.33161 93.8

a ET=ESpecies+ZPE.b ER=ET−E(R1+R2) for reaction (1) and reaction (3), ER=ET−E(P1+R2) for reaction (2), and ER=ET−E(INT3+R2) forreaction (4).

P3.2) which appear in reaction (3) between Me2Ge=Ge:and acetaldehyde are given in Fig.4. The energies arelisted in Table I, and the potential energy profile forthe cycloaddition reaction is shown in Fig.2. Accord-ing to Fig.2, it can be seen that reaction (3) consistsof four steps: the first step is that the two reactants(R1, R2) form a four-membered Ge-heterocyclic ringgermylene (INT3), which is a barrier-free exothermicreaction of 127.2 kJ/mol. The second and third stepis that the INT3 undergoes Me-transfer Ge1−Ge2 andC1−Ge2 via transition states TS3 and TS3.1 with en-ergy barriers of 35.0 and 56.9 kJ/mol, resulting in theformation of products P3 and P3.1. The fourth step isthat the INT3 undergoes H-transfer C1−Ge2 via tran-sition state TS3.2 with energy barrier of 11.0 kJ/mol,resulting in the formation of product P3.2. Because theenegies of P3 are 1.4 kJ/mol higher than that of INT3and the energy barrier of TS3.1 is 45.9 kJ/mol higherthan that of TS3.2, so INT3→P3.2 is the dominant re-

action pathway of reaction (3).According to Fig.1, Fig.2, and Fig.4, it can be seen

that INT1 and INT3 are isomerides, the equilibriumdistributions of INT1 and INT3 are

PrINT1=KINT1/KINT1+KINT3≈0.0PrINT3 =KINT3/KINT1+KINT3≈1.0

So, INT3 is the main distribution.

D. Reaction (4): channel of forming spiro-Ge-heterocyclicring compound (P4)

In reaction (4), the four-membered Ge-heterocyclicring germylene (INT3) further reacts with acetalde-hyde (R2) to form a spiro-Ge-heterocyclic ring com-pound (P4). The geometrical parameters of interme-diate (INT4), transition state (TS4) and product (P4)which appear in reaction (4) are given in Fig.5. Theenergies are listed in Table I, and the potential energy



69.490.8123.3

1.843

Ge1Ge2O1C1=-4.9

C3C3

C3

C4C4C4

C1C1C1 C2C2

C2Ge2Ge2Ge2

Ge1Ge1Ge1

O1O1O1

1.858

1.838

2.698

1.235

2.200

1.848

Ge1Ge2O1C1=-5.8 Ge1Ge2O1C1=-8.6

C5 C6

O2 C5

C6O2

C5

C6O2

1.447

O2Ge2Ge1C1=-91.9 O2Ge2Ge1C1=-91.6 O2Ge2Ge1C1=-102.8

C5O2Ge2Ge1=-90.4 C5O2Ge2Ge1=165.7 C5O2Ge2Ge1=-160.4 INT2 TS2 P2

FIG. 3 Optimized B3LYP/6-31G∗ geometrical parameters of INT2, TS2, P2, and the atomic numbering for cycloadditionreaction (2). Bond lengths are in A, bond angles and dihedral angles are in (◦).

2.528

98.8

98.677.3103.3

79.786.298.2102.5

80.3

Ge1Ge2C1O=-1.3

C3

99.976.578.1

1.324

99.175.2C4

C3C3C3

C3

C3C3

C4C4

C4

C4C4

C4

C1

C1

C1C1C1C1

C2

C1

C2

C2

C2C2C2C2

Ge2Ge2

Ge2

Ge2Ge2Ge2

Ge2

Ge1 Ge1Ge1

Ge1Ge1Ge1Ge1

OOO

O

OOO1.815

1.4561.817

1.4321.851

2.357

2.481

1.285

2.514

1.299

2.476

2.00

2.4122.497

1.3301.9271.453

Ge1Ge2C1O=-5.3

Ge1Ge2C1O=17.5

Ge1Ge2C1O=0.0

Ge1Ge2C1O=-18.1

Ge1Ge2C1O=-0.7

Ge1Ge2C1O=12.2

INT3 TS3 P3 TS3.1

P3.1 TS3.2 P3.2

1.990

FIG. 4 Optimized B3LYP/6-31G∗ geometrical parameters of INT3, TS3, P3, TS3.1, P3.1, TS3.2, P3.2, and the atomicnumbering for cycloaddition reaction (3). Bond lengths are in A, bond angles and dihedral angles are in (◦).

profile for the cycloaddition reaction is shown in Fig.2.

According to Fig.2, it can be seen that the processof reaction (4) as follows: on the basis of the two reac-tants (R1, R2) to form INT3, it further reacts with ac-etaldehyde (R2) to form an intermediate (INT4), whichis a barrier-free exothermic reaction of 88.9 kJ/mol.And then intermediate (INT4) isomerizes to a spiro-Ge-heterocyclic ring compound (P4) via a transition state(TS4) with an energy barrier of 39.7 kJ/mol. Com-paring reaction (4) with reaction (3), it is realized thatthe two reactions compete mutually due to scramblingfor INT3 together. In reaction (4), INT3+R2→INT4can directly reduce the system energy of 88.9 kJ/mol.In reaction (3), the energy barrier of INT3→P3.2 is11.0 kJ/mol, therefore, reaction (4) is the dominant re-action channel.

E. Theoretical analysis and explanation of the dominantreaction channel

According to the above analysis, there is only onedominant reaction channel of the cycloaddition reac-tion between singlet Me2Ge=Ge: and acetaldehyde asfollows:

R1+R2→INT3+R2→INT4

TS4→P4 (4)In the reaction, the frontier molecular orbitals of R2

and INT3 are shown in Fig.6. According Fig.6, thefrontier molecular orbitals of R2 and INT3 can be ex-pressed in schematic diagram (Fig.7). The mechanismof the reaction could be explained with the molecu-lar orbital diagram (Fig.7) and Fig.1, Fig.4, and Fig.5.According to Fig.1 and Fig.4, as Me2Ge=Ge: ini-tially interacts with acetaldehyde, the [2+2] cycload-



1.422

97.6126.71.245

Ge2Ge1O1C1=18.4

C3 C3C3

C4C4

C4

C1C1C1

C2C2C2

Ge2Ge2

Ge2

Ge1Ge1Ge1

O1O1O1

1.878

1.230

2.4882.0602.490

Ge2Ge1O1C1=-1.9 Ge2Ge1O1C1=2.3

C5C6

O2

C5C6

O2

C5

C6O2

2.4122.439

70.2

O2Ge2Ge1O1=-106.1 O2Ge2Ge1O1=-85.7 O2Ge2Ge1O1=-113.0

C5O2Ge2Ge1=-80.5

C5O2Ge2Ge1=-128.8

C5O2Ge2Ge1=-143.9 INT4 TS4 P4

FIG. 5 Optimized B3LYP/6-31G∗ geometrical parameters of INT4, TS4, P4 and the atomic numbering for cycloadditionreaction (4). Bond lengths are in A, bond angles and dihedral angles are in (◦).

HOMO of R2 HOMO of INT3 LOMO of INT3

sp 4p

π

FIG. 6 The frontier molecular orbitals of R2 and INT3.

dition of the bonding π-orbitals firstly results in a four-membered Ge-heterocyclic ring germylene (INT3). Be-cause the INT3 is an active intermediate, INT3 fur-ther reacts with acetaldehyde (R2) to form a spiro-Ge-heterocyclic ring compound (P4). The mechanism ofthe reaction could be explained with Fig.5 and Fig.7, ac-cording to orbital symmetry matching condition, whenINT3 interacts with acetaldehyde (R2), the 4p unoc-cupied orbital of the Ge2 atom in INT3 will insertthe π orbital of acetaldehyde from oxygen side, thenthe shift of π-electrons to the p unoccupied orbitalfrom a π→p donor-acceptor bond, leading to the for-mation of intermediate (INT4). As the reaction goeson, the ∠C5O2Ge2Ge1 (INT4: −80.5◦, TS4: −128.8◦,P4: −143.9◦) gradually increase, ∠C5O2Ge2 (INT4:126.7◦, TS4: 97.6◦, P4: 70.2◦) gradually decrease, theGe2 in INT4 happens sp3 hybridization after the tran-sition state (TS4), forming a spiro-Ge-heterocyclic ringcompound (P4).

IV. CONCLUSION

On the basis of the potential energy profile the cy-cloaddition reaction between singlet Me2Ge=Ge: andacetaldehyde obtained with the B3LYP/6-31G∗ methodcan be predicted. This reaction has one dominant chan-

C5

Ge1

INT3

R2 O2π

O1

Ge2

Me

Me

Me

H

_

+

C1

4p

sp

H

Me

FIG. 7 A schematic interaction diagram for the frontierorbitals of INT3 and MeHC=O (R2).

nel. It consists of three steps: the first step is thatthe two reactants (R1, R2) form a four-membered Ge-heterocyclic ring germylene (INT3), which is a barrier-free exothermic reaction of 127.2 kJ/mol; the secondstep is that INT3 further reacts with acetaldehyde (R2)to form an intermediate (INT4), which is also a barrier-free exothermic reaction of 88.9 kJ/mol; the third stepis that intermediate (INT4) isomerizes to a spiro-Ge-heterocyclic ring compound (P4) via a transition state(TS4) with an energy barrier of 39.7 kJ/mol.

The π orbital of X2Ge=Ge: (X=H, Me, F, Cl, Br,Ph, Ar, . . .) and the 4p unoccupied orbital of Ge: inX2Ge=Ge: (X=H, Me, F, Cl, Br, Ph, Ar, . . .) are theobject in cycloaddition reaction of X2Ge=Ge: and theasymmetric π-bonded compounds. The [2+2] cycload-dition reaction between the π orbital of X2Ge=Ge: andthe bonding π orbital of the asymmetric π-bonded com-pounds leads to the formation of the four-memberedGe-heterocyclic ring germylene. The 4p unoccupied or-bital of Ge: atom in the four-membered Ge-heterocyclicring germylene further reacts with the bonding π or-bital of the asymmetric π-bonded compounds to form



an intermediate. The Ge: atom in the intermediatehappens sp3 hybridization, the intermediate isomerizesto a spiro-Ge-heterocyclic ring compound.

V. ACKNOWLEDGMENT

This work was supported by the National NaturalScience Foundation of China (No.51102114).

[1] W. H. Harper, E. A. Ferrall, R. K. Hilliard, S. M.Stogner, R. S. Grev, and D. J. Clouthier, J. Am. Chem.Soc. 119, 8361 (1997).

[2] D. A. Hostutler, T. C. Smith, H. Y. Li, and D. J.Clouthier, J. Chem. Phys. 111, 950 (1999).

[3] D. A. Hostutler, D. J. Clouthier, and S. W. Pauls, J.Chem. Phys. 116, 1417 (2002).

[4] S. G. He, B. S. Tackett, and D. J. Clouthier, J. Chem.Phys. 121, 257 (2004).

[5] S. M. Stogner and R. S. Grev, J. Chem. Phys. 108,5458 (1998).

[6] X. H. Lu, Y. H. Xu, H. B. Yu, and W. R. Wu, J. Phys.Chem. 109, 6970 (2005).

[7] X. H Lu, Y. H Xu, P. P Xiang, and X. Che, Int. J.Quant. Chem. 108, 75 (2008).

[8] C. L Tian, Y. H Xu, and X. H Lu, Int. J. Quant. Chem.110, 1675 (2010).

[9] X. H. Lu, Y. H. Xu, L. Y. Shi, J. F. Han, and Z. X.Lian, J. Organomet. Chem. 694, 4062 (2009).

[10] C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785(1988).

[11] K. Fukui, J. Phys. Chem. 74, 4161 (1970).[12] K. Ishida, K. Morokuma, and A. Komornicki, J. Chem.

Phys. 66, 2153 (1981).


article density functional theory study on mechanism of

Documents