ORIGINAL RESEARCH

Theoretical investigation of the noble gas molecular anionsXAuNgX2 and HAuNgX2 (X 5 F, Cl, Br; Ng 5 Xe, Kr, Ar)

Guoqun Liu • Yanli Zhang • Xue Bai •

Fang He • Xianxi Zhang • Zhixin Wang •

Wangxi Zhang

Received: 20 September 2011 / Accepted: 14 February 2012 / Published online: 29 February 2012

� Springer Science+Business Media, LLC 2012

Abstract The geometries, atomic charge distributions,

vibrational frequencies, and relative energies of the noble

gas molecular anions XAuNgX- and HAuNgX- (X = F,

Cl, Br; Ng = Xe, Kr, Ar) were investigated at the MP2 and

CCSD(T) levels of theory. The Au–Ng bond length of

X(H)AuNgX- is mainly dependent on the electronegative

fragment bonded to the Au atom rather than on that bonded

to the Ng atom. The presence of the right X- anion sta-

bilizes the Au–Ng bond of X(H)AuNg. Based on the

interatomic distances and atomic charge distributions,

X(H)AuNgX- may be better described as X(H)AuNg���X-

rather than as X(H)-���AuNgX. The MP2 calculations

indicate that, for the Xe, Kr, and Ar molecular anion series,

(i) X(H)AuNgX- is less stable than the global mini-

mum X(H)AuX- ? Ng by ca. 25–35, 33–48, and 37–57

kcal/mol, respectively, (ii) the reaction barriers are ca.

5–14, 3–9, and 2–5 kcal/mol, respectively, when the anion

dissociates into X(H)AuX- ? Ng through the bending

transition state, and (iii) X(H)AuNgX- is more stable than

the dissociation limit X(H)AuNg ? X- by ca. 14–38,

11–30, and 9–25 kcal/mol, respectively.

Keywords Noble gas molecular anions � Molecular

complexes � Gold–xenon bond � FAuXeF- �MP2 and CCSD(T) calculations

Introduction

Noble gas chemistry has developed rapidly since 1962, in the

year of which the landmark compounds XePtF6 [1], XeF4 [2],

and XeF2 [3] were prepared. In 1990, Frenking and Cremer

[4] reviewed the experimental and theoretical researches of

the diatomic cations, polyatomic cations, and neutral com-

pounds of helium, neon, and argon. In 2001, Christe [5]

highlighted four categories of discoveries in the field of

noble gas chemistry, i.e., (i) the formation of new Xe(II)–

heteroatom linkages or known Xe–heteroatom connectivi-

ties that involve higher oxidation states of xenon, (ii) the

ability of XeF2 to act as a ligand for numerous naked metal

ions, (iii) the ability of xenon to act as a ligand, and (iv) the

observation of the first ground state argon compound con-

taining covalent Ar–heteroatom bonds. In 2007, Grochala

[6] described the fascinating experimental and theoretical

advances of the noble gas chemistry and then highlighted the

perspectives for future development. In 2009, Khriachtchev

et al. [7] reviewed experimental preparation and identifica-

tion, formation mechanisms, complexes and interaction with

matrix, and the nature of chemical bonding and stability of

the noble gas hydrides HNgY (where Ng is a noble gas atom

and Y is an electronegative fragment).

In 1995, Pyykko [8] investigated the bond lengths,

vibrational frequencies, and bond energies of AuNg?

Electronic supplementary material The online version of thisarticle (doi:10.1007/s11224-012-9978-1) contains supplementarymaterial, which is available to authorized users.

G. Liu (&) � X. Bai � F. He � Z. Wang � W. Zhang

School of Materials and Chemical Engineering, Zhongyuan

University of Technology, Zhongyuan Road 41#, Zhengzhou

450007, People’s Republic of China

e-mail: flyskyliugq@126.com

Y. Zhang

College of Chemistry and Chemical Engineering, Henan

University, Kaifeng 475001, People’s Republic of China

X. Zhang

School of Chemistry and Chemical Engineering, Liaocheng

University, Liaocheng 252059, People’s Republic of China

123

Struct Chem (2012) 23:1693–1710

DOI 10.1007/s11224-012-9978-1

(Ng = He, Ne, Ar, Kr, Xe) at the MP2 and

CCSD(T) levels of theory. The CCSD(T) calculations

indicate that the bond length and bond energy of AuXe?

is 2.698 A and 26.75 kcal/mol [8], respectively. Pyykko

[8] also investigated the bond lengths and vibrational

frequencies of NgAuNg? (Ng = Ar, Kr, Xe) at the MP2

level of theory. The MP2 calculations indicate that the

bond length of Au–Xe in XeAuXe? is 2.66 A [8]. In

1998, Schroder et al. [9] confirmed the identity of AuXe?,

XeAuXe?, and C6F6AuXe? by high resolution mass

analysis as well as the typical isotope pattern, and pro-

vided the theoretical estimate of the (Au–Xe)? bond

length and bond energy as 2.574 A and 30.1 kcal/mol. In

2008, Zeng and Klobukowski [10] studied the Au?Xe

system using relativistic model core potentials and a

variety of post-Hartree–Fock methods, including renor-

malized and completely renormalized coupled cluster, and

density functional theory methods. The CR-CCSD(TQ)_B

calculations indicate that the bond length and energy of

Au?Xe is 2.647 A and 22.37 kcal/mol, respectively [10].

On the other hand, Dixon et al. [11] have predicted the

atomization energies and heats of formation of KrF?,

KrF-, KrF2, KrF3?, KrF4, KrF5

?, and KrF6 at the

CCSD(T) level of theory with the corrections for core-

valence effects, scalar relativistic effects, and first-order

atomic spin–orbit effects. The calculation results indicate

that KrF4 possesses an energy barrier of 10 kcal/mol

toward fluorine atom loss, while the corresponding barrier

in KrF6 is only 0.9 kcal/mol [11]. Grant et al. [12] have

calculated the atomization energies and heats of formation

of XeF3?, XeF3

-, XeF5?, XeF7

?, XeF7-, and XeF8 at the

CCSD(T) level of theory with the three additional cor-

rections. XeF8 is predicted to be exothermic by 22.3 kcal/

mol at 0 K with respect to loss of F2 and is thus ther-

modynamically unstable [12].

In 2000, Seidel and Seppelt [13] prepared the single

crystal of [AuXe4]2?([Sb2F11]-)2, in which the Au atom

and the four Xe atoms are directly bonded and the average

bond length of the four Au–Xe bonds is determined as

2.739 A. The Au–Xe bond length of [AuXe4]2? was cal-

culated as 2.871 [13], 2.787 [13], and 2.807 A [14],

respectively, at the B3LYP, MP2, and CCSD(T) levels.

Subsequently, Seppelt and coworkers [15] also prepared

the single crystals of cis-[Xe–Au(II)–Xe]2?([Sb2F11]-)2,

trans-[Xe–Au(II)–Xe]2?([SbF6]-)2 [15], [Xe–Au(II)–

F(-I)–Au(II)–Xe]3?([SbF6]-)3 [15], trans-[Xe2Au(III)–

F(-I)]2?[SbF6]-[Sb2F11]- [15], and [(F3As)Au(I)Xe]?

[SbF6]- [16], in which the Au–Xe bond length is deter-

mined as 2.665 (averaged), 2.709, 2.647, 2.606 (averaged),

and 2.607 A, respectively. In addition, Gerken et al. [17]

have determined the crystal structure of [Xe3OF3][AsF6]

and [Xe3OF3][SbF6], in which the FXeOXeFXeF? cation

has a Z-shaped rather than linear structure.

From 2000 to 2006, Gerry and coworkers have mea-

sured the microwave spectra of ArAgX (X = F, Cl, Br)

[18], ArCuX (X = F, Cl, Br) [19], NgAuCl (Ng = Ar, Kr)

[20], ArAuX (X = F, Br) [21], KrCuX (X = F, Cl) [22],

KrAuF, KrAgF, KrAgBr [23], XeAuF [24], and XeCuF,

XeCuCl [25], and determined their geometrical parameters.

The Xe–Au bond length of XeAuF was determined as

2.543 A from the experimental rotational constants [24]. In

2003, Lovallo and Klobukowski [26] calculated the bond

lengths and binding energies of Ng–MX (Ng = Ar, Kr, Xe;

M = Cu, Ag, Au; X = F, Cl) at the MP2 level of theory.

For XeAuF, the calculated BSSE-corrected binding energy

is 23.3 kcal/mol [26]. In 2008, Belpassi et al. [27] inves-

tigated the nature of the chemical bond in the complexes

NgAuF and NgAu? (Ng = Ar, Kr, Xe) at the fully rela-

tivistic DC-CCSD(T) and DC-BLYP levels of theory. The

Xe–Au bond length of XeAuF was calculated as 2.573 A at

the DC-CCSD(T) level. Furthermore, the Xe–Au bond can

be considered as a weak covalent chemical bond according

to the contour plots of the electron density difference

between XeAuF and the Xe and AuF fragments calculated

at the DC-BLYP level [27]. On the other hand, in 2005 and

2006, Ghanty has investigated the structure and stability of

noble gas insertion compounds AuNgX (Ng = Kr, Xe;

X = F, OH) [28] and MNgF (M = Cu, Ag; Ng = Ar, Kr,

Xe) at the MP2 level of theory [29]. The MP2 calculations

indicate that (i) AuXeF is less stable than the AuF ? Xe

limit by 39.7 kcal/mol, (ii) the dissociation barrier height

corresponding to the bent transition state is 28.5 kcal/mol,

and (iii) AuXeF is more stable than the Au ? Xe ? F limit

by 27.0 kcal/mol [28].

In the 1995 article, Pyykko [8] has also investigated the

molecular properties of AuXe- at the MP2 and

CCSD(T) levels of theory. The CCSD(T) calculations

indicate that the bond length and energy of AuXe- is

4.18 A and 1.91 kcal/mol [8], respectively. In 2005, Li

et al. [30] investigated the structures and energetics of

FNgO- (Ng = He, Ar, Kr) at the MP2 and CCSD(T) lev-

els. The CCSD(T)/aug-cc-pVTZ calculations indicate that

the F–Kr and Kr–O bond length of the singlet FKrO- is

2.259 and 1.854 A, respectively, and that the S–T gap, the

relative energies of the singlet FKrO- with respect to

F- ? Kr ? O (S), F- ? KrO, F ? Kr ? O-, F- ? Kr ?

O (T), and FO- ? Kr, and the energy barrier for the dis-

sociation reaction FKrO- ? FO- ? Kr are 52.7, -58.1,

-37.4, -52.9, -7.3, 16.4, and 49.0 kcal/mol, respectively

[30]. In 2008 and 2009, Borocci et al. investigated

the similar species FNgS- [31] and FNgSe- (Ng = He,

Ar, Kr, Xe) [32] at the MP2 and CCSD(T) levels.

The CCSD(T)/aug-cc-pVTZ/SDD calculations indicate

that the dissociation energy and the energy barrier at 0 K

of the reaction FXeS- ? FS- ? Xe are -27.9 and 36.1

kcal/mol [31], respectively, and that the corresponding

1694 Struct Chem (2012) 23:1693–1710

123

energies of the reaction FXeSe- ? FSe- ? Xe are -31.6

and 30.2 kcal/mol [32], respectively. In addition, in 2007,

Antoniotti et al. [33] have investigated the FNgBN-

(Ng = He–Xe) anions at the MP2 and CCSD(T) levels of

theory. The CCSD(T)/aug-cc-pVTZ/SDD calculations

indicate that the dissociation energy and the energy barrier

at 0 K of the reaction FXeBN- ? FBN- ? Xe are -74.3

and 24.6 kcal/mol [33], respectively.

On the other hand, in 2007, Krouse et al. [34] investi-

gated the bonding and electronic structure of XeF3-. The

Xe–F bond dissociation energy in XeF3- was measured as

19.37 ± 1.38 kcal/mol by the energy-resolved collision-

induced dissociation studies [34]. In 2010, Vasdev et al.

[35] have also investigated the XeF3- anion both experi-

mentally and theoretically. The enthalpy of activation for

the exchange between F- and XeF2 in CH3CN solution was

determined by use of single selective inversion 19F NMR

spectroscopy to be 17.7 ± 1.2 kcal/mol (0.18 M) or

13.6 ± 1.6 kcal/mol (0.36 M) for equimolar amounts of

[N(CH3)4][F] and XeF2 in CH3CN solvent [35]. In 2010,

Sun et al. [36] investigated XeNO2-, XeNO3

-, XeNO2Li,

and XeNO3Li at the B3LYP, MPW1PW91, MP2, and

CCSD(T) levels, respectively. The CCSD(T)/aug-cc-

pVQZ-pp calculations indicate that the atomization ener-

gies of the four xenon–nitrogen compounds are 50.1, 100.7,

115.5, and 149.3 kcal/mol, respectively, while the lowest

unimolecular dissociation barriers of the four species are

42.0, 42.6, 30.7, and 33.6 kcal/mol, respectively [36].

Recently, Jayasekharan and Ghanty [37] have predicted

the structure, stability, charge redistribution, bonding, and

harmonic vibrational frequencies of FMNgF (M = Be,

Mg; Ng = Ar, Kr, Xe) at the MP2 and CCSD(T) levels of

theory. The CCSD(T) calculations indicate that (i) FBeXeF

and FMgXeF are less stable by 111.74 and 93.26 kcal/mol,

respectively, than the corresponding global minima

BeF2 ? Xe and MgF2 ? Xe and (ii) the bending dissoci-

ation (FMXeF ? MF2 ? Xe, M = Be, Mg) barrier

heights are 13.8 and 7.7 kcal/mol for the two xenon com-

pounds [37]. Jimenez-Halla et al. [38] have investigated

HNgNgF (Ng = Ar, Kr, Xe) at the M05-2X, MP2, and

CCSD(T) levels. According to the CCSD(T) calculations,

the dissociation (HXeXeF ? HXeF ? Xe) barrier is

13.1 kcal mol-1 [38].

Very recently, we have investigated CH3NgF (Ng =

He, Ar, Kr, Xe) [39], RXeXeR0 (such as C6H5XeXeF or

CH3XeXeF etc.) [40], and (HXeCN)n (n = 2, 3, 4) [41] at

the MP2 level of theory. In addition, we have also inves-

tigated XHgNgX and HHgNgX (X = F, Cl, Br; Ng = Xe,

Kr, Ar) at the MP2 and CCSD(T) levels of theory [42].

To improve the readability of the article, all the above-

investigated noble gas compounds have been summarized

in Table 1. If the mercury atom of XHgNgX and HHgNgX

is replaced by the isoelectronic gold anion (Au-), we will

obtain the corresponding noble gas molecular anions

XAuNgX- and HAuNgX-. Interestingly, XAuNgX- can

also be considered formed by XAuNg ? X- or formed by

X- ? AuNgX, whereas both XAuNg [24, 26] and AuNgX

[28] have been theoretically investigated.

Computational details

Quantum chemical calculations of the title molecular

anions XAuNgX- and HAuNgX- (X = F, Cl, Br; Ng =

Xe, Kr, Ar) were performed with the Gaussian 09 programs

[43]. Some of the calculations were performed on the IBM

P690 system in the Shandong Province High Performance

Computer Center. The levels of theory applied are

MP2(FC) and CCSD(T). MP2(FC) requests a Hartree–

Fock calculation followed by a second order Møller–

Plesset correlation energy correction [44–46] and requests

the inner shells excluded from the correlation calculation.

CCSD(T) is the coupled cluster theory with single, double,

and perturbative triple excitations [47]. For H, F, Cl, Br,

Kr, and Ar atoms, the 6-311??g(2d,2p) [48] basis set was

used throughout all of the calculations unless otherwise

stated explicitly. For Xe atom, the Stuttgart/Dresden

Wood-Boring (WB) quasi-relativistic effective core

potential (ECP) MWB46 and the corresponding Gaussian-

type orbital (GTO) valence basis set (6s6p3d1f)/[4s4p3d1f]

[49] were applied. For Au atom, the Stuttgart/Dresden

quasi-relativistic ECP MWB60 [50] was used in conjunc-

tion with two GTO valence basis sets. One is the smaller

valence basis set, (8s7p6d)/[6s5p3d] [50], and the other is

the larger valence basis set, (8s7p6d2f1g)/[6s5p3d2f1g]

[51].

At both the MP2 and CCSD(T) levels of theory, for the

geometry optimizations of the equilibrium structure, all of

the 18 molecular anions X(H)AuNgX- were kept linear

and only the bond lengths of X(H)–Au, Au–Ng, and Ng–X

were allowed optimized. At the CCSD(T) level of theory,

for the geometry optimizations of the transition structure,

both the X(H)AuNgX dihedral angle and the X(H)AuNg

bond angle of the 18 anions were fixed at 180.0�, and only

the other four variables (the bond lengths of X(H)–Au, Au–

Ng, Ng–X, and the bond angle of AuNgX) were allowed

optimized. When the smaller valence basis set of the gold

atom is adopted, at both the MP2 and CCSD(T) levels, for

all of the xenon, krypton, and argon molecular anions, the

optimized stationary point was then validated to be an

energy minimum or a transition state by followed harmonic

frequency calculations as long as the geometry optimiza-

tion converged to a stationary point. Results calculated

from the smaller basis set are presented in the Supporting

Information. When the larger valence basis set of the gold

atom is adopted, at the MP2 level of theory, the harmonic

Struct Chem (2012) 23:1693–1710 1695

123

frequency calculations were also performed for all of the

three noble gas molecular anion series when a stationary

point was reached. However, at the CCSD(T) level of

theory, for the sake of saving computational time, the

harmonic frequency calculations were performed only for

most of the xenon molecular anions (except for BrA-

uXeBr-) but not for any of the krypton and the argon

molecular anions when a stationary point was reached. In

Table 1 Overview of the investigated noble gas compounds relevant to the present investigations (separated by experiment and theoretical

calculations)

Time Compounds Methods Refs.

Experimental characterization of the noble gas compounds

1998 AuXe?, XeAuXe?, and C6F6AuXe? Mass spectrometry [9]

2000 [AuXe4]2?([Sb2F11]-)2 X-Ray single crystal diffraction [13]

2002 cis-[Xe–Au(II)–Xe]2?([Sb2F11]-)2 X-Ray single crystal diffraction [15]

2002 trans-[Xe–Au(II)–Xe]2?([SbF6]-)2 X-Ray single crystal diffraction [15]

2002 [Xe–Au(II)–F(-I)–Au(II)–Xe]3?([SbF6]-)3 X-Ray single crystal diffraction [15]

2002 trans-[Xe2Au(III)–F(-I)]2?[SbF6]-[Sb2F11]- X-Ray single crystal diffraction [15]

2003 [(F3As)Au(I)Xe]?[SbF6]- X-Ray single crystal diffraction [16]

2009 [Xe3OF3][AsF6] and [Xe3OF3][SbF6] X-Ray single crystal diffraction [17]

2000 ArAgX (X = F, Cl, Br) Microwave spectra [18]

2000 ArCuX (X = F, Cl, Br) Microwave spectra [19]

2000 NgAuCl (Ng = Ar, Kr) Microwave spectra [20]

2000 ArAuX (X = F, Br) Microwave spectra [21]

2004 KrCuX (X = F, Cl) Microwave spectra [22]

2004 KrAuF, KrAgF, and KrAgBr Microwave spectra [23]

2004 XeAuF Microwave spectra [24]

2006 XeCuF, XeCuCl Microwave spectra [25]

2007 XeF3- Energy-resolved collision-induced dissociation [34]

2010 XeF3- 19F NMR spectroscopy [35]

Theoretical characterization of the noble gas compounds

1995 AuNg? (Ng = He, Ne, Ar, Kr, Xe) MP2 and CCSD(T) [8]

1995 NgAuNg? (Ng = Ar, Kr, Xe) MP2 [8]

2008 AuXe? CR-CCSD(TQ)_B [10]

2007 KrF?, KrF-, KrF2, KrF3?, KrF4, KrF5

?, and KrF6 CCSD(T) [11]

2010 XeF3?, XeF3

-, XeF5?, XeF7

?, XeF7-, and XeF8 CCSD(T) [12]

2001 [AuXe4]2? CCSD(T) [14]

2003 NgMX (Ng = Ar, Kr, Xe; M = Cu, Ag, Au; X = F, Cl) MP2 [26]

2008 NgAuF and NgAu? (Ng = Ar, Kr, Xe) DC-CCSD(T), DC-BLYP [27]

2005 AuNgX (Ng = Kr, Xe; X = F, OH) MP2 [28]

2006 MNgF (M = Cu, Ag; Ng = Ar, Kr, Xe) MP2 [29]

1995 AuXe- MP2 and CCSD(T) [8]

2005 FNgO- (Ng = He, Ar, Kr) MP2 and CCSD(T) [30]

2008 FNgS- (Ng = He, Ar, Kr, Xe) MP2 and CCSD(T) [31]

2009 FNgSe- (Ng = He, Ar, Kr, Xe) MP2 and CCSD(T) [32]

2007 FNgBN- (Ng = He–Xe) MP2 and CCSD(T) [33]

2010 XeNO2-, XeNO3

-, XeNO2Li, and XeNO3Li MP2 and CCSD(T) [36]

2008 FMNgF (M = Be, Mg; Ng = Ar, Kr, Xe) MP2 and CCSD(T) [37]

2009 HNgNgF (Ng = Ar, Kr, Xe) MP2 and CCSD(T) [38]

2010 CH3NgF (Ng = He, Ar, Kr, Xe) MP2 [39]

2011 RXeXeR0 (such as C6H5XeXeF or CH3XeXeF etc.) MP2 [40]

2011 (HXeCN)n (n = 2, 3, 4) MP2 and CCSD(T) [41]

2011 XHgNgX, HHgNgX (X = F, Cl, Br; Ng = Xe, Kr, Ar) MP2 and CCSD(T) [42]

1696 Struct Chem (2012) 23:1693–1710

123

addition to the Mulliken population analysis [52], the

natural population analysis (NPA) [53] was also performed

to analyze the charge distribution of the equilibrium

structure of the title molecular anions.

Results and discussions

Geometries, atomic charge distributions, bonding

character, and harmonic vibrational frequencies

of the equilibrium structures

At the MP2 and CCSD(T) levels of theory, when the larger

valence basis set of the gold atom was applied, the bond

length and T1 diagnostic of the equilibrium structure of the

molecular anions X(H)AuXeX-, X(H)AuKrX-, and

X(H)AuArX- (X = F, Cl, Br) are presented in Figs. 1, 2,

and 3, respectively. The corresponding results calculated

from the smaller valence basis set of the gold atom are

presented in Tables S1, S2, S3, respectively. As shown in

Fig. 1 and Table S1, Fig. 2 and Table S2, and Fig. 3 and

Table S3, for all of the 18 molecular anions, the Au–Ng

bond length calculated with the larger valence basis set is

always shorter than that calculated with the smaller valence

basis set. For example, at the CCSD(T) level, the Au–Xe

bond length of FAuXeF- is 2.580 (Fig. 1) and 2.623 A

(Table S1), respectively, when the larger and the smaller

basis set was applied.

Since, at the CCSD(T) level, the Au–Xe bond length of

FAuXe was calculated as 2.613 and 2.676 A, respectively,

with the larger and smaller basis set, and the corresponding

experimental bond length is 2.543 A [24], the Au–Xe bond

length calculated with the larger basis set is apparently in

better agreement with the experiment. Interestingly, at the

MP2 level, the Au–Xe bond length was calculated as 2.550

and 2.641 A, respectively, with the larger and smaller basis

set, which are fortuitously in better agreement with the

experiment than the corresponding CCSD(T) values. These

are also the cases for both the Au–Kr bond length of

FAuKr (the experimental value is 2.461 A [23]) and the

Au–Ar bond length of FAuAr (the experimental value is

2.391 A [21]). In the following, the discussions are mainly

based on the results calculated with the larger valence basis

set.

As shown in Figs. 1, 2, and 3, for all of the three anionic

noble gas molecule series, both the MP2 and

CCSD(T) calculations indicate that the Au–Ng bond

length is increased as follows, FAuNgF- \ ClAuNgCl- \BrAuNgBr- \ HAuNgF- \HAuNgCl- \HAuNgBr-. In

contrast, for the X(H)HgXeX (X = F, Cl, Br) neutral

molecules, the Hg–Xe bond length is increased as follows,

FHgXeF \ HHgXeF \ HHgXeCl \ ClHgXeCl \ HHg-

XeBr \ BrHgXeBr [42]. It seems that, for the X(H)

AuNgX- anions, the Au–Ng bond length will become

shorter when the X(H) atom bonded to the Au atom has

larger electronegativity, while for the X(H)HgXeX neutral

molecules, the Hg–Xe bond length will become shorter

when the X atom bonded to the Xe atom has larger elec-

tronegativity. In other words, the Au–Ng bond length is

more dependent on the electronegative fragment that bon-

ded to the Au atom rather than on the electronegative

fragment that bonded to the Ng atom, while the dependence

relationship is exactly opposite for the Hg–Ng bond length.

Since X(H)AuNgX- can be considered formed either by

X(H)AuNg and X- or by X(H)- and AuNgX, it will be

interesting to compare the bond lengths of X(H)AuNgX-

with those of X(H)AuNg and AuNgX. To realize the

comparisons, we have also investigated the X(H)AuNg and

AuNgX species at the MP2 and CCSD(T) levels with the

same basis sets as those used for the X(H)AuNgX- anions.

The calculated bond lengths of X(H)AuNg and AuNgX

(X = F, Cl, Br; Ng = Xe, Kr, Ar) are presented in

Tables 2, 3, and 4. As shown in Figs. 1, 2, and 3 and

Fig. 1 Bond length (A) and the T1 diagnostic of the equilibrium

structure of XAuXeX- and HAuXeX- (X = F, Cl, Br) computed at

the MP2 and CCSD(T) (in parentheses) levels

Struct Chem (2012) 23:1693–1710 1697

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Tables 2, 3, and 4, for all of the three noble gas molecule

series, the X(H)–Au bond length of X(H)AuNgX- is larger

than those of the corresponding X(H)AuNg, while the Au–

Ng bond length of the former is smaller than those of the

latter. For example, at the CCSD(T) level of theory, the F–

Au and Au–Xe bond lengths of FAuXeF- are 1.988 and

2.580 A, respectively, while the two bond lengths of

FAuXe are 1.946 and 2.613 A, respectively. This may

indicate that the presence of the X- anion can strengthen

the Au–Ng bond of X(H)AuNg while weaken its X(H)–Au

bond. On the other hand, for all of the three noble gas

molecule series, the Ng–X bond length of X(H)AuNgX- is

significantly larger than that of AuNgX. For example, at

the MP2 (CCSD(T)) level of theory, the Xe–F bond length

of FAuXeF- is 2.488 (2.499) A while that of AuXeF is

2.127 (2.198) A (Table 3).

As shown in Fig. 1, at the CCSD(T) level of theory, the

Au–Xe bond length of FAuXeF-, ClAuXeCl-, and BrA-

uXeBr- is 2.580, 2.615, and 2.631 A, respectively. The

CCSD(T) calculations indicate that the optimized bond

length of the structural moieties Au–Xe, [Au–Xe]?, and

[Au–Xe]2? is 3.669, 2.642, and 2.684 A, respectively. In

the crystal structure of [XeAuFAuXe]3?([SbF6]-)3, the

Au–Xe bond length was determined as 2.647 A [15]. In

addition, according to the covalent radii proposed by

Cordero et al. [54], the Au–Xe covalent bond length is

2.76 A. According to the molecular single- [55], double-

[56], and triple-bond [57] covalent radii proposed by

Pyykko and coworkers, the Au–Xe single-, double-, and

triple-bond length is 2.55, 2.56, and 2.45 A, respectively.

As a consequence, the Au–Xe bond of the three molecular

anions may have partial covalent character. Similarly, the

Au–Kr and Au–Ar bonds of FAuKrF- and FAuArF- may

also have partial covalent character.

The Mulliken and NBO atomic charge distributions as

well as the dipole moment of the three X(H)AuNgX-

(Ng = Xe, Kr, Ar) series calculated at the MP2 level with

the MP2-optimized geometry are presented in Tables 5, 6,

and 7, respectively. As shown in these three tables, for all

of these three molecular anion series, the most character-

istic charge distribution is that the Ng-bonded X atom

always carries approximately -1 NBO charges. On the

other hand, according to the single-bond covalent radii

Fig. 2 Bond length (A) and the T1 diagnostic of the equilibrium

structure of XAuKrX- and HAuKrX- (X = F, Cl, Br) computed at

the MP2 and CCSD(T) (in parentheses) levelsFig. 3 Bond length (A) and the T1 diagnostic of the equilibrium

structure of XAuArX- and HAuArX- (X = F, Cl, Br) computed at

the MP2 and CCSD(T) (in parentheses) levels

1698 Struct Chem (2012) 23:1693–1710

123

proposed by Pyykko and Atsumi [55], the F–Au, H–Au,

Cl–Au, and Br–Au covalent bond length is 1.88, 1.56, 2.23,

and 2.38 A, respectively, which are very close in magni-

tude to the corresponding bond lengths of FAuNgF-,

HAuNgF-, HAuNgCl-, HAuNgBr-, ClAuNgCl-, and

BrAuNgBr- (Ng = Xe, Kr, Ar). Thus, the four bonds of

the 18 molecular anions may have considerable covalent

character. In contrast, the Xe–F, Xe–Cl, Xe–Br, Kr–F, Kr–

Cl, Kr–Br, Ar–F, Ar–Cl, and Ar–Br covalent bond length

[55] is 1.95, 2.30, 2.45, 1.81, 2.16, 2.31, 1.60, 1.95, and

2.10 A, respectively, which are much shorter than the

corresponding bond lengths of the 18 noble gas molecular

anions.

Considering both the atomic charge distributions and the

interatomic distances, the X(H)AuNgX- anions may be

more appropriately described as X(H)AuNg���X- rather

than as X(H)-���AuNgX. Interestingly, this structural

character is very similar to that of the vast majority of the

recently investigated noble gas molecular anions, e.g.,

FNgO- (Ng = He, Ar, Kr; which can be viewed as

ONg���F-) [30], F-(NgO)n (Ng = He, Ar, Kr; n = 1–6;

which can be viewed as (ONg)n���F-) [58], FNgBN-

(Ng = He - Xe; which can be viewed as NBNg���F-)

[33], FNgS- (Ng = He, Ar, Kr, Xe; which can be viewed

as SNg���F-) [31], and FNgSe- (Ng = He, Ar, Kr, Xe;

which can be viewed as SeNg���F-) [32]. Furthermore, for

Table 2 Computed bond lengths (A) of the equilibrium structure of X(H)AuXe and AuXeX (X = F, Cl, Br)

Methods r(X(H)–Au) r(Au–Xe)a r(Au–Xe)b r(Xe–X)

FAuXe ? AuXeF MP2 1.924 2.550 2.538 2.127

CCSD(T) 1.946 2.613 2.618 2.198

HAuXe ? AuXeF MP2 1.519 2.766 2.538 2.127

CCSD(T) 1.543 2.852 2.618 2.198

HAuXe ? AuXeCl MP2 1.519 2.766 2.570 2.604

CCSD(T) 1.543 2.852 2.692 2.754

HAuXe ? AuXeBr MP2 1.519 2.766 2.586 2.765

CCSD(T) 1.543 2.852 –c –c

ClAuXe ? AuXeCl MP2 2.223 2.595 2.570 2.604

CCSD(T) 2.260 2.663 2.692 2.754

BrAuXe ? AuXeBr MP2 2.343 2.611 2.586 2.765

CCSD(T) 2.385 2.683 –c –c

a The Au–Xe bond length of the X(H)AuXe moleculeb The Au–Xe bond length of the AuXeX moleculec At the CCSD(T) level of theory, the AuXeBr molecule dissociates into atomic fragments during the geometry optimizations

Table 3 Computed bond lengths (A) of the equilibrium structure of X(H)AuKr and AuKrX (X = F, Cl, Br)

Methods r(X(H)–Au) r(Au–Kr)a r(Au–Kr)b r(Kr–X)

FAuKr ? AuKrF MP2 1.914 2.496 2.443 2.089

CCSD(T) 1.938 2.563 –c –c

HAuKr ? AuKrF MP2 1.507 2.756 2.443 2.089

CCSD(T) 1.533 2.839 –c –c

HAuKr ? AuKrCl MP2 1.507 2.756 2.510 2.544

CCSD(T) 1.533 2.839 –c –c

HAuKr ? AuKrBr MP2 1.507 2.756 2.550 2.686

CCSD(T) 1.533 2.839 –c –c

ClAuKr ? AuKrCl MP2 2.211 2.560 2.510 2.544

CCSD(T) 2.251 2.630 –c –c

BrAuKr ? AuKrBr MP2 2.332 2.580 2.550 2.686

CCSD(T) 2.375 2.654 –c –c

a The Au–Kr bond length of the X(H)AuKr moleculeb The Au–Kr bond length of the AuKrX moleculec At the CCSD(T) level of theory, the AuKrF, AuKrCl, and AuKrBr molecules dissociate into atomic fragments during the geometry

optimizations

Struct Chem (2012) 23:1693–1710 1699

123

all of the above five noble gas molecule series and the

molecular anions investigated here, the halogen anion (F-

or X-) has always a significant stabilization effect on the

neighboring neutral noble gas molecule [ONg, (ONg)n,

NBNg, SNg, SeNg, or X(H)AuNg].

As shown in Tables 5, 6, and 7, for the three XAuXeX-

(X = F, Cl, Br) molecular anions, the Xe atom carries

larger positive NBO charges than the Au atom does, while

for the three XAuArX- (X = F, Cl, Br) molecular anions,

the Au atom rather than the Ar atom carries larger positive

NBO charges. On the other hand, both the Au and noble

gas atoms of HAuNgX- (X = F, Cl, Br; Ng = Xe, Kr, Ar)

carry notably smaller NBO charges than the corresponding

atoms of XAuNgX-. As shown in Tables 5, 6, and 7, the

Table 4 Computed bond lengths (A) of the equilibrium structure of X(H)AuAr and AuArX (X = F, Cl, Br)

Methods r(X(H)–Au) r(Au–Ar)a r(Au–Ar)b r(Ar–X)

FAuAr ? AuArF MP2 1.911 2.413 2.347 2.069

CCSD(T) 1.935 2.481 –c –c

HAuAr ? AuArF MP2 1.501 2.683 2.347 2.069

CCSD(T) 1.528 2.778 –c –c

HAuAr ? AuArCl MP2 1.501 2.683 2.453 2.502

CCSD(T) 1.528 2.778 –c –c

HAuAr ? AuArBr MP2 1.501 2.683 2.534 2.634

CCSD(T) 1.528 2.778 –c –c

ClAuAr ? AuArCl MP2 2.207 2.483 2.453 2.502

CCSD(T) 2.247 2.560 –c –c

BrAuAr ? AuArBr MP2 2.328 2.512 2.534 2.634

CCSD(T) 2.372 2.590 –c –c

a The Au–Ar bond length of the X(H)AuAr moleculeb The Au–Ar bond length of the AuArX moleculec At the CCSD(T) level of theory, the AuArF, AuArCl, and AuArBr molecules dissociate into atomic fragments during the geometry

optimizations

Table 5 Mulliken (NBO) atomic charges of the equilibrium structure of XAuXeX- and HAuXeX- (X = F, Cl, Br) computed at the MP2 level

of theory

q(X(H)) q(Au) q(Xe) q(X) l/D

FAuXeF- -0.497(-0.718) -0.140(0.241) 0.455(0.419) -0.819(-0.942) 6.09

HAuXeF- -0.286(-0.240) -0.171(-0.096) 0.320(0.302) -0.862(-0.967) 10.35

HAuXeCl- -0.248(-0.211) -0.119(-0.066) 0.300(0.257) -0.933(-0.980) 13.88

HAuXeBr- -0.243(-0.205) -0.122(-0.062) 0.330(0.247) -0.964(-0.981) 12.61

ClAuXeCl- -0.731(-0.537) 0.275(0.123) 0.356(0.374) -0.901(-0.959) 10.22

BrAuXeBr- -0.493(-0.481) 0.015(0.081) 0.418(0.361) -0.940(-0.961) 10.83

The MP2 rather than the SCF density was used to compute the properties

Table 6 Mulliken (NBO) atomic charges of the equilibrium structure of XAuKrX- and HAuKrX- (X = F, Cl, Br) computed at the MP2 level

of theory

q(X(H)) q(Au) q(Kr) q(X) l/D

FAuKrF- -0.466(-0.702) 0.186(0.375) 0.157(0.292) -0.877(-0.966) 9.04

HAuKrF- -0.202(-0.202) 0.016(-0.011) 0.098(0.195) -0.912(-0.983) 13.19

HAuKrCl- -0.161(-0.176) 0.004(0.002) 0.109(0.163) -0.952(-0.989) 15.83

HAuKrBr- -0.149(-0.171) 0.001(0.004) 0.135(0.156) -0.986(-0.990) 14.15

ClAuKrCl- -0.573(-0.524) 0.358(0.247) 0.140(0.250) -0.925(-0.973) 12.61

BrAuKrBr- -0.421(-0.468) 0.205(0.202) 0.182(0.244) -0.967(-0.978) 13.02

The MP2 rather than the SCF density was used to compute the properties

1700 Struct Chem (2012) 23:1693–1710

123

dipole moments of the xenon, krypton, and argon molec-

ular anions are ca. 6–14, 9–16, and 11–17 D, respectively.

It should be noted that, for all of the three noble gas

molecular anion series, HAuNgCl- rather than HAuNgBr-

has the largest dipole moment. In contrast, for the six

X(H)HgNgX (X = F, Cl, Br) molecules, HHgXeBr rather

than HHgXeCl has the largest dipole moment [42].

The characteristic stretching vibrational frequencies and

infrared intensities of the three noble gas molecular anion

series are presented in Tables 8 and 9, respectively. As

shown in these two tables, the X(H)–Au stretching mode

always has considerably large infrared intensity. In addi-

tion, this mode is hardly coupled with other vibrational

modes. Thus, the stretching mode should be well suited for

the experimental identification. In contrast, for almost all of

the 18 X(H)AuNgX- molecular anions, the Au–Ng

stretching mode is fairly, or even highly, coupled with the

Ng–X stretching mode. At the MP2 level of theory, the

Au–Ng stretching frequencies are ca. 135–188, 126–202,

and 191–316 cm-1, respectively, for the Xe, Kr, and Ar

anions.

Geometries of the bending transition state

As expected, on the potential energy surface of the

X(H)AuNgX- molecular anions, the linear structure is a

local minimum but not a global minimum, which corre-

sponds to the complex structure [X(H)AuX]-���Ng. At the

MP2 level of theory, for all of the 18 molecular anions, the

linear local minimum will dissociate into the global mini-

mum after traversing a transition structure characterized by

the AuNgX bending vibration. At the CCSD(T) level of

theory, when the larger valence basis set of the gold atom

was applied, the bending transition structure was located

successfully for the molecular anions FAuXeF-, HAuXeF-,

HAuXeCl-, HAuXeBr-, ClAuXeCl-, and HAuArF- but

failed to be located for the other 12 molecular anions.

Geometrical parameters and the T1 diagnostic of the

bending transition structure of the 18 molecular anions are

presented in Figs. 4, 5, and 6, respectively.

As shown in Figs. 4, 5, 6 and 1, 2, 3, the MP2 calcu-

lations indicate that, for all of the 18 X(H)AuNgX-

molecular anions, the X(H)–Au bond of the transition

Table 7 Mulliken (NBO) atomic charges of the equilibrium structure of XAuArX- and HAuArX- (X = F, Cl, Br) computed at the MP2 level

of theory

q(X(H)) q(Au) q(Ar) q(X) l/D

FAuArF- -0.457(-0.693) 0.144(0.456) 0.229(0.219) -0.916(-0.982) 11.49

HAuArF- -0.237(-0.181) 0.032(0.032) 0.146(0.140) -0.941(-0.992) 15.47

HAuArCl- -0.203(-0.159) 0.020(0.035) 0.166(0.118) -0.983(-0.994) 17.42

HAuArBr- -0.197(-0.154) 0.030(0.035) 0.156(0.114) -0.988(-0.995) 15.21

ClAuArCl- -0.689(-0.517) 0.466(0.316) 0.191(0.188) -0.969(-0.988) 14.64

BrAuArBr- -0.450(-0.462) 0.217(0.272) 0.205(0.178) -0.972(-0.989) 14.74

The MP2 rather than the SCF density was used to compute the properties

Table 8 Computed harmonic vibrational frequencies (cm-1) and infrared intensities (km/mol) of the equilibrium structure of XAuXeX- and

HAuXeX- (X = F, Cl, Br)

Methods m(X(H)–Au) m(Au–Xe) m(Xe–X)

FAuXeF- MP2 536.6/116 178.3/29 254.2/198

CCSD(T) 511.4 162.7 250.6

HAuXeF- MP2 2290.9/240 135.4/36 214.1/129

CCSD(T) 2130.9 124.6 212.0

HAuXeCl- MP2 2321.2/183 152.1/7 92.5/49

CCSD(T) 2167.3 140.4 87.5

HAuXeBr- MP2 2325.9/180 144.5/0 63.2/21

CCSD(T) 2171.7 131.3 60.2

ClAuXeCl- MP2 372.8/42 188.3/19 113.8/63

CCSD(T) 348.5 172.1 109.1

BrAuXeBr-a MP2 261.6/17 171.0/9 75.1/28

a The BrAuXeBr- molecule has been optimized to a stationary point at the CCSD(T) level of theory. However, the followed CCSD(T)

frequency calculations were not performed for the sake of saving the computational time

Struct Chem (2012) 23:1693–1710 1701

123

structure is only slightly shorter than that of the equilibrium

structure, while the Au–Ng and Ng–X bonds of the tran-

sition structure are significantly longer than those of the

equilibrium structure. This is also the case for the available

CCSD(T) structures. Thus, it may be considered that the

transition state concerns the weakening of both the Au–Ng

and Ng–X bonds. In contrast, for the X(H)HgXeX (X = F,

Cl, Br) neutral molecules, both the X(H)–Hg and Hg–Xe

bonds become shorter while the Xe–X bond becomes

longer when the bending transition structure is formed [42].

Dissociation energy and reaction barrier height

Relative energies of the dissociation limits X(H)AuX- ?

Ng, X(H)AuNg ? X-, X(H)- ? AuNgX, X(H) ? Au ?

Ng ? X-, X(H)- ? Au ? Ng ? X, and the bending

transition state with respect to the corresponding X(H)

AuNgX- molecular anions are presented in Figs. 7, 8, 9,

10, 11, and 12. It should be pointed out that at the MP2

level, the zero-point energy (ZPE) was corrected for all of

the 18 molecular anions. However, at the CCSD(T) level,

the ZPE was not corrected for BrAuXeBr- and all of the

krypton and argon anions, and corrected for the other five

xenon anions.

It should be stated that the computational accuracy of both

the MP2 and CCSD(T) calculations is on the order of several

kcal/mol. On the other hand, it was shown in a very recent

study [59] that, when predicting the thermochemical stability

of XNgY (where Ng is a noble gas atom, and X and Y are

suitable functional groups or atoms) compounds, the error of

the MP2 calculations may arrive up to some kcal/mol.

As shown in Figs. 7, 8, 9, 10, 11, and 12, for most of the

relative energies (including the dissociation barrier ener-

gies), the MP2 values differ only slightly from the avail-

able CCSD(T) values. For example, the calculated

dissociation barrier of FAuXeF- is ca. 14 and 13 kcal/mol,

respectively, at the MP2 and CCSD(T) levels. Thus, the

MP2 values may be reliable for the energetics analysis.

As shown in Figs. 7, 8, 9, 10, 11, and 12, the MP2 cal-

culations indicate that the X(H)AuNgX- anion is less stable

than the dissociation limit X(H)AuX- ? Ng by ca. 25–35,

33–48, and 37–57 kcal/mol, respectively, for the Xe, Kr, and

Ar series. As a comparison, the CCSD(T) calculations

indicate that the X(H)HgXeX molecule is less stable than the

global minimum X(H)HgX���Xe by ca. 60–70 kcal/mol [42].

As shown in Figs. 7, 8, 9, 10, 11, and 12, when X(H)AuN-

gX- dissociates into the global minimum X(H)AuX- ? Ng

through the bending transition state, the MP2 calculations

indicate that the reaction barrier energies are ca. 5–14, 3–9,

and 2–5 kcal/mol for the Xe, Kr, and Ar series, respectively.

It appears likely that the extremely small barriers effectively

negate any hope of detecting the krypton or argon species. As

shown in Figs. 7, 8, 9, 10, 11, and 12, the molecular anions

X(H)AuNgX- are all more stable than the correspond-

ing X(H)AuNg ? X-, X(H)- ? AuNgX, X(H) ? Au ?

Ng ? X-, and X(H)- ? Au ? Ng ? X dissociation limits.

In particular, at the MP2 level of theory, X(H)AuNgX- are

more stable than X(H)AuNg ? X- by ca. 14–38, 11–30, and

9–25 kcal/mol, respectively, for the Xe, Kr, and Ar seires.

Since both X(H)AuNg and X- are chemically stable species,

some of the molecular anions X(H)AuNgX- (especially

FAuXeF-) may probably be produced by these two species

(such as FAuXe and F-).

Lignell et al. [60] have suggested to estimating the

accuracy of the calculated energies by comparing the

interval between the two-body (X(H)AuX- ? Ng) and

three-body (X(H)Au ? Ng ? X-) asymptotes with the

experimental dissociation energies. This approach may also

be applied to the present molecular anions. However,

unfortunately, for all of the six X(H)AuX- (X = F, Cl, Br)

anions, the experimental dissociation energies are not

available.

Table 9 Harmonic vibrational

frequencies (cm-1) and infrared

intensities (km/mol) of the

equilibrium structure of

XAuNgX- and HAuNgX-

(Ng = Kr, Ar; X = F, Cl, Br)

computed at the MP2 level of

theory

m(X(H)–Au) m(Au–Ng) m(Ng–X)

FAuKrF- 558.1/98 169.8/64 262.3/90

FAuArF- 570.1/85 316.3/23 156.8/83

HAuKrF- 2367.0/136 126.3/59 213.3/56

HAuArF- 2406.4/85 244.6/9 120.3/76

HAuKrCl- 2385.2/105 159.4/2 81.3/42

HAuArCl- 2415.5/69 199.8/0 72.8/36

HAuKrBr- 2387.7/103 150.4/0 55.4/18

HAuArBr- 2417.3/67 190.7/2 48.9/15

ClAuKrCl- 383.2/34 201.7/7 101.9/51

ClAuArCl- 391.0/28 258.3/1 91.5/42

BrAuKrBr- 268.0/16 183.0/2 66.9/22

BrAuArBr- 278.2/14 231.9/1 59.2/18

1702 Struct Chem (2012) 23:1693–1710

123

The Born–Haber cycle for the Na[FXeAuF] compound

As X(H)AuNgX- are of anionic form, it is of interest if

these species could exist in bulk stabilized by their lattice

energies. In the following, the Born–Haber cycle (Fig. 13)

for one of the most prominent compounds, Na[FXeAuF],

was calculated.

As shown in Fig. 13, if the solid compound Na[F-

XeAuF] is prepared from the solid Na, solid Au, gaseous

Xe and gaseous F2, the enthalpy of formation may be

calculated as follows:

DHf ¼ DHIE þ DHEA þ DH0f þ DHL þ DHf1 þ DHsub

þ DHf2 þ DHsub1 þ DHdecomp;

where DHf is the enthalpy of formation of the solid

Na[FXeAuF]; DHIE is the ionization energy of the sodium

atom, 118.5 kcal/mol [61]; DHEA is the electron affinity of

the fluorine atom, -78.4 kcal/mol [62]; DHf0 is the

enthalpy of formation of the gaseous molecular anion

FAuXeF-, which can be obtained from the present MP2

calculations (sum of electronic and thermal enthalpies of

the species concerned),

Fig. 4 Bond length (A) and

angle (�) and the T1 diagnostic

of the transition structure of

XAuXeX- and HAuXeX-

(X = F, Cl, Br) computed at the

MP2 and CCSD(T) (inparentheses) levels

Struct Chem (2012) 23:1693–1710 1703

123

DH0f ¼ �350:236882� �250:475323ð Þ � �99:701471ð Þ½ �� 627:5095 ¼ �37:7 kcal=molð Þ;

DHL is the lattice energy of the ionic solid Na[FXeAuF],

which can be calculated approximately from the

Kapustinskii equation [63]

DHL ¼ �Km zþj j z�j jrþ þ r�

1� d

rþ þ r�

� �;

where K = 1.2025 9 10-4 J m mol-1, d = 3.45 9 10-11 m,

m is the number of ions in the empirical formula, z? and z- are

the numbers of elementary charge on the cation and anion,

respectively, r? and r- are the radii of the cation and anion,

respectively.

The Pauling ionic radius of the Na? cation is

95 9 10-12 m [64]. From the present MP2 calculations, in

the molecular anion FAuXeF-, the distance between the

two terminal F atoms is 698 9 10-12 m. Thus, the radius

of the molecular anion FAuXeF- can be taken approxi-

mately as 349 9 10-12 m. As a consequence,

DHL ¼�Km zþj j z�j jrþ þ r�

1� d

rþ þ r�

� �¼�1:2025� 10�4

� 2� 1� 1

95þ 349ð Þ� 10�12� 1� 3:45� 10�11

95þ 349ð Þ� 10�12

� �

¼�5:42� 105� 1� 0:078ð Þ¼�5:00� 105 J=mol¼�119:5 kcal=mol

DHf1 is the enthalpy of formation of the gaseous molecule

FAuXe, which can be obtained from the present MP2

calculations (sum of electronic and thermal enthalpies of

the species concerned),

Fig. 5 Bond length (A) and

angle (�) and the T1 diagnostic

of the transition structure of

XAuKrX- and HAuKrX-

(X = F, Cl, Br) computed at the

MP2 level

1704 Struct Chem (2012) 23:1693–1710

123

DHf1 ¼ �250:475323� �235:007516ð Þ � �15:426662ð Þ½ �� 627:5095

¼ �25:8 kcal=mol

DHsub is the enthalpy of sublimation of the solid sodium,

25.9 kcal/mol [65]; DHf2 is the enthalpy of formation of

the gaseous molecule AuF, which can be obtained from the

present MP2 calculations (sum of electronic and thermal

enthalpies of the species concerned),

DHf2 ¼ �235:007516� �99:576243ð Þ � �135:325276ð Þ½ �� 627:5095

¼ �66:5 kcal=mol

DHsub1 is the enthalpy of sublimation of the solid gold,

88.0 kcal/mol [66]; DHdecomp is the enthalpy of decompo-

sition of the gaseous fluoride molecule, 37.5 kcal/mol [67].

As a consequence,

DHf ¼ 118:5þ �78:4ð Þ þ �37:7ð Þ þ �119:5ð Þþ �25:8ð Þ þ 25:9þ �66:5ð Þ þ 88:0þ 37:5

¼ �58:0 kcal=mol

Thus, if the solid compound Na[FXeAuF] is prepared

from the solid Na, solid Au, gaseous Xe and gaseous F2,

the estimated enthalpy of formation will be ca. -58 kcal/

mol.

Conclusions

The equilibrium structure and the bending transition

structure of the 18 noble gas molecular anions X(H)AuN-

gX- (X = F, Cl, Br; Ng = Xe, Kr, Ar) were investigated

at the MP2 and CCSD(T) levels of theory. For most of the

18 molecular anions, geometry optimizations of the

Fig. 6 Bond length (A) and

angle (�) and the T1 diagnostic

of the transition structure of

XAuArX- and HAuArX-

(X = F, Cl, Br) computed at the

MP2 and CCSD(T) (inparentheses) levels

Struct Chem (2012) 23:1693–1710 1705

123

transition structure have encountered various difficulties.

Such computational difficulties are most probably due to

the weak intramolecular interaction nature of the molecular

anions but not probably due to the multi-configuration

nature of the molecular anions. Such computational diffi-

culties have been overcome at the MP2 level with the

‘‘CalcFC’’ option of the ‘‘Opt’’ keyword of the Gaussian 09

programs but not overcome at the CCSD(T) level.

Both the MP2 and CCSD(T) calculations indicate that

the Au–Ng bond length of the equilibrium structure

is increased following the order FAuNgF- \ ClAu-

NgCl- \ BrAuNgBr- \ HAuNgF- \ HAuNgCl- \

Fig. 7 Relative energies

(kcal/mol) of the related

dissociation limits with respect

to FAuNgF- (Ng = Xe, Kr,

Ar). The MP2 values were

corrected for the ZPE for all of

the molecular anions. The

CCSD(T) values (inparentheses) were corrected for

the ZPE for the xenon anion, but

not corrected for the ZPE for the

krypton and argon anions

Fig. 8 Relative energies

(kcal/mol) of the related

dissociation limits with respect

to HAuNgF- (Ng = Xe, Kr,

Ar). The MP2 values were

corrected for the ZPE for all of

the molecular anions. The

CCSD(T) values (inparentheses) were corrected for

the ZPE for the xenon anion, but

not corrected for the ZPE for the

krypton and argon anions

1706 Struct Chem (2012) 23:1693–1710

123

HAuNgBr-. Thus, the Au–Ng bond length of X(H)A

uNgX- is more dependent on the electronegative

fragment that is bonded to the Au atom rather than on

the electronegative fragment that is bonded to the Ng

atom.

The X(H)–Au bond of X(H)AuNgX- is very approxi-

mate to that of X(H)AuNg, the Au–Ng bond of X(H)

AuNgX- is apparently shorter than that of X(H)AuNg,

while the Ng–X bond of X(H)AuNgX- is considerably

longer than that of AuNgX. In other words, the presence of

the right X- anion makes the Au–Ng bond of X(H)AuNg

become stronger while the presence of the left X(H)-

anion makes the Ng–X bond of AuNgX become weaker.

Based on the interatomic distances and atomic charge

distributions, X(H)AuNgX- may be better described as

X(H)AuNg���X- rather than as X(H)-���AuNgX, which is

consistent with that X(H)AuNg is more stable than the

corresponding isomer AuNgX(H).

Fig. 9 Relative energies (kcal/

mol) of the related dissociation

limits with respect to

HAuNgCl- (Ng = Xe, Kr, Ar).

The MP2 values were corrected

for the ZPE for all of the

molecular anions. The

CCSD(T) values (inparentheses) were corrected for

the ZPE for the xenon anion, but

not corrected for the ZPE for the

krypton and argon anions

Fig. 10 Relative energies (kcal/

mol) of the related dissociation

limits with respect to

HAuNgBr- (Ng = Xe, Kr, Ar).

The MP2 values were corrected

for the ZPE for all of the

molecular anions. The

CCSD(T) values (inparentheses) were corrected for

the ZPE for the xenon anion, but

not corrected for the ZPE for the

krypton and argon anions

Struct Chem (2012) 23:1693–1710 1707

123

For almost all of the noble gas molecular anions, the

Au–Ng stretching mode is fairly or even highly coupled

with the Ng–X stretching mode while the X(H)–Au

stretching mode is hardly coupled with other modes.

The MP2 calculations indicate that the Au–Ng

stretching frequencies are ca. 135–188, 126–202, and

190–316 cm-1 for the Xe, Kr, and Ar molecular anions,

respectively.

For most of the relative energies, the MP2 values are

approximate to the available CCSD(T) values. At the MP2

Fig. 11 Relative energies (kcal/

mol) of the related dissociation

limits with respect to

ClAuNgCl- (Ng = Xe, Kr, Ar).

The MP2 values were corrected

for the ZPE for all of the

molecular anions. The

CCSD(T) values (inparentheses) were corrected for

the ZPE for the xenon anion, but

not corrected for the ZPE for the

krypton and argon anions

Fig. 12 Relative energies (kcal/

mol) of the related dissociation

limits with respect to

BrAuNgBr- (Ng = Xe, Kr,

Ar). The MP2 values were

corrected for the ZPE for all of

the molecular anions. The

CCSD(T) values (inparentheses) were not corrected

for the ZPE for all of the

molecular anions

1708 Struct Chem (2012) 23:1693–1710

123

level of theory, X(H)AuNgX- is less stable than the global

minimum X(H)AuX- ? Ng by ca. 25–35, 33–48, and

37–57 kcal/mol for the Xe, Kr, and Ar series, respectively.

The reaction barriers are ca. 5–14, 3–9, and 2–5 kcal/mol,

respectively, for the three series when the anion dissociates

into X(H)AuX- ? Ng through the bending transition state.

In addition, X(H)AuNgX- are more stable than

X(H)AuNg ? X- by ca. 14–38, 11–30, and 9–25 kcal/

mol, respectively, for the three series.

Supporting information

Results calculated using the smaller valence basis set of the

gold atom and the computational difficulties of the inves-

tigated species are presented in the Supporting Information.

Acknowledgments This study was supported by the Natural

Science Research Foundation of the Education Department of Henan

Province of China (Grant No. 2009A150032), by the Basic and

Frontier Technical Research Project of Henan Province of China

(Grant No. 102300410202), by the National Basic Research Program

of China (Grant No. 2011CBA00701), and by the National Natural

Science Foundation of China (Grant No. 21171084). Four anonymous

reviewers are greatly acknowledged for helping us improving the

original manuscript.

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