Theoretical Investigation of the M+–RG2 (M = Alkaline Earth Metal; RG = Rare Gas) Complexes

Adrian M. Gardner, Richard J. Plowright, Jack Graneek, Timothy G. Wright and W. H. Breckenridge

67th International Symposium on Molecular SpectroscopyOhio State University

22nd June 2012

M+–RG Complexes: A Model of Solvation• The M+–RG complexes are prototypical systems for the

investigation of solvation.

• Experimental studies have focused on the electronic spectroscopy of complexes containing alkaline earth metal cations.1

• The complexes of the closed shell alkali metal cations have been studied intensely using high level ab intio techniques.2

• Trends in equilibrium bond length and dissociation energy of the closed shell complexes are easy to rationalize.

• Whereas trends in the open shell M+–RG complexes were not!

1. See for example, M. A. Duncan, Annu. Rev. Phys. Chem., 48, 69, (1997).2. See for example, Breckenridge et al., Chem. Phys., 333, 77 (2007).

M+–RG Complexes: A Model of Solvation

Gardner et al., J. Phys. Chem. A., 114, 7631, (2010).

M+–RG Complexes: A Model of Solvation• The M+–RG complexes are prototypical systems for the

investigation of solvation.

• Experimental studies have focused on the electronic spectroscopy of complexes containing alkaline earth metal cations.1

• The complexes of the closed shell alkali metal cations have been studied intensely using high level ab intio techniques.2

• Trends in equilibrium bond length and dissociation energy of the closed shell complexes are easy to rationalize.

• Whereas trends in the open shell M+–RG complexes were not!

• In the present investigation aim to investigate increasing levels of solvation of Li+ and Be+ cations.

1. See for example, M. A. Duncan, Annu. Rev. Phys. Chem., 48, 69, (1997).2. See for example, Breckenridge et al., Chem. Phys., 333, 77 (2007).

Computational Methodology

• Standard aug-cc-pVTZ basis sets were employed for He, Ne and Ar.

• For Kr, and Xe the ECP10MDF and ECP28MDF effective core potentials along with the aug-cc-pwCVTZ-PP basis sets were utilized.

• For the metals, Li+ and Be+, aug-cc-pwCVTZ basis sets were employed.

• All calculations were carried out at the MP2 level of theory.

• Geometry optimizations and dissociation energies have been calculated using QZ and 5Z versions of the basis sets described above, but are not discussed herein.

• MOLPRO was used for all geometry optimization and energy calculations.

0 60 120 180 240 300 360

-700

-600

-500

-400

-300

-200

-100

0

He–Li+–He Bond Angle / oIn

tera

ction

Ene

rgy

Rela

tive

to th

e Li

+–He

+ H

e a

sym

ptot

e/ c

m-1

“Prototypical” Systems: Li+–He2

• A global minimum is found with a bond angle of 180o.

• The Li+–He bond length and dissociation energy calculated for the Li+–He2 complex is

almost identical to that of the Li+–He dimer complex.

• A stationary point is found with a linear Li+–He–He conformation, with the He–He separation shorter than calculated for the He2 cluster.

0 60 120 180 240 300 360

-640

-630

-620

-610

-600

-590

-580

He–Li+–He Bond Angle / oIn

tera

ction

Ene

rgy

/ cm

-1

“Prototypical” Systems: Li+–He2

• A very shallow minimum is observed at bond angle of ≈115o.

• This conformation has a slightly longer He–He bond length than in the He2 cluster.

“Prototypical” Systems: Li+–Xe2

0 60 120 180 240 300 360

-4000

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

Xe–Li+–Xe Bond Angle / oIn

tera

ction

Ene

rgy

/ cm

-1

• A global minimum is found with a Xe–Li+–Xe bond angle of 180o.

• A second minimum is observed with a linear Li+–Xe–Xe conformation, with a Xe–Xe separation that is shorter than in the Xe2 cluster.

Open Shell Complexes: Be+–He2

0 60 120 180 240 300 360

-120

-100

-80

-60

-40

-20

0

He–Be+–He Bond Angle / oIn

tera

ction

Ene

rgy

/ cm

-1

The calculated He-He bond length in the helium dimer is 3.06 Å.

0 60 120 180 240 300 360

-2500

-2000

-1500

-1000

-500

0

Ar–Be+–Ar Bond Angle / oIn

tera

ction

Ene

rgy

/ cm

-1

Open Shell Complexes: Be+–Ar2

The calculated Ar-Ar bond length in the argon dimer is 3.77 Å

The De calculated for the Be+–Ar complex is 4050 cm-1.

Open Shell Complexes: Be+–Ar2

Δoccupancy Charge

Be+ +0.6892s -0.042px 0.022py 0.082pz 0.22Ar +0.1553s -0.033px -0.013py -0.063pz -0.05

Natural Population Analysis

Open Shell Complexes: Be+–Ar2

Eint = -379 cm-1 Eint = +200 cm-1

Open Shell Complexes: Be+–Ar2

Eint = -379 cm-1 Eint = +200 cm-1

Open Shell Complexes: Be+–Ar2

Eint = -379 cm-1 Eint = +200 cm-1

Δoccupancy Charge

Be+ +0.852s 0.002px 0.012py 0.012pz 0.12Ar +0.143s -0.023px -0.013py -0.013pz -0.10Ar +0.013s 0.003px 0.003py 0.003pz -0.01

Δoccupancy Charge

Be+ +0.852s 0.052px 0.012py 0.012pz 0.06Ar +0.073s -0.013px -0.013py -0.013pz -0.05Ar +0.073s -0.013px -0.013py -0.013pz -0.05

Δoccupancy Charge

Be+ +0.852s -0.022px 0.012py 0.012pz 0.13Ar +0.153s -0.023px -0.013py -0.013pz -0.10

Eint = -4050 cm-1

Conclusions

• Slices through the Li+–RG2 and Be+–RG2 potential energy surfaces have been presented and discussed.

• Even for the expectedly simple, closed shell Li+–RG2

complexes, multiple minima were observed.

• The linear RG–Li+–RG conformations were determined to be the most stable for all Li+–RG2 complexes.

• The Be+–RG2 surfaces were considerably more complicated.

• Bent RG–Be+–RG conformations were determined to be the most stable for all Be+–RG2 complexes.

• This was determined to be an effect of synergic interactions within the complex; sp2 hybridization of the Be+ orbital, and charge transfer from the RG2 dimer to Be+.

Prof. Timothy Wright Prof. Bill BreckenridgeDr. Richard PlowrightJack Graneek

Acknowledgements