Ionization energies of Yn(n = 1−4)

26 May 1995

CHEMICAL PHYSICS LETTERS

ELSEVIER

ChemicalPhysics Letters238 (1995) 203-207

Ionization energies of Y, (

n =

l-4)

Dingguo Dai, K. Balasubramanian Department of Chemistry, Arizona State Vniversiry, Tempe, AZ 85287-1604, USA

Received 16 December1994; in final form 20 February 1995

Abstract We have studied the vertical ionization energies of yttrium clusters using complete active space multi-configuration followed by multi-reference configuration interaction calculations which included 2.7 million configurations. The computed ionization energies and the overall trend for the ionization potentials as a function of cluster size agree with the recent photoionization spectra of yttrium clusters reported by Knickelbein.

1. Introduction Transition metal clusters are intriguing as a result of the large number of electronic states of different spin multiplicities and the complexity of the metalmetal bond involving the metal s, p and d orbitals. Experimental and theoretical studies aimed at comprehending the nature of low-lying electronic states are on the increase in recent years [l-22]. Experimental studies on yttrium clusters are limited in that earlier studies were focused mainly on Y2 and Y3

[21,22]. The current theoretical investigation

on the ionization potentials of the yttrium clusters is motivated by the recent photoionization spectrum of yttrium clusters reported by Knickelbein [l]. This led to the measurement of the ionization potentials of Y, and Y,O for n = 2-31. One of the most striking features of the spectrum is the absence of magic numbers or odd-even alternations. Knickelbein suggested that

this would imply that the threshold for photoionization occurs mainly from a localized 4d orbital rather than from a 5s orbital of Y. Furthermore the vertical ionization potentials were found to decrease rapidly

and monotonically for smaller clusters. These observations need to be explained. The nature of the orbitals involved in the ionization process should be studied. The objective of this Letter is to seek answers to these intriguing questions pertinent to the yttrium clusters as a function of cluster size. We compute the ionization potentials for Y, (n = l-4) using relativistic ab initio CASSCF/MRCI techniques. We also analyze the nature of the orbital from which the electron is removed during the ionization process and the overall nature of the orbitals after the ionization process. We found considerable orbital relaxation effects upon ionizing the clusters. Our computed ionization energies and the overall trend agree with the recent spectrum reported by Knickelbein [l].

2. Method of computations We employed relativistic effective core potentials (RECPs) which retained the outer 4s24p65s24d’ electrons of the yttrium atom in the valence space replacing rest of the core electrons by RECPs. The RECPs

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D. Dai, K. Balasubranumian/Chemical

together with the (5s5p4d) valence Gaussian basis sets reported by LaJohn et al. [23] were used in the current study. The basis functions corresponding to the 4s and 4p orbitals were contracted together with the (4d/3d) contraction which resulted in a (4s3p3d) basis set. This was augmented further with one set of ten-component 4f functions with or = 0.2. The resulting basis is labelled (4s3p3dlf). For the Y atom and YZ dimer both basis sets were compared and it was found that the effect of 4f functions is to increase the IP by 0.04-0.09 eV. Consequently, for the Y3 and Y4 clusters we did not include the 4f functions in the basis sets. We used the CASSCF method to generate the orbitals for higher-order CI computations. The 4s and 4p orbitals of the yttrium atoms were kept in core at the CASSCF stage. The active space for Y2 and Yl consisted of all 4d and 5s orbitals of Y at infinite separation although at the equilibrium geometry the active orbitals were composed of 4d, 5s and 5p atomic orbitals of Y. For Y3, Y4, Y3f and Yl restricted CAS-MCSCF computations had to be used since the full active space generates too many configurations. In the case of Y3 and Yc ,five a,, four b,, three b, and one a2 orbitals arising from 4s and 4p orbitals of Y were inactive in that these orbitals were allowed to relax but excitations from these orbitals were not allowed. Remaining electrons were distributed in all possible ways among the remaining three a,, three b,, one b,, and one a2 orbitals, which were the most important set of orbitals composed of 4d, 5s, and 5p of Y near the equilibrium geometry. For Y4 and Yl again 4s and 4p orbitals of Y were kept inactive (that is six a,, four b,, four b,, and two a,) and the remaining electrons were distributed in all possible ways among four a,, three b, and three b, orbitals. All electrons which correspond to 5s24d’ of Y atoms at infinite separation were distributed in all possible ways among these orbitals. The multi-reference configuration interaction computations were carried out following the CASSCF for Y3, Y3+, Y4 and Yl. All configurations in the CASSCF with coefficients > 0.07 as well as 0.05 were included as reference configurations; single and double excitations were allowed from these reference configurations in the MRCI. The MRCI included up to 2.7 million configurations. We found that the computed ionization energies changed by 0.13 eV

Physics Letters 238 (1995) 203-207

out of 4.8 eV for Y3 due to the difference in the threshold of 0.05 and 0.07. The neutral yttrium clusters were studied before by comparable levels of theories by the authors [20]. The most probable ground states of Y2, Y3 and Y4 were found to be ‘2: <“L!!‘~,2A!1;Da,), and c3T,, ‘Al; T,), respectively, where the electronic states within parentheses stand for nearly degenerate electronic states. Based on the highest-occupied orbitals of these clusters, alternative electronic states were considered for Y,‘. All computations were carried out using one of the author’s [24] modified version of ALCHEMY II codes ’ to include RECPs.

3. Results and discussions We start with the discussion of alternative electronic states considered for Y,. Since the neutral dimer exhibits two very low-lying electronic states of 5Z; and ‘2: symmetries [20], we computed the properties of the 4Z; and 211Uelectronic states of Y + . The former arises from ionizing the HOMO of ‘Z; while the latter from ionizing the HOMO of *Z’p’. The 42; state of Yc was found to be lower by 0.58 eV at the full second-order configuration interaction (SOCI) level of theory. Both nearly degenerate “X2 and ‘A! electronic states of Y3 [20] yield the closed-shell A, electronic state for Y:. This state would exhibit D,, geometry and not undergo Jahn-Teller distortion. In the case of Yi removal of an electron from the 2t, HOMO [20] for both 3T, and ‘A1 yields the 2T2 electronic state. Clearly this state would undergo Jahn-Teller distortion. The neutral 3T, state would also undergo Jahn-Teller distortion. Table 1 shows the vertical ionization potentials for small Y,, clusters using two different basis sets (only for the dimer and the atom). The values listed under the CI + Q column are included to show the effect of unlinked quadruple clusters through the Davidson correction. As seen from Table 1, the 4f functions increase the IP by only 0.04-0.09 eV for

’ The major authors of ALCHEMY11 are B. Liu, B. Lengsfield and M. Yoshimine.

205

D. Dai, K. Balasubramanian / Chemical Physics Letters 238 (1995) 203-207

Y2 and Y, respectively. We thus conclude that 4f functions do not play a significant role for the IPs. As seen from Table 1, our computed ionization potentials and the overall trend are consistent with the recent experimental results of Knickelbein [l]. Our computed results are within 0.02-0.45 eV of the experimental results. For the tetramer both the neutral and positive ion would undergo Jahn-Teller distortion and thus the computed result is somewhat less accurate. The IP of the yttrium atom was obtained as the difference in the energies of Y2 and Y2+ at the dissociation limit. Atomic computations of Y and Y+ were also made with different basis sets. The direct atomic computations were made to test the effect of further extension of basis sets. The atomic IP of the yttrium atom obtained using the larger (5s5p4dlf) basis set is only 0.06 eV higher than the SOCI value obtained using the (4s3p3dlf) basis set. This suggests that the computations have converged with respect to the basis set. However the direct atomic SOCI + Q value of 5.93 eV is a bit smaller than the value inferred from Y2 + Y: at the dissociation limit shown in Table 1. At any rate the computed IPs for larger clusters are expected to be uniformly smaller than the experiment. In agreement with the experiment, we find a large drop in the IP of the dimer compared to the isolated atom. The IP for the trimer increases slightly compared to the dimer. In Table 2 we have reported IPs

Table 1 Vertical ionization n

1 2

3 4

potentials

of yttrium clusters

at the CI level ’

Basis set

IP (eV) CI

CI+Q

exp.

4s3p3d 4s3p3dlf 4s3p3d 4s3p3dlf 4s3p3dlf 4s3p3dlf 4s3p3d 4s3p3d

5.98 6.05 4.83 4.85 d 3.97 = 4.27 f 4.93 3.82

6.03 6.12 4.88 4.92 d 4.05 = 4.35 f 5.13 3.95

6.22 6.22 4.96 4.96

b b ’ ’

5.00 c 4.55 c

“For Y+Y+ and Y,-Y: the SOCI method was employed while for Ys + Y: and Y4 + Yl the MRSDCI method was employed. b Ref. 1251. ’ Ref. [l]. d For Y#8; l-+ Y: c48, ) process. e For Y#Si )+ Y; t4H, 1 process. f For Yr(‘2: ) + Y; (‘II,) process.

Table 2 The population analysis clusters of yttrium Percentage

of the HOMO

in the neutral

atom or

(%)

S

P

d

0 0 0 1.4

0 13.9 40.6 23.9

100 86.1 59.4 74.7

for Y,(‘C;) + Y,<“C,), Y,<‘Z,‘> + Y,‘<“X;> and Y,
206

D. Dai, K. Balasubramanian/

Table 3 The comparison of the population analysis between atom or clusters and the positive ions of yttrium a n

2b 2= 3 4

Y. S

1.120 0.985 1.232 1.464

Chemical Physics Letters 238 (1995) 203-207

the neutral

Y,’ P

d

s

P

d

0.570 0.377 0.691 0.686

1.310 1.638 1.077 0.850

0.846 0.885 1.164 1.087

0.266 0.219 0.450 0.584

1.388 1.396 1.052 1.079

a The population values of Y, or Y,’ refer to the average population per Y atom. b For Y2(58; I-+ Y: (‘I;, 1. ’ ForY,(1X~)+Y~(211,).

A notable feature is that after ionization the orbitals of yttrium clusters undergo considerable relaxation resulting in an overall Mulliken population that is different from the Mulliken population analysis of the HOMO. This is illustrated in Table 3 where the total Mulliken populations of the appropriate electronic states of the neutral Y, and the Y,’ ions are shown. As seen from Table 3, although the HOMO of the neutral dimer is 86% 4d and 14% 5s, the difference in the Mulliken populations of Y2 and Yc per atom (Table 3) suggests that there is an increase in the 4d Mulliken population for Y2f while the pulations decrease. This effect is overall 5p and 5s B” for the 5C; and C[ states of YZ and Yl, respectively. A striking feature is that for the Y,(‘ZZ’)) + Y2(2 II,) ionization process, there is a large decrease in the 4d population while the corresponding population is not affected much for the Y2(5 XC;) -+ Y2(4 c, ) process. In the case of Y3 and Y.j+, the primarily loss of Mulliken population is in the Y (5~) and Y (5s). For the tetramer again we find that the 5s and 5p populations decrease after ionization while the 4d population increases. These findings suggest that there is considerable orbital reorganization and relaxation after ionization. This is not too surprising since Koopman’s theorem does not hold for the ionization of transitions metal clusters. The ionization energies of clusters of yttrium are considerably smaller compared to the single yttrium atom (see Table 1). This is typical of metal clusters which in general exhibit smaller IPs for the clusters compared to the single atom. The experimental measurements of Knickelbein closely follow the theoretical trend. This is a large drop in the IP of the dimer

compared to the yttrium atom. The IP of the trimer increases slightly and then again the IP of the tetramer is smaller than the trimer. Hence although larger clusters do not exhibit odd-even alternation, there is a small alternation in that the IPs of dimer and tetramer are smaller than the trimer. The sudden drop in the IP of the dimer compared to the atom can be explained based on the orbital relaxation effects for Yc . The Mulliken populations listed in Tables 2 and 3 provide valuable guide lines. For the yttrium atom ionization takes place from the 4d orbital of Y (see, Table 2). The HOMO of the Y2 dimer is 86% 4d and 14% 5p in character. This population is substantially different from the actual Y; Mulliken population in Table 3 for the “2; state. As seen from Table 3, the Y2’ ion exhibits 4d’.3!?5sa.855p0.27 character which differs substantially from the HOMO of neutral Y2 which exhibits no 5s character at all. Consequently, up on ionization, the orbitals of Yl undergo substantial rearrangement. The orbital relaxation effect is thus responsible for the significantly smaller IP of the dimer. That is, the positive ion of Y2 is more stabilized compared to the neutral Y2 upon ionization. Comparison of the total Mulliken populations of the neutral and ionic clusters in Table 3 reveals that the d population is virtually unaffected for Y2 and Y3 but the Y4 tetramer exhibits some change in the 4d population. The 5s populations of Y2 and Y4 decrease by 0.27 and 0.38, respectively, while the 5s population of Y3 decreases by only 0.07. Thus the IP is larger for smaller changes in the 5s population.

Acknowledgement This research was supported by the US Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division, under the grant number DEFG02-86-ER13558.

References [l] M. Knickelbein, J. Chem. Phys., in press. [2] M.D. Morse, Chem. Rev. 86 (1986) 1049. [3] W. Weltner and R.J. Van Zee, Ann. Rev. Phys. Chem. 35 (1986) 291.

D. Dai, K. Balasubramanian / Chemical Physics Letters 238 (1995) 203-207 [4] K. Balasubramanian, J. Mol. Struct. Theochem. 202 (1991) 291. [S] D.M. Cox, R.L. Whetten, M.R. Zakin, D.J. Trevor, K.C. Reichmann and A. Kaldor, in: Advances in laser sciences Vol. 146, eds. W.C. Stwalley and M. Lapp (ALP, New York, 1986) p. 527. [6] G.A. Bishea and M.D. Morse, J. Chem. Phys. 95 (1991) 5646. [7] R.J. Van Zee, Y.M. Hamrick, S. Li and W. Weltner, Chem. Phys. Letters 195 (1992) 214. [8] D.G. Leopold, 3. Ho and W.C. Lineberger, J. Chem. Phys. 86 (1987) 1715. [9] W.E. Klotzbiicher and G.A. Ozin, Inorg. Chem. 19 (1980) 3767. [lo] K.M. Ervin, J. Ho and W.C. Lineberger, J. Chem. Phys. 89 (1988) 4514. [ll] G. Alameddin, J. Hunter, D. Cameron and M.M. Kappes, Chem. Phys. Letters 192 (1992) 122. [12] L. Goodmin and D.R. Salahub, Phys. Rev. A 47 (1993) 774. [13] M.A. Nygren, P.E.M. Siegbahn, U. Wahlgren and H. Akeby, J. Phys. Chem. 96 (1992) 9633.

207

[14] M.B. Knickelbein, Chem. Phys. Letters 192 (1992) 129. [15] E.A. Rohlfing, D.M. Cox and A. Kaldor, 3. Chem. Phys. 81 (1984) 3846. [16] M.B. Knickelbein, S. Yang and S.J. Riley, J. Chem. Phys. 93 (1990) 94. [17] T.P. Martin, T. Bergmann, H. Gijhlich and T. Lange, J. Phys. Chem. 95 (1991) 6421. [18] K. Balasubramanian, J. Chem. Phys. 90 (1988) 6310. [19] K. Balasubramanian and Ch. Ravimohan, Chem. Phys. Letters 145 (1988) 39. [20] D. Dai and K. Balasubramanian, J. Chem. Phys. 98 (1993) 7098. [21] S. Verhagen, S. Smoes and J. Drowart, J. Chem. Phys. 40 (1966) 239. [22] L.B. Knight, R.W. Woodward, R.J. Van Zee and W. Weltner, J. Chem. Phys. 79 (1983) 5820. [23] L.A. LaJohn, P.A. Christiansen, R.B. Ross, T. Atashroo and WC. Ermler, J. Chem. Phys. 87 (1987) 2812. [24] K. Balasubramanian, Chem. Phys. Letters 127 (1986) 585. [25] C.E. Moore, Table of atomic energy levels, NRDRS-NBS, Circular No. 467 (US GPO, Washington, 1971).