Existing problems in theoretical determination of red-shifted

or blue-shifted hydrogen bond

Ping Lua, Guo-Qun Liub,*, Ji-Chao Lic

aSchool of Chemistry and Chemical Engineering, Jinan University, Jinan 250022, ChinabNew Material Research Institute, Shandong Academy of Sciences, Keyuan Road 19, Jinan 250014, China

cSchool of Physics and Microelectronics, Shandong University, Jinan 250100, China

Received 20 October 2004; accepted 20 January 2005

Available online 2 April 2005

Abstract

Both Hobza (Int. J. Quantum Chem., 90 (2002) 1071) and Li et al. (J. Am. Chem. Soc., 124 (2002) 9639) have predicted a blue-

shifted or improper N–H/F hydrogen bond existing in the F2N–H/FH complex with the method of Hartree–Fock calculation

followed by Møller–Plesset correlation energy correction truncated at second order (MP2/6-31G** and MP2/6-311CG**,

respectively). Unexpectedly, our density functional calculation (B3LYP) has predicted a red-shifted or normal N–H/F hydrogen

bond in this complex whether the counterpoise-corrected gradient optimization and frequency calculation is applied or not. Changing

the basis set from 6-311CG(d,p) to 6-311CCG(3df,3pd) does not change the red-shifted hydrogen bond prediction. Experimental

identification should be provided for evaluating relative performance of these two theoretical methods in predicting correct hydrogen

bond stretching vibration frequency shift upon complex formation. X–H bond length change and its vibrational frequency change do

not necessarily have monotonic corresponding relationship, i.e. blue-shift does not necessarily mean X–H bond length contraction, and

vice versa. Much more attention or consideration should be paid in theoretical hydrogen bond type prediction such as red-shifted or

blue-shifted.

q 2005 Elsevier B.V. All rights reserved.

Keywords: Hydrogen bond; Red-shift and blue-shift; MP2 and B3LYP; F2N–H/FH complex

1. Introduction

Theoretical computation plays an increasingly important

role in the determination of red-shifted or blue-shifted

hydrogen bonds (H-bonds) [1–5]. Generally, H-bond has the

form of X–H/Y, where X is an electronegative atom and Y

is either an electronegative atom or p-electrons of aromatic

systems. Red-shifted H-bond formation leads to decrease of

the X–H stretching vibrational frequency and usually to

X–H bond length elongation while blue-shifted H-bond

formation leads to increase of X–H vibrational frequency

and usually to X–H bond length contraction [6,7]. Thus it is

0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.theochem.2005.01.034

* Corresponding author. Tel.: C86 5312605935; fax: C86 5312962527.

E-mail addresses: liugq@keylab.net (G.-Q. Liu), liugq@icm.sdu.

edu.cn (G.-Q. Liu).

easy to predict the H-bond type by calculating and

comparing X–H bond length and vibrational frequency of

the H-bonded system with those of the monomer or non-H-

bonded system. Many theoretical methods, such as MP2 and

B3LYP, can implement this prediction and their perform-

ance is decided by whether the predicted results are in

accord with the experimental measurement or not.

Up to now, there is no contradictory hydrogen bond type

prediction reported between MP2 and B3LYP calculations.

Alabugin et al. have compared the results obtained by

MP2(FC)/6-31CG* calculation with those obtained by

B3LYP/6-311CG** computation and concluded that ‘the

B3LYP results parallel the MP2 data quite closely’ in

studying C–H/Y hydrogen bond formed by F3C–H and

other related molecules [5]. Both MP2 and B3LYP

computation have their own supporting instances from the

point of agreement between theoretical prediction and

experimental measurement. MP2/6-31G* counterpoise

(CP)-corrected gradient optimization, harmonic and

Journal of Molecular Structure: THEOCHEM 723 (2005) 95–100

www.elsevier.com/locate/theochem

P. Lu et al. / Journal of Molecular Structure: THEOCHEM 723 (2005) 95–10096

anharmonic vibrational analysis is in accord with the

double-resonance infrared ion-depletion spectroscopy in

identification of the C–H/p improper hydrogen bond

formed by Cl3C–H and fluorobenzene with the blue-shift

being 12 (theoretical) and 14 (experimental) cmK1,

respectively [8]. On the other hand, Matsuura et al. have

evidenced an intramolecular C–H/O improper hydrogen

bond in the TG(TjG 0) conformer of 1-methoxy-2-(dimethyl-

amino)ethane with the aid of matrix-isolation infrared

spectroscopy and density functional calculation (B3LYP/

6-311CG**) [1]. In this paper, we will report the first

occurrence of disagreement between MP2 and B3LYP

calculation in predicting hydrogen bond type of the

F2N–H/FH complex.

Li et al. have drawn three plots of the X–H vibrational

frequency against the X–H bond length, which gives straight

lines with high correlation coefficients (0.9900–0.9991), and

concluded that ‘blue-shift means X–H contraction, and vice

versa’ [4]. Alabugin et al. have predicted the normal or

improper H-bonds based on elongation or contraction of the

X–H bond length, which obviously follows Li et al.’s

conclusion [5]. However, as a matter of fact, in the complex

of F2N–H/FH, Li et al. have identified the improper

H-bond based on the vibrational frequency change but not

the N–H bond length change between the monomer and the

complex. In this paper, we will discuss the relationship

between X–H bond length change and X–H vibrational

frequency change so that we can choose a more rigid and

credible criterion to identify the H-bond type.

Fig. 1. Structure and atom labels of F2NH/FH complex.

2. Computational description

All computation was performed with the Gaussian 03

program [9]. Theoretical methods used for identifying

hydrogen bond include Hartree–Fock (HF), density func-

tional theory (Becke’s three parameter hybrid functional

[10] in conjunction with Lee, Yang, and Parr’s correlation

functional [11], abbreviated as B3LYP), and MP2 (request-

ing a Hartree–Fock calculation followed by Møller–Plesset

correlation energy correction truncated at second order

[12,13]). The MP2 method still includes two types of

calculations, i.e. FC (FrozenCore, in which inner shells are

excluded from the correlation calculation) and Full (which

specifies that all electrons be included in the correlation

calculation). The monomers F2N–H and F3C–H are kept as

Cs and C3v symmetry, respectively while the complexes

F2N–H/FH and F3C–H/NH3 are broken the symmetry

constraint during the optimization and frequency calcu-

lation process. For the complexes F2N–H/FH and

F3C–H/NH3, both standard and counterpoise-corrected

[14,15] gradient optimization are performed and followed

by vibrational frequency calculation to confirm the actual

minima obtained.

3. Results and discussion

3.1. Contradictory hydrogen bond type prediction between

MP2 and B3LYP calculation for the complex F2N–H/FH

Fig. 1 shows the hydrogen-bonded structure of F2N–H/FH. From N–H vibrational frequency change between the

monomer and the complex shown in Table 1, we can see

that contradictory H-bond type prediction between MP2 and

B3LYP calculation is obvious. For example, B3LYP/

6-31CG** computation predicts that N–H vibrational

frequency of the monomer and the complex is 3369 and

3354 cmK1, respectively, which implies 15 cmK1 red-shift

of the N–H vibrational frequency after the H-bond

formation. On the other hand, MP2(FC)/6-31CG** com-

putation predicts 4 cmK1 blue-shift of the N–H vibrational

frequency with that of the monomer and the complex being

3472 and 3476 cmK1, respectively. The full electrons

correlation (MP2(FU)/6-31CG**) result, which predicts

3 cmK1 blue-shift, has almost no difference with that of the

frozen core correlation calculation. As far as the H-bond

type prediction is concerned, the HF/6-31CG** compu-

tation results are in accord with those of the MP2 but not

with those of B3LYP, which also implies that electron

correlation is not crucial for H-bond type identification

[4,5]. As shown in columns 2, 3 and 7, 8 of Table 1, it seems

that the larger the basis set is (from 6-31CG** to 6-311CG**), the less the difference of bond length change (from

0.0004, 0.0009 A to 0.0001, 0.0001 A) and vibrational

frequency change (from 11, 4 cmK1 to 14, 16 cmK1)

between Hartree–Fock and MP2 calculation is, which

implies that basis set choice is important in H-bond

determination. Influence of basis sets is also investigated

for B3LYP calculation, which proves that the largest built-

in basis set available in Gaussian 03 program, 6-311CCG(3df,3pd), cannot change its red-shifted H-bond prediction

either.

Taking the (HF)2 dimer as an example, Hobza and Havlas

have pointed out the necessity of using the CP-corrected

gradient optimization [16]. Whether the CP-correction is

applied or not will affect not only the interaction energy but

also the geometry and vibrational frequency of the X–H/Y

H-bond [17,18]. However, contradictory N–H H-bond type

prediction for the F2N–H/FH complex between B3LYP

Table 1

Geometrical and vibrational frequency parameters of the monomers F2NH and HF, as well as their complex F2NH/FH at different level of theory and with different (standard or CP-corrected) gradient

optimization and frequency calculation

Method HF HF B3LYP B3LYP B3LYP MP2(FC) MP2(FC) MP2(FU) MP2(FU)

Basis 6-31CG** 6-311CG** 6-31CG** 6-311CG** 6-311CC

G(3df,3pd)

6-31CG** 6-311CG** 6-31CG** 6-311CG**

r(N–H1),ma 1.0056 1.0055 1.0308 1.0295 1.0266 1.0265 1.0263 1.0256 1.0257

r(N–F1),m 1.3541 1.3433 1.4102 1.4035 1.3977 1.4154 1.3915 1.4140 1.3903

r(N–H1),ca,b 1.0060 1.0056 1.0331 1.0311 1.0286 1.0274 1.0264 1.0265 1.0258

CP-correctedb 1.0057 1.0054 1.0329 1.0308 1.0281 1.0269 1.0261 1.0259 1.0255

r(N–F1),c 1.3532 1.3432 1.4029 1.3966 1.3899 1.4109 1.3901 1.4099 1.3892

CP-corrected 1.3546 1.3441 1.4037 1.3979 1.3899 1.4122 1.3915 1.4114 1.3904

r(N–F2),c 1.3625 1.3501 1.4286 1.4203 1.4168 1.4274 1.4009 1.4265 1.4001

CP-corrected 1.3605 1.3485 1.4271 1.4181 1.4151 1.4242 1.3983 1.4227 1.3971

n(N–H1)/Ic,m 3736/10 3707/7 3369/2 3352/1 3363/2 3472/3 3441/2 3476/3 3346/2

n(N–H1)/I,c 3747/46 3721/37 3354/40 3344/36 3351/35 3476/40 3457/32 3479/38 3462/32

CP-corrected 3750/51 3724/41 3356/42 3348/36 3356/37 3483/42 3462/32 3487/42 3467/33

Dr(N–H1)d 0.0004 0.0001 0.0023 0.0016 0.0020 0.0009 0.0001 0.0009 0.0001

CP-corrected 0.0001 K0.0001 0.0021 0.0013 0.0015 0.0004 K0.0002 0.0003 K0.0002

Dn(N–H1)d,e 11 14 K15 K8 K12 4 16 3 16

CP-corrected 14 17 K13 K4 K7 11 21 11 21

:N–H1/F3f 134.4 135.0 132.7 133.0 131.0 134.7 136.1 134.8 136.1

CP-corrected 140.3 140.8 134.2 133.0 132.8 140.0 142.1 140.1 142.2

r(H1/F3) 2.2157 2.2240 2.1452 2.1531 2.1829 2.1514 2.1647 2.1508 2.1642

CP-corrected 2.1963 2.2116 2.1452 2.1531 2.1741 2.1597 2.1923 2.1591 2.1915

r(F3–H2),m 0.9021 0.8976 0.9279 0.9222 0.9221 0.9265 0.9166 0.9262 0.9163

r(F3–H2),c 0.9050 0.9002 0.9332 0.9273 0.9279 0.9308 0.9201 0.9306 0.9198

CP-corrected 0.9046 0.8998 0.9326 0.9265 0.9272 0.9295 0.9191 0.9293 0.9188

n(F3–H2),m 4473/176 4489/192 4068/115 4096/130 4090/106 4118/125 4198/142 4118/127 4201/142

n(F3–H2),c 4425/187 4428/204 3978/145 4016/146 3985/157 4053/138 4148/147 4052/138 4150/148

CP-corrected 4433/196 4454/216 3990/137 4029/145 4000/139 4076/138 4163/160 4073/138 4165/160

Dr(F3–H2) 0.0029 0.0026 0.0053 0.0051 0.0058 0.0043 0.0035 0.0044 0.0035

CP-corrected 0.0025 0.0022 0.0047 0.0043 0.0051 0.0030 0.0025 0.0031 0.0025

Dn(F3–H2) K48 K41 K90 K80 K105 K65 K50 K66 K50

CP-corrected K60 K35 K78 K67 K90 K42 K35 K45 K36

:F3–H2/F2 102.8 96.3 119.3 114.4 125.6 113.5 103.8 113.5 103.8

CP-corrected 91.5 85.7 116.1 111.0 122.3 102.3 91.3 102.0 91.0

r(H2/F2) 2.4928 2.6263 2.1254 2.2130 2.0525 2.2552 2.4612 2.2549 2.4606

CP-corrected 2.7987 2.9295 2.2052 2.2990 2.1287 2.5518 2.8304 2.5588 2.8375

a m refers to the monomers while c refers to the complex.b Standardly and CP-correctedly optimized parameters for the complex.c Calculated infrared intensity.d These differences are between the monomers and the complex.e Units for bond length, bond angle, and stretching vibrational frequency are A, degree, and cmK1 respectively.f Atom labels are referred to Fig. 1.

P.

Lu

eta

l./

Jou

rna

lo

fM

olecu

lar

Stru

cture:

TH

EO

CH

EM

72

3(2

00

5)

95

–1

00

97

P. Lu et al. / Journal of Molecular Structure: THEOCHEM 723 (2005) 95–10098

and MP2 calculation still exists, as shown in Table 1, in spite

of application of the CP-correction. Consequently, this

contradictory prediction cannot originate from the effect of

basis set superposition error. On the other hand, the

introduction of CP-correction makes vibrational frequency

difference between the monomer and the complex become

smaller for the B3LYP calculation but larger for the MP2

calculation.

As shown in Fig. 1 and Table 1, there probably exists

another red-shifted F3–H2/F2 H-bond [19]. Relative to the

N–H1/F3 H-bond, its vibrational frequency difference

between the monomer and the complex is very large at all

kinds of theoretical levels. This large difference is partly due

to the F3–H2 bond weakening brought on by the N–H1/F3

H-bond formation [4,5]. Another origin will be the formation

of the H-bond F3–H2/F2, which is reflected by the bond

length difference between N–F1 and N–F2 shown in Table 1.

Thus the question appears naturally that whether the

contradictory prediction is brought on by the double

H-bond system or not since the complex is formed by two

weakly-interacted independent molecules? This is also not

the case. Li et al. have identified an intramolecular blue-

shifted H-bond system (C7H8N2O2) as shown in Fig. 2(b) at

Fig. 2. A geometrically constrained hydrogen bonding system (a) not

hydrogen bonded (b) hydrogen bonded.

the MP2(FC)/6-311CG(d,p) level of theory with Gaussian

99 [4]. According to their computation, N–H bond length and

vibrational frequency of the non-hydrogen bonded and

hydrogen bonded system are 0.9934 A, 3899.7 cmK1 and

0.9920 A, 3916.0 cmK1, respectively. However, our com-

putation at the B3LYP/6-311CG(d,p) level of theory reveals

that N–H bond length and vibrational frequency of the non-

hydrogen bonded and hydrogen bonded system are 1.0100 A,

3613.4 cmK1 and 1.0102 A, 3595.7 cmK1, respectively, for

the same two stable planar conformers (a) and (b) shown in

Fig. 2, which shows contradictory prediction between MP2

and B3LYP computation again!

3.2. Relationship between X–H bond length change and its

stretching vibrational frequency change in a hydrogen

bonded system

Experimentally considering, the red-shifted H-bond

refers to that the measured infrared vibrational frequency

of an X–H bond in the complex is lower than that in the

monomer and blue-shifted H-bond refers to that the

measured frequency of the complex is higher than that of

the monomer. Thus both of them, whether red-shifted or

blue-shifted H-bond, can be determined experimentally by

frequency red-shift or blue-shift. However, the X–H bond

length change is too hard to distinguish in the experimental

manner. (The X-ray diffraction experiment cannot determine

the hydrogen atom and the neutron diffraction experiment

has no enough resolving power to distinguish the tiny change

of the X–H bond length upon the H-bond formation.) From

the point of theoretical computation, both of the X–H bond

length change and its stretching vibrational frequency

change can be identified easily. For small complex molecules

such as F2N–H/FH and F3C–H/NH3, the X–H bond

length and vibrational frequency can be computed easily in

both of the B3LYP and MP2 level of theory with moderate

basis set. For larger molecules such as shown in Fig. 2(a) and

(b), B3LYP calculation has no much more difficulty while it

is not a piece of cake for MP2 calculation because of the large

disk and memory usage. For much more larger complex

molecules, B3LYP is also difficult for frequency calculation.

As we know, bond length calculation (i.e. geometry

optimization) is much easier than frequency calculation,

especially for larger systems. If we can confirm that the X–H

bond length change is completely in accord with the X–H

vibrational frequency change upon H-bond formation, then

the X–H bond length change will be preferred as a criterion

for identifying H-bond type.

Although Li et al. have provided such description that

‘blue-shift means X–H contraction, and vice versa’ they still

use the frequency change criterion but not the bond length

change criterion to identify H-bond type for N–H hydrogen

bond in the complex F2N–H/FH (see Table 2 of ref. [4]).

Alabugin et al. have predicted the red-shifted or blue-shifted

H-bonds based on the elongation or contraction of the X–H

bond length and obviously followed the above Li et al.’s

Table 2

Geometry and vibrational frequency parameters of the C–H/N H-bond in

the F3C–H/NH3 complex at MP2/6-311CG(d,p) and B3LYP/6-311C

G(d,p) level of theory

Parameters MP2 B3LYP

r(C–H)/A, ma 1.0877 1.0898

r(C–H)/A, ca,b 1.0875 1.0923

CP-correctedb 1.0878 1.0919

Dr(C–H)/A K0.0002 0.0025

CP-corrected 0.0001 0.0021

n(C–H)/cmK1, m 3223.4 3140.2

n(C–H)/cmK1, c 3221.5 3101.8

CP-corrected 3222.5 3109.1

Dn(C–H)/cmK1 K1.9 K38.4

CP-corrected K0.9 K31.1

:C–H/N/ 179.75 179.75

CP-corrected 179.76 178.52

Conformationc Eclipsed Eclipsed

CP-corrected Eclipsed Staggered

a m refers to the monomer F3C–H while c refers to the complex.b Standardly and CP-correctedly optimized parameters for the complex.c This refers to the relative position between the three fluorine atoms of

the F3CH molecule and the three hydrogen atoms of the NH3 molecule

viewing along the approximate C3 axes of the complex.

P. Lu et al. / Journal of Molecular Structure: THEOCHEM 723 (2005) 95–100 99

description since only X–H bond length and its change upon

H-bond formation are listed in their Tables [5]. Thus what’s

on earth the relationship between X–H bond length change

and its vibrational frequency change?

As listed in Table 2 of Ref. [4], at the MP2(FC)/6-311CG(d,p) level of theory, N–H bond length of the monomer

F2NH is 1.0261 A and its vibrational frequency is

3443.4 cmK1 while these two parameters become

1.0264 A and 3456.8 cmK1, respectively, for the complex

F2N–H/FH. Thus the situation appears that blue-shift is

accompanied by X–H bond length elongation. X. Li has

attributed this abnormality of bond length change to

‘computational error or uncertainty’ [20]. For the same

system F2N–H/FH, at the MP2/6-31G** level of theory,

Hobza has also noticed and confirmed the same N–H bond

length elongation (0.0004 A) and its vibrational frequency

increase (17 cmK1) upon hydrogen bond formation [19].

Both Li et al. [4] and Alabugin et al. [5] have studied the

C–H/N hydrogen bond of the complex F3C–H/NH3 at

the MP2(FC)/6–311CG(d,p) and MP2(FC)/6-31CG* level

of theory, respectively. In the calculation results from Li

et al., bond length of C–H and its vibrational frequency of

the monomer and complex are 1.0878 A, 3222.3 cmK1 and

1.0875 A, 3221.5 cmK1, respectively, while C–H bond

length of the monomer and complex is 1.0876 and

1.0888 A, respectively, in Alabugin et al.’s results.

Obviously, C–H bond length difference between the

monomer and the complex calculated from these two

research groups is K0.0003 and 0.0012 A, respectively.

Thus if ‘blue-shift means X–H contraction, and vice versa’

it will be hard for us to judge the hydrogen bond type of this

C–H/N H-bond. Furthermore, results from the former

research group deserve further consideration for the small

difference of the bond length change (K0.0003 A) and of

the vibrational frequency change (K0.8 cmK1). If the

0.0003 A difference (see above for F2N–H/FH) is

attributed to computational error or uncertainty then the

0.8 cmK1 difference attributes to what? Thus just in this

theoretical level (MP2(FC)/6-311CG(d,p)), it will be very

difficult for us to determine the type of H-bond according to

whether bond length change or vibrational frequency

change and it will be not a piece of cake either for

experimental identification if the frequency difference is just

only 0.8 cmK1.

Consequently, the X–H bond length change is not

necessarily in accord with the vibrational frequency change,

i.e. blue-shift does not necessarily mean X–H contraction,

and vice versa. This in accordance will appear in following

situations: (i) Different basis sets. As mentioned above, for

the C–H/N hydrogen bond of the complex F3C–H/NH3

at the MP2(FC) level of theory, the 6-311CG(d,p) basis set

used by Li et al. got K0.0003 A and K0.8 cmK1 for the

bond length change and vibrational frequency change. For

the 6-31CG* basis set used by Alabugin et al., only C–H

bond length of the monomer and the complex was given and

their difference is as large as 0.0012 A. According to our

knowledge, the X–H bond length abnormality has generally

up to 0.0005 A difference and the 0.0012 A difference

cannot lead to abnormality. At the MP2(FC)/6-31CG*

level of theory, we also repeated Alabugin et al.’s

calculation with Gaussian 03 [9] so as to get the bond

length and vibrational frequency difference parameters and

they are: 0.0015 A (1.0873 and 1.0888 A for the monomer

and the complex, respectively) and K17.1 cmK1

(3257.8 and 3240.7 cmK1 [21] for the monomer and the

complex, respectively). (ii) Different systems and theoreti-

cal methods. For the two conformers shown in Fig. 2(a) and

(b), at the B3LYP/6-311CG(d,p) level of theory, N–H

parameters of non-hydrogen bonded and hydrogen bonded

systems are 1.0100 A, 3613.4 cmK1 and 1.0102 A,

3595.7 cmK1, respectively. Thus vibrational frequency

difference still reaches K17.7 cmK1 although bond length

difference is only 0.0002 A. For the F2N–H/FH complex

at the MP2(FC)/6-311CG(d,p) level of theory, N–H bond

length difference is 0.0003 A but the vibrational frequency

difference is 13.4 cmK1, which appears abnormal. It seems

that the abnormal relationship between bond length change

and vibrational frequency change occurs more frequently in

intermolecular H-bonded systems than in intramolecular

H-bonded systems, and more frequently at the MP2 level of

theory than at the B3LYP level of theory. Tables 1 and 2

support some of this argument. (iii) As shown in Tables 1

and 2, the basis set superposition effect can also influence

this abnormality for Hartree–Fock and MP2 calculation. For

example, at the MP2(FC)/6-311CG(d,p) level of theory, the

standard gradient optimization gives 0.0001 A and 16 cmK1

for the N–H parameters while the CP-corrected gradient

optimization gives K0.0002 A and 21 cmK1.

P. Lu et al. / Journal of Molecular Structure: THEOCHEM 723 (2005) 95–100100

4. Conclusions

We have found a noticeable phenomenon in H-bond type

prediction: B3LYP and MP2 calculation have a contra-

dictory performance. For N–H/F H-bond in F2N–H/FH

complex, B3LYP computation predicts a red-shifted

H-bond while MP2 computation predicts a blue-shifted

one. This contradictory prediction cannot originate from

basis set superposition error effect that can be corrected by

counterpoise calculation. At present we cannot decide

which hydrogen bond type it is from the point of theory.

The relative performance of the B3LYP and MP2

computation in hydrogen bond prediction can only be

resolved with the aid of experimental infrared spectra

measurement. Next, before the experimental measurement,

such hydrogen bonded complex F2N–H/FH as theoreti-

cally predicted geometry should be synthesized. Since X–H

bond length change is very small even theoretically

considering; it is very dangerous to identify hydrogen

bond type by bond length change. The X–H bond length

change is not always in accord with its vibrational frequency

change. And this abnormality is related to theoretical

methods, basis set, and counterpoise-correction or not.

References

[1] H. Matsuura, H. Yoshida, M. Hieda, S.-y. Yamanaka, T. Harada,

K. Shin-ya, K. Ohno, J. Am. Chem. Soc. 125 (2003) 13910.

[2] R.L.T. Parreira, S.E. Galembeck, J. Am. Chem. Soc. 125 (2003)

15614.

[3] R.A. Vergenz, I. Yazji, C. Whittington, J. Daw, K.T. Tran, J. Am.

Chem. Soc. 125 (2003) 12318.

[4] X. Li, L. Liu, H.B. Schlegel, J. Am. Chem. Soc. 124 (2002) 9639.

[5] I.V. Alabugin, M. Manoharan, S. Peabody, F. Weinhold, J. Am.

Chem. Soc. 125 (2003) 5973.

[6] G.R. Desiraju, Acc. Chem. Res. 35 (2002) 565.

[7] P. Hobza, V. Spirko, H.L. Selzle, E.W. Schlag, J. Phys. Chem. A 102

(1998) 2501.

[8] P. Hobza, V. Spirko, Z. Havlas, K. Buchhold, B. Reimann, H.-

D. Barth, B. Brutschy, Chem. Phys. Lett. 299 (1999) 180.

[9] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb,

J.R. Cheeseman, J.A. Montgomery, Jr., T. Vreven, K.N. Kudin, J.C.

Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B.

Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H.

Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M.

Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li,

J.E. Knox, H.P. Hratchian, J.B. Cross, C. Adamo, J. Jaramillo, R.

Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C.

Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P.

Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D.

Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K.

Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S.

Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P.

Piskorz, I. Komaromi, 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, C. Gonzalez, J.A. Pople, Gaussian

03, Revision B.5, Gaussian, Inc., Pittsburgh PA, 2003.

[10] A.D. Becke, J. Chem. Phys. 98 (1993) 5648.

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

[12] C. Møller, M.S. Plesset, Phys. Rev. 46 (1934) 618.

[13] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166

(1990) 281.

[14] S. Simon, M. Duran, J.J. Dannenberg, J. Chem. Phys. 105 (1996)

11024.

[15] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553.

[16] P. Hobza, Z. Halvas, Theor. Chim. Acta 99 (1998) 372.

[17] P. Hobza, Z. Halvas, Chem. Phys. Lett. 303 (1999) 447.

[18] S. Scheiner, Hydrogen Bonding. A Theoretical Perspective, Oxford

University Press, New York, 1997.

[19] P. Hobza, Int. J. Quantum Chem. 90 (2002) 1071.

[20] Xiaosong Li (Department of Chemistry, Yale University, New Haven,

CT 06520, USA. E-mail: xiaosong.li@yale.edu), personal communi-

cation, 2004.

[21] In our geometry optimization and frequency calculation, the initial

geometrical parameters of F3C–H/NH3 are taken from the Support-

ing Information (S6) of the Ref. [5]. Our optimization process proves

that their geometry is indeed a stationary point. However, their

geometry is not a local minimum but a transition state (indicated by

one imaginary frequency K16.9 cmK1. This imaginary frequency

vibrational mode corresponds to that the three hydrogen atoms of the

NH3 molecule rotate consistently along its C3 axes.).