A note on geometry relaxation of molecular positron complexesJosé R. Mohallem and Cristina P. Gonçalves Citation: The Journal of Chemical Physics 121, 5553 (2004); doi: 10.1063/1.1781617 View online: http://dx.doi.org/10.1063/1.1781617 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/121/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Intermolecular interactions of trifluorohalomethanes with Lewis bases in the gas phase: An ab initio study J. Chem. Phys. 141, 134308 (2014); 10.1063/1.4896899 Accurate determination of the binding energy of the formic acid dimer: The importance of geometry relaxation J. Chem. Phys. 140, 084315 (2014); 10.1063/1.4866696 Geometry relaxation effects for molecules as a result of binding with a positron J. Chem. Phys. 121, 9191 (2004); 10.1063/1.1805493 Characteristics and relaxation dynamics of van der Waals complexes between p-difluorobenzene and Ne J. Chem. Phys. 120, 11469 (2004); 10.1063/1.1747847 Many-body interaction in glycine –( water ) 3 complex using density functional theory method J. Chem. Phys. 120, 170 (2004); 10.1063/1.1630019

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A note on geometry relaxation of molecular positron complexesJose R. Mohallem and Cristina P. GoncalvesLaboratorio de Atomos e Mole´culas Especiais, Departamento de Fı´sica, ICEx,Universidade Federal de Minas Gerais, P.O. Box 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil

~Received 8 January 2004; accepted 18 June 2004!

@DOI: 10.1063/1.1781617#

The study of the formation of bound states of a positron(e1) with a molecule~a positron complex! is a matter ofincreasing interest.1 The calculations of energies and wavefunctions of bound states of a positron complex are, how-ever, restricted by their very nature~three different kinds ofparticles!, as the most simplifying step of molecular calcula-tions, the Born-Oppenheimer approximation, becomes inap-plicable to the whole complex. Treating all particles on acommon footing, with full optimization of the electron-positron wave function and the parent molecule geometry, isfeasible just for very small systems, even though with analmost prohibitive computational burden.2 To make calcula-tions with most interesting systems, scientists have claimedthat, in view of the small positron mass, its binding energy~or positron affinity! could be obtained by keeping the samegeometry of the isolated molecule in the calculation of thecomplex. Recent examples are the applications to the@urea;e1# and@acetone;e1# complexes,3 based on a molecu-lar orbital-configuration-interaction approach in which theelectron-positron correlation is described on theconfiguration-interaction level. An important and reliableconclusion is that the positron attaches to the electroniccloud of the oxygen atom, which imparts to it some kind oflocalization. On the other hand, the positron affinities re-ported in Ref. 3 are very small. As the positron has the samecharge as that of a proton, we could expect the parent mol-ecule geometry to relax in a way that the relaxation energywould contribute an important amount to the positron affin-ity. This conjecture is supported by the knowledge that, forexample, the positronium (e1,e2) atom is more electro-negative than alkaline elements;4 that is, the positron must beable to substantially change atomic bonds.

We check this hypothesis with the@urea;e1# complex,for which we expect the CO bond to be the most affected.This is done within the molecular model for positron com-plex, developed in our group, in which we treate1 as anextra nucleus of an exotic molecule, provided we account forthe finite nuclear mass effects on a variational adiabaticbasis.5,6 We have been able to generate potential energy sur-faces for nuclei and positron motions whose absolute minimaidentify the equilibrium geometries of heavy nuclei~in thepresence ofe1) and the average position ofe1. For ex-ample, we have recently considered the@LiH; e1# complex.6

We found a ‘‘linear configuration’’ for this exotic molecularion in which the Li-H bond distance of 3.36 a.u. becomesabout 11.3% larger than the same bond distance in the neu-tral LiH molecule ~3.016 a.u.!, due to electron polarizationtoward the positron. This result is in excellent agreement

with a fully correlated calculation of Ref. 2 that yields 3.35a.u. As the ionization potential of LiH depends on its geom-etry, which changes in the presence of the positron, it be-comes clear that simple energetic considerations based onfixed geometry properties of the parent molecule as the ion-ization potential have limited power of prediction.7 We thinkthe same reasoning applies to the attainment of bound statesand, to a lesser extent, to the prediction of positron position-ing and annihilation rates in positron complexes.

In the @urea;e1# case such a huge geometry change isnot expected. But in view of the reported very small positronaffinity,3 of about 531024 a.u. it seems that even small ge-ometry changes can affect the predictions in a considerableextension. To check this we apply our method to the complex@urea;e1# on the electronic second-order Mo¨ller-Plessetlevel, using a@6-31G1one polarizedp function# basis set.We first optimize the geometry of urea, which becomesslightly different from that in Fig. 1 of Ref. 3. Here we focuson just the CO bond distance for which we obtainedRCO

51,260 Å and on the corresponding energyE152224, 3685a.u. With this fixed geometry we attach a positron and opti-mize its ‘‘position’’, which agrees with the prediction of Ref.3 concerning the site of positron bonding; that is, it binds tothe O atom outside the CO bond, although not in a linearconfiguration due to the asymmetry of the field of the otheratoms. The energy obtained in this way isE252224, 6034a.u. Next we allow the geometry of the whole complex torelax and observe substantial changes. The CO distance be-comesRCO51,315 Å and the energy becomesE352224,6113 a.u. It is important to stress that it is not correct toidentify the energy differenceE12E350.2428 a.u. with thepositron affinity, because theEi are minimal points on po-tential energy surfaces for nuclei and positron motions ratherthan actual energy eigenstates. But the energy difference thatwe obtained between the fixed and the relaxed geometries ofthe complex,E22E350.0079 a.u. is two orders of magni-tude larger than the positron affinity reported.3 Once we relyon our method of geometry relaxation, which has already-worked well for @LiH; e1#, there is a much larger stabiliza-tion of the complex@urea;e1# due to geometry relaxation,which comes along with the substantial increase of about 4%of the CO bond. In conclusion, our calculations reinforce theprediction of Ref. 3 concerning the existence of a bound stateof (urea;e1) but with a much larger positron affinity.

The above considerations show that molecular relaxationin the presence of a positron could play a fundamental role inthe process of binding of a positron to a molecule. In fact,much work must be done until this point is fully clarified. To

JOURNAL OF CHEMICAL PHYSICS VOLUME 121, NUMBER 11 15 SEPTEMBER 2004

55530021-9606/2004/121(11)/5553/2/$22.00 © 2004 American Institute of Physics

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do this, we propose that our method could be used as aneconomic geometry relaxation first step of a calculation of apositron complex, in connection with another one that treatselectron-positron correlation well, in a second step.

This research was supported by CNPq and Capes.

1Y. C. Jean, P. E. Mallon, and D. M. Schrader,Principles and Applicationsof Positron and Positronium Chemistry~World Scientific, Singapore,2003!.

2K. Strasburger, J. Chem. Phys.114, 615 ~2001!.3M. Tachikawa, R. J. Buenker, and M. Kimura, J. Chem. Phys.119, 5005~2003!.

4J. Mitroy, M. W. Bromley, and G. G. Ryzhikh, J. Phys. B35, R1~2002!.

5F. Rolim, J. P. Braga, and J. R. Mohallem, Chem. Phys. Lett.332, 139~2000!.

6J. R. Mohallem, F. Rolim, and C. P. Gonc¸alves, J. Phys. B37, 1045~2004!.

7See also M. Mella, G. Morosi, and D. Bressanini, J. Chem. Phys.112,3928 ~2000!.

5554 J. Chem. Phys., Vol. 121, No. 11, 15 September 2004 J. R. Mohallem and C. P. Goncalves

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