First-Principles Calculations of the Electronic and ... - ACS Publications

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First-Principles Calculations of the Electronic and Geometrical Structures of Neutral [Sc,O,H] Molecules and the Monocations, ScOH0,þ and HScO0,þ Evangelos Miliordos and Katharine L. C. Hunt* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States ABSTRACT: Using multireference configuration interaction and coupled-cluster methodologies, with quadruple-ζ basis sets, we explored the potential energy surfaces of the ground and excited states of the neutral and cationic triatomics [Sc,O,H]0,þ. In its ground state, the neutral species is trapped into either a linear ScOH or a bent HScO conformation; these two minima are approximately equal in energy and separated by a barrier of 40 kcal/mol. The linear ScOH structure is preferred by the excited states of the neutral species and by all of the electronic states of the charged molecular systems that we studied in this work. Both ScOH and ScOHþ present ionic characters, ScþOH- and Sc2þOH-, similar to those found for the isovalent ScF0,þ species. The HScO0,þ structures are obtained by covalent or dative interaction of hydrogen and ScO0,þ. For most of the minima located in this work, we calculated geometries, vibrational frequencies, binding energies, excitation energies, and dipole moments. Our numerical results agree well with existing experimental data.

1. INTRODUCTION This work focuses on the electronic structure and energetics of the ground and low-lying excited states of the neutral triatomics containing Sc, O, H and their monocations. Experimental and theoretical data on the first-row transition metal monohydroxides are relatively limited in the literature to date. Spectroscopically, the vibrational frequencies are known only for the ground states of ScOH,1,2 TiOH,3,4 CrOH,5 MnOH,6 CoOH,6 NiOH,6,7 and CuOH,4,8 while two excited states of CuOH have been observed.4,8 The large number of electronic states of transition metal atoms that are close in energy, accompanied by the different geometries available to triatomics, makes theoretical examination of these molecules challenging. We carried out a high-level ab initio study of the first member of this group of molecules, with the composition [Sc, O, H], with the goal of providing information that will be useful for spectroscopic analyses. Currently, less experimental information is available about ScOH than about YOH, the monohydroxide of the next heavier element in group 3, below scandium; for YOH, the exact geometry of the ground state, the vibrational frequencies, and the excitation energies of two additional states have been determined spectroscopically.9 Scandium monohydroxide was first observed just one decade ago, when Zhang, Dong, and Zhou assigned the IR absorptions at 1391.1, 922.3, and 765.6 cm-1 to the Sc-H and Sc-O stretching modes of HScO and to a vibration of its isomer ScOH, respectively.1 Employing the DFT-B3LYP methodology, Zhang et al. provided the geometrical structures of both conformations, their energy separation, and their interconversion barrier. A similar theoretical study by Guo and Goodings a r 2011 American Chemical Society

year later gave consistent results,10 and the most recent experimental work by Wang and Andrews confirmed the stretching frequency of 922 cm-1.2 All of the available experimental and theoretical results for [Sc, O, H] (to our knowledge) are included in Table 1. ScOHþ has gained more attention in the literature than its neutral counterpart. The first experimental study on ScOHþ seems to be that of Magnera, David, and Michl in 1989.11 The authors studied the reactions of Sc(H2O)2þ, ScOH(H2O)þ, and argon atoms, reporting an Scþ-OH binding energy of 87.8 kcal/mol, somewhat smaller than the more accurate value of 119 ( 2 kcal/mol obtained by Clemmer, Aristov, and Armentrout 4 years later, from studies of the ScOþ þ D2 reaction.12 The same authors estimated the ScOþ-D dissociation energy as 58 ( 2 kcal/mol. Several theoretical analyses of the monocation have been reported in the literature, the first by Tilson and Harrison in 1991.13 They examined two electronic states of ScOHþ with 2Δ and 2Σþ symmetry. They reported bond lengths and binding energies for both states at the MCSCFþ1þ 2 level of theory and also determined binding energies for a higher-lying HScOþ structure. A second set of analyses, by Bauschlicher and coworkers, was limited to the ground 2Δ state,14 reporting its geometry at the B3LYP level and its Sc-OH binding energy at the CCSD(T) level. All numerical results along with the experimental findings are listed in Table 2. Received: October 30, 2010 Revised: January 29, 2011 Published: April 13, 2011 4436

dx.doi.org/10.1021/jp110378d | J. Phys. Chem. A 2011, 115, 4436–4447

The Journal of Physical Chemistry A

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Table 1. Experimental and Theoretical Results for [Sc,O,H] Molecules in the Literature. Bond Lengths re, Bond Angles O, Harmonic Frequencies ωe and Energy Separations ΔE Species

re(Sc-O) (Å)

ωe (cm-1)

φ(HXY) (deg)a

re(X-H) (Å)a

ΔE (kcal/mol)

Experiment ScOHb

765.6

HScOb HScOd

1391.1, 922.3c 922.4 Theory 1 0 e

HScO ( A )

1.671

1.879

119.2

1459.2, 977.4, 391.0

0.0

ScOH (1Σþ)e

1.800

0.957

180.0

3958.8, 778.8, 322.5

6.8

ScOH (3Δ)e

1.873

0.955

180.0

3976.3, 691.3, 303.9

7.5

ScOH (1Σþ)f

1.783-1.798

0.955-0.966

180.0

HScO (1A)f

1.664-1.677

1.866-1.882

115.1-119.3

a

spread of valuesf

b

X, Y = Sc, O for HScO, and X, Y = O, Sc for ScOH. Reference 1; reaction of laser-ablated Sc atoms with H2O, combined with IR spectroscopy. c The first value is assigned to the Sc-H stretching mode and the second to the Sc-O stretching mode of bent HScO. d Reference 2; same as footnote b but Sc þ H2O2 or (H2, O2) mixture. e Reference 1; B3LYP/[8s6p4d/Sc 6-311þþG(d,p)/H,O]. De(Sc-OH; 1Σþ) = 108.9 kcal/mol and the transition energy barrier from ScOH to HScO (28.9 kcal/mol) are also reported. The Sc-H, Sc-O, and O-H bond lengths of the transition state are 1.832, 1.717, and 1.473 Å, respectively. f Reference 10. This work gives a spread of values, depending on the methodology used: B3LYP or BP86 combined with 311þþG(3df,3pd) or TZVP basis sets. Harmonic frequencies are also given: 3827-3944, 779-808, and 266-338 cm-1 for ScOH(1Σþ) and 14281482, 950-991, and 393-416 cm-1 for HScO (1A).

Table 2. Experimental and Theoretical Results for ScOHþ in the Literature. Binding Energies D0, Bond Lengths re, and Energy Separations ΔE State

D0(Scþ-OH) (kcal/mol)

D0(ScOþ-H) (kcal/mol)a

re(Sc-OH) (Å)

re(ScO-H) (Å)

ΔE (kcal/mol)

1.855

0.964

0.0

1.811

0.966

0.0 0.0

1.842

0.972

17.2

Experiment ?b

87.8

30

119.2 ( 2

58 ( 2

2

Δd

108.0

59.6

Δe 2 f Δ

118.8 117.5

Xc

Theory 2

2 þd

Σ

90.8

42.4

With respect to ScOþ(X1Σþ)þH(2S). b Reference 11; collision-induced dissociation. The ScOþ-H dissociation energy value was obtained using D0(H-OH) = 118 kcal/mol and D0(O-H) = 101 kcal/mol. c Reference 12; guided ion-beam mass spectrometry. d Reference 13; MCSCFþ1þ 2/[5s4p3d/Sc 4s3p1d/O 2s1p/H]. The authors report an HScOþ (2Σþ) structure that is 92 kcal/mol above ScOHþ (2Δ), with D0[H-ScOþ f ScOþ(3Δ) þ H(2S)] = 47.2 kcal/mol. e Reference 14; B3LYP/[8s6p5d/Sc DZ/O,H]. f Reference 14; CCSD(T)/[7s8p6d3f2g/Sc aug-cc-pVTZ/O,H] at the B3LYP geometry. a

Here we present the first ab initio theoretical examination of scandium monohydroxide and its isomers, not based on density functional theory, as well as systematic theoretical work on its cation. We study the ground state and the lowest excited electronic states, providing accurate geometries, harmonic and anharmonic frequencies, binding energies, excitation energies, and dipole moments. The majority of these values are reported for the first time. The bonding scheme in these species is also explained through the construction of potential energy profiles. In section 2 we predict the electronic and geometric structures of the lowest minima on the [Sc, O, H] potential energy surfaces, based on an analysis involving the dissociation energies of the fragments, possible bonding mechanisms, the behavior of the Sc þ F system (which is analogous to Sc þ OH), ionization energies, and electron affinities. Section 3 describes the computational approach employed. In brief, we used correlation-consistent quadruple-ζ (cc-pVQZ) basis sets for hydrogen and

scandium and an augmented cc-pVQZ basis set for oxygen. We employed both multireference configuration interaction (MRCI) and single-reference restricted coupled-cluster techniques. The MRCI calculations start from a state-average complete active space self-consistent field (SA-CASSCF) wave function, with all possible configurations of 10 valence electrons in 11 active orbitals for the neutral species and of 9 valence electrons in 11 orbitals for the cation. Then, all single and double excitations from the SA-CASSCF space are included, to obtain the MRCI wave function. In the single-reference restricted coupled-cluster calculations [RCCSD(T)], single and double excitations are contained in the exponential operator applied to the reference state, thus creating linked excitations of all higher orders as well; triple excitations are treated perturbatively. In section 4 we give our results for the ground states of the fragments. In section 5 we present and analyze the results for the [Sc, O, H] and [Sc, O, H]þ species. Finally, in section 6 we summarize our findings. 4437

dx.doi.org/10.1021/jp110378d |J. Phys. Chem. A 2011, 115, 4436–4447


2. CHEMICAL INSIGHTS The most stable adiabatic dissociation product of a molecule containing Sc, O, and H (one atom of each kind) is ScO þ H; Sc þ OH is the next most stable, while the least favorable combination of two fragments is ScH þ O, based on the relative order of their ground-state binding energies: D0(ScO) ≈ 160 kcal/ mol,15 D0(OH) ≈ 102 kcal/mol,16 and D0(ScH) ≈50 kcal/ mol.17 If a hydrogen atom approaches ScO on the side toward oxygen, no attractive interaction is expected, since oxygen is “closed” to approaches from any direction, at least in the lowest electronic states of ScO.18 On the other hand, a bond can readily be formed between the scandium center and a hydrogen atom. As noted in ref 18, the ScO state X2Σþ, the quartet states a4Π, b4Φ and their companion doublets E2Π and D2Φ, and the states c4Σþ and d4Δ all have an unpaired σ electron localized at the metal end. Thus, H may form a pure single bond, giving linear HScO. The strength of such a bond is expected to be of the same order as in the diatomic ScH. As a result, the atomization energy (AE) of a linear HScO species must be approximately 160 þ 50 = 210 kcal/ mol. In addition, δ and π unpaired electron density is present in the first two excited states of ScO, A0 2Δ and A2Π, creating a possibility for H to form bent H-ScO structures. The behavior of the next adiabatic channel, Sc þ OH, can be compared to that of the isoelectronic Sc þ F system. The latter is of ionic character, ScþF-, and its ground state X1Σþ has a binding energy of 140 kcal/mol.19 Following our chemical intuition, we expect a similar ScþOH- ionic form but with a somewhat weaker bond due to the lower electron affinity (EA) of hydroxyl than of fluorine (EAOH = 1.83 eV,20 EAF = 3.40 eV21). A rough estimate of the difference between their binding energies can be achieved by using the relation D(ScX f Scþ þ X-) = D0(ScX f Sc þ X) þ IE(Sc) - EA(X), where X = OH or F and IE(Sc) is the ionization energy of Sc, and then assuming that the Coulombic dissociation energy D(ScX f Scþ þ X-) is almost independent of X. Then D0(Sc-OH) ≈ D0(ScF) - EA(F) þ EA(OH) = 140 - 36.2 ≈ 104 kcal/mol. Consequently, the atomization energy (AE) of the Sc-OH molecule is estimated to be approximately 102 þ 104 = 206 kcal/mol, very close indeed to the estimate of 210 kcal/mol for HScO. The ionization energies (IE) of the three atoms are IESc = 6.5615 eV,22 IEO ≈ IEH ≈ 13.6 eV.23,24 Apparently, the most stable atomic fragments are Scþ, O, and H, and with respect to these fragments, the binding energies (D0) of ScOþ, OH, and ScHþ are 165,18 102,16 and 5625 kcal/mol. Therefore, the lowest dissociation paths lead to ScOþ þ H and Scþ þ OH. The electronic structure of ScOþ does not possess a lone valence σ electron at the Sc atom that would permit the hydrogen atom to form a single bond, at least in the lowest electronic states of ScOþ.18 Thus, a weak dative half bond is anticipated, as confirmed by our results (vide infra). Thus, the AE of the HScOþ ground state is estimated at ∼170 kcal/mol. On the other hand, assuming that ScOHþ behaves like its isovalent counterpart ScFþ, with a binding energy approximately equal to that of ScF, then a Sc-OH dissociation energy of about 104 kcal/mol would be expected for ScOHþ.19 Thus, the AE of ScOHþ is 104 þ 102 ≈ 210 kcal/mol, 40 kcal/mol higher than that of HScOþ. To summarize, the electronic states stemming from both the HScO and the ScOH configurations are expected to lie close to one another, making the potential energy surfaces complicated. In contrast, for the monocation the ScOHþ structures are rather

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Table 3. Results for the ScO, ScH, and OH Species. Total Energies E, Equilibrium Bond Lengths re, Binding Energies D0, Harmonic Frequencies ωe, and Dipole Moments μ Method -E (a.u.)

ScO

ScH

OH

MRCI

835.014913 760.366619

75.655015

MRCIþQ

835.023782 760.367060

75.664065

RCCSD(T)

835.02257a 760.365725

75.664097

C-RCCSD(T) 835.37801a 760.712824 re (Å)

MRCI MRCIþQ

1.685 1.689

1.794 1.794

0.9711 0.9728

RCCSD(T)

1.698a

1.793

0.9713

C-RCCSD(T) 1.668a

1.764

Expt D0 (kcal/mol) MRCI

1.6656b

1.775c

0.96966d 98.9

159.2

44.0

MRCIþQ

156.7

51.6

100.2

RCCSD(T)

154.3a

51.7

100.9

50.8 C-RCCSD(T) 158.4a Expt 159.6 ( 0.2e 47.5 ( 2.0f -1

ωe (cm )

MRCI

962

1577

3734

MRCIþQ

950

1577

3718

RCCSD(T)

972a

1590

3730

C-RCCSD(T) 974a

1603

Expt μ (D)

∼102g

975.7b a

RCCSD(T)

3.73

Expt

4.55 ( 0.08h

1547(=ΔG1/2)c 3738d 1.41

1.649 1.655 ( 0.001i

a Results identical to those found in ref 18. b Reference 35. c Reference 36. Our C-RCCSD(T) ΔG1/2 is 1557 cm-1. d Reference 37. e Reference 15. f Reference 17. g Reference 16. h Reference 38. i Reference 39.

dominant, simplifying the shapes of the potential energy surfaces. These predictions are confirmed below (see section 5).

3. COMPUTATIONAL DETAILS Our basis set includes the quadruple-ζ correlation-consistent basis sets of Dunning for hydrogen and oxygen26,27 and of Balabanov and Peterson for scandium.28 The basis set for oxygen is augmented so that we can account for the anionic behavior of the hydroxyl ion (OH-); see section 4. Thus, the full basis set is cc-pVQZ/Sc,H aug-cc-pVQZ/O=[8s7p5d3f2g1h/Sc 6s5p4d3f2g/O 4s3p2d1f/H] consisting of a total of 214 basis functions. As noted above, two methodologies have been used: multireference configuration interaction (MRCI) and a single-reference restricted coupled-cluster technique [RCCSD(T)].29 For the MRCI wave function, the reference space was constructed by allowing all possible configurations of 10 or 9 valence electrons in 11 orbitals (4s3d/Sc þ 2s2p/O þ 1s/H) for the neutral and charged species, respectively, using the state-average complete active space self-consistent field (SA-CASSCF) approach.30 To keep the calculations manageable, internal contraction31 in the CI expansion was applied, as implemented in the MOLPRO suite of codes (icMRCI MRCI).32 To reduce the size nonextensivity error, the Davidson correction (MRCIþQ) was employed.33 Excitations of the semicore 3s3p electrons of Sc are expected to reduce the bond lengths considerably,18 and thus, their effects were also treated in both types of calculations [C-MRCI(þQ), C-RCCSD(T)], employing the core-tuned basis sets of Balabanov and Peterson on Sc (cc-pwCVQZ).28 Relativistic 4438



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Table 4. Results for Linear ScOH from the Current Work. Total Energies E, Bond Lengths re, Binding Energies De, Harmonic Frequencies ωe, and Excitation Energies Te Method

-E (a.u.)

re(Sc-OH) (Å)

re(ScO-H) (Å)

De(Sc-OH) (kcal/mol)a

ωe (cm-1)b

Te (cm-1)

~1Σþ X MRCI

835.605312

1.823

0.950

115.4

3981, 752, 302

0.0

MRCIþQ C-MRCI

835.623004 835.896639

1.823 1.800

0.956 0.949

116.2 111.6

3982, 754, 288 3970, 760, 305

0.0 0.0

C-MRCIþQ

835.956889

1.799

0.953

113.5

3961, 768, 295

0.0

RCCSD(T)

835.626954

1.839

0.953

115.0

3986, 748, 283

0.0

C-RCCSD(T)

835.975741

1.800

0.954

115.1

3967, 765, 282

0.0

~a3Δ MRCI

835.603141

1.914

0.951

114.0

4002, 633, 325

476

MRCIþQ

835.610378

1.914

0.952

108.2

4001, 631, 316

2771

RCCSD(T)

835.609899

1.931

0.952

104.3

3994, 635, 305

3743

C-RCCSD(T)

835.963308

1.882

0.953

107.3

3974, 658, 289

2729

~1Δ A MRCI

835.588408

1.919

0.951

104.8

3980, 639, 288

3710

MRCIþQ

835.598614

1.916

0.952

100.9

3979, 635, 292

5353

~b3Π MRCI

835.574884

1.937

0.949

96.3

4013, 584, 385

6678

MRCIþQ

835.591638

1.934

0.952

96.5

4016, 575, 380

6884

RCCSD(T)

835.593014

1.942

0.952

93.7

4021, 570, 364

7449

84.0 84.8

4033, 580, 344 4035, 577, 351

10959 10987

~1Π B MRCI MRCIþQ

835.555378 835.572945

1.968 1.968

0.949 0.951

a With respect to ground-state fragments: Sc(2D) þ OH(X2Π). b The first two numbers correspond to the O-H and Sc-O stretching modes, whereas the third value corresponds to the doubly degenerate bending mode.

calculations were not performed, since relativistic corrections are not expected to play a significant role here.18 The binding energies were calculated via the supermolecule approach, and dipole moments were calculated with the finitefield technique at the RCCSD(T) or MRCI level of theory; we performed calculations with two fields of equal strength (10-4 a.u.) but opposite direction. Harmonic frequencies were obtained upon diagonalizing the Hessian matrix in the internal coordinates. We also computed anharmonic frequencies with vibrational configuration interaction (VCISDTQ) calculations34 at the RCCSD(T) level but employing the somewhat smaller cc-pVTZ/Sc,H aug-cc-pVTZ/O basis sets.26-28 Finally, the C2v point group was used for the linear species and Cs for the planar ones. All calculations were done using MOLPRO.32

4. MOLECULAR FRAGMENTS ScO, ScH, AND OH In this section we present our results for the ground states of ScO (X2Σþ), ScH (X1Σþ), and OH (X2Π). Scandium monoxide has been studied extensively in earlier work.18 For comparison, in the current work we included the 2s orbitals of oxygen in the reference CASSCF space but left out the 4p orbitals of Sc. Preliminary calculations on the triatomics have shown that inclusion of the 2sO orbitals is indispensable but that contributions from the Sc 4p orbitals are not as important. In Table 3, all of our numerical values are listed and compared with experiment and with earlier results from the literature. First, we note that the 3s3p/Sc (core) correlation shortens the bond length of ScO and ScH by 0.03 Å, bringing the theoretical

values into agreement with the experimental results. The predicted bond lengths at our highest level of calculation differ from the experimental values by no more than 0.01 Å (see Table 3). A similar trend is observed for the calculated binding energies and the harmonic frequencies. For ScO, core correlation enhances D0 by ∼4 kcal/mol, whereas D0 is reduced by ∼1 kcal/mol for ScH; ωe values increase by 15-20 cm-1 for both species. In all cases, our calculated values converge toward the available experimental values. A final comment concerns the dipole moments, calculated at the RCCSD(T) level of theory using the finite-field approach. The calculated dipole moment of ScO is 20% lower than the experimental dipole moment, suggesting that the experimental value might be overestimated.18 For ScH we recommend a value of 1.41 D for the dipole, while previous theoretical values have ranged from 1.1 to 2.5 D.40 Our value for μe(OH) agrees with experiment (Table 3). We note that adding augmented functions on H reduces μe(ScH) by 0.03 D and increases μe(OH) by 0.006 D, so the values remain practically unaffected. The same holds true for EA(OH), which is computed at the RCCSD(T) level as 1.797 or 1.790 eV with or without augmentation of the basis on the hydrogen center, respectively, as compared to the experimental value of 1.828 eV.20 However, if augmented functions on O are omitted, then the RCCSD(T) value of EA(OH) is only 1.11 eV. The MRCI (MRCIþQ) values for EA(OH) with the augmented basis on oxygen are 1.42 (1.65) eV. This rather small value is due to the difficulty of extracting the correlation energy of the oxygen anion with the MRCI methodology.41 4439



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Figure 1. MRCI potential energy profiles for the linear approach of Sc to OH. The energies are shifted up by 835 a.u.

Figure 2. MRCI potential energy profiles for the linear approach of H to ScO. The energies are shifted up by 835 a.u.

Our results in Table 3 are in very good agreement with the corresponding experimental values, validating the methodology followed. Therefore, we expect that our results for the triatomics [Sc,O,H]0,þ (given below) will be quite accurate, especially after taking into account the 3s3p/Sc correlation. Due to the inability of MRCI(þQ) to reproduce the experimental EA(OH), we believe that the binding energies are obtained more accurately at the CC level of theory.

Figure 1. The proposed bonding scheme is identical to that of ScþF-.19 We observe also that the O-H bond distance is equal to 0.95 Å for all states studied vs re(OH) ≈ re(OH-) ≈ 0.97 Å. Next, we discuss our numerical results listed in Table 4. The Sc-OH bond length in the ground state is calculated as 1.823 [1.839] Å at the MRCI [RCCSD(T)] level, shortened to 1.800 Å with both methods after including the 3s3p/Sc electron correlation. The same behavior as in ScO is observed (see section 4). We note that the Sc-F bond distance is 1.79 Å,19 close to our value of 1.800 Å . The Sc-OH binding energy is practically the same in all MRCI and CC methods. Our suggested value is De(Sc-OH) = 114 ( 2 kcal/mol, considering the accuracy of our results for the fragments in section 4. No experimental value exists, while the DFT value of Zhang et al.1 falls short of ours by about 5 kcal/ mol. Taking into account the zero-point energies (ZPE) of ScOH and OH, we obtain D0(Sc-OH) = De(Sc-OH) ZPE(ScOH) þ ZPE(OH) = (114 ( 2) kcal/mol -1/2 (3967 þ 765 þ 2 282) cm-1 þ 1/2 (3730) cm-1 = 112 ( 2 kcal/ mol (see Tables 3 and 4). We find De(ScO-H) = 65.5 [61.3] kcal/mol at the RCCSD(T) [C-RCCSD(T)] level, giving D0(ScO-H) = De(ScO-H) - ZPE(ScOH) þ ZPE(ScO) = 59.3 [55.1] kcal/mol, roughly one-half of the 102 kcal/mol binding energy of the free hydroxyl.16 Finally, our ScO-H and Sc-OH stretching harmonic frequencies are 3960-3990 and 750-770 cm-1, respectively. Solving the rovibrational Schr€odinger equation through the VCISDTQ technique (see section 3), we find the corresponding anharmonic frequencies to be 181 and 5 cm-1 lower. These values are typical of an O-H and Sc-O bond, respectively. For instance, our anharmonicities (2ωexe) of the diatomics OH and ScO are 155 and 7.2 cm-1 at the RCCSD(T) level of theory. At our highest level of computation, C-RCCSD(T), the value for ωe(Sc-OH) is 765 cm-1, which becomes 760 cm-1 after subtracting the anharmonicity. The latter value is in very good agreement with the experimental value of 765.6 cm-1.1 For the ScO-H anharmonic frequency, our suggested value is 3967 [C-RCCSD(T)] - 181 = 3886 cm-1. Concerning the first excited state, ~a3Δ, the effect of the core correlation is similar: re(Sc-OH) contracts by 0.05 Å at the

5. RESULTS AND DISCUSSION 5.1. ScOH and HScO. First, we focus on ScOH. Experimentally, only a vibrational frequency of 765.6 cm-1 is known.1 Two theoretical studies of ScOH have been performed with density functional methods,1,10 reporting geometries and harmonic frequencies for the ground state 1Σþ and a state of 3Δ symmetry. A binding energy of De(1Σþ) = 108.9 kcal/mol has been obtained in the density functional work as well as a separation of 250 cm-1 between these two states (see Table 1). The last two numbers differ considerably from ours (vide infra). Here, we examine the five lowest electronic states of this isomer, X~1Σþ, ~1Π, reporting equilibrium bond lengths, ~a3Δ, A~1Δ, ~b3Π, and B frequencies, binding energies, and relative energies, as listed in Table 4. All five states are of ionic character, ScþOH-, with a positive Mulliken charge on Sc ranging from 0.6 to 0.7. The ground state is a closed-shell singlet, while 1Δ and 1Π are the (open) singlets relative to the 3Δ and 3Π states. The 1,3Δ and 1,3Π states correspond to σ1δ1 and σ1π1 configurations, respectively. The principal contribution to this σ molecular orbital comes from the 4s atomic orbital of Sc, while π and δ correspond closely to the 3dπ and 3dδ scandium orbitals. This picture clearly indicates that the 3Δ and 3Π states stem from Scþ(3D; 4s13d1) þ OH-(X1Σþ), while the 1Δ and 1Π states stem from Scþ(1D; 4s13d1) þ OH-(X1Σþ). Indeed, the energy gaps of 2582 cm-1 for 3Δ-1Δ and 3103 cm-1 for 3Π-1Π at the MRCIþQ level (Table 4) resemble the experimental gap for the atomic ion states Scþ(1D) r Scþ(3D) of 2435 cm-1.42 However, all five states dissociate adiabatically to Sc(2D; 4s23d1) þ OH(X2Π); see

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Table 5. Results for Linear HScO from the Current Work. Total Energies E, Bond Lengths re, Binding Energies De, Harmonic Frequencies ωe, and Excitation Energies Te Method

-E (a.u.)

re(HSc-O) (Å)

De(H-ScO) (kcal/mol)a

re(H-ScO) (Å)

ωe (cm-1)b

Te (cm-1)

1 þ

Σ

MRCI

835.604710

1.710

1.998

56.5

1386, 900, 107i

0.0

MRCIþQ C-MRCI

835.615781 835.907042

1.722 1.682

2.019 1.991

57.8 53.8

1387, 901, 113i

0.0 0.0

C-MRCIþQ

835.955675

1.689

2.002

55.7

RCCSD(T)

835.614640

1.719

2.012

57.8

1343, 921, 268i

0.0

C-RCCSD(T)

835.965702

1.689

1.998

55.0

1359, 925, 254i

0.0

3

0.0

Π

MRCI

835.489122

2.058

1.978

32.7

1413, 531, 65

25 369

MRCIþQ

835.500026

2.056

1.976

33.5

1409, 528, 110

25 405

59.7 61.9

1413, 531, 49 1409, 529, 107

25 377 25 225

Φ

3

MRCI MRCIþQ

835.489082 835.500849

2.058 2.057

1.978 1.976 Φ

1

MRCI

835.489503

2.060

1.978

60.9

1418, 535, 51

25 285

MRCIþQ

835.501512

2.057

1.977

63.0

1410, 532, 147

25 079

1

Π

MRCI

835.487677

2.068

1.978

33.9

1418, 540, 399ic

25 686

MRCIþQ

835.499575

2.066

1.977

34.6

1410, 537, 488ic

25 504

Δ

3

MRCI

835.477949

1.923

1.952

22.7

27 821

MRCIþQ

835.486737

1.919

1.946

22.2

28 322

Δ

1

MRCI

835.472250

1.928

1.945

19.1

29 072

MRCIþQ

835.483693

1.933

1.950

20.2

28 990

With respect to their adiabatic fragments: ScOH(1Σþ, 1,3Π, 3Φ, 1Φ, 1,3Δ) f ScO(X2Σþ, A2Π, b4Φ, D2Φ, A0 2Δ) þ H(2S), respectively. b The first two numbers correspond to the Sc-H and Sc-O stretching modes, whereas the third value corresponds to the doubly degenerate bending mode. c The ~1Π. For the A00 state, we obtain ωe = 52 (148) cm-1 at the MRCI (MRCIþQ) level. bending frequency corresponds to the A0 component of B a

coupled-cluster (CC) level. Thus, for the remaining three states, where core correlation is not considered, one should reduce the re(Sc-OH) values in Table 4 by approximately 0.04 Å. The excitation energy X~1Σþ r ~a3Δ is calculated to be 476 cm-1 at the simple MRCI level; however, it increases to 2771 cm-1 when size nonextensivity is ameliorated, through the Davidson correction. Similar values are obtained with the CC approach. Our suggested value of 2700 cm-1 compares favorably with the X1Σþ r a3Δ gap in ScF, where the excitation energy Te ≈ 2000 cm-1.19 For the remaining four states, we obtain Te(A~1Δ) ≈ ~3Π) ≈ 7000 cm-1, and Te(B ~1Π) ≈ 11 000 cm-1 5000 cm-1, Te(b at the MRCIþQ level of theory. Next, we turn to the linear HScO configuration. As already stated, its lowest electronic states originate from the states of ScO with a σ electron distribution at the “back” of Sc, interacting with H(2S). These ScO states are X2Σþ, the quartets a4Π, b4Φ, d4Δ, and their companion doublets E2Π, D2Φ, 22Δ.18 Note that E2Π was not fully studied by the authors of ref 18 due to technical problems. The potential energy curves of Figure 2 support our interpretation: HScO (1Σþ) is formed by ScO(X2Σþ) þ H(2S) and 1,3Φ by ScO(D2Φ,b4Φ) þ H(2S). The 1,3Π and 1,3Δ states are formed by ScO(E2Π,a4Π) þ H(2S) and ScO(22Δ,d4Δ) þ H(2S), but they dissociate to the lower-energy species

ScO(A2Π) þ H(2S) and ScO(A0 2Δ) þ H(2S), respectively. For reasons of completeness, we show also the repulsive potential energy curve of the 3Σþ state stemming from ScO(X2Σþ) þ H(2S); the two lone electrons of ScO and H are coupled into a nonbonding triplet. According to the results of ref 18 the states 2,4 (Π,Φ) and 2,4Δ of ScO lie about 26 000 and 29 000 cm-1 above X2Σþ. This pattern is reflected in HScO, with the 1,3(Π,Φ) and 1,3Δ states being about 25 000 and 28 500 cm-1 above 1Σþ (see Table 5). For all seven states we report equilibrium geometries, binding energies, and energy separations, while for the first five we also give harmonic frequencies (see Table 5). The calculated HSc-O bond length of 1Σþ is 1.72 Å at the MRCI, MRCIþQ, and RCCSD(T) levels but reduces to 1.69 Å after core correlation is added. To obtain more accurate re(HScO) values for the remaining states, the same reduction should be applied. Thus, for the 1,3(Π,Φ) states we obtain re(HSc-O) ≈ 2.03 Å. The corresponding values for the X2Σþ and 2,4(Π,Φ) states of ScO are 1.689 and 2.0 Å,18 showing that the ScO bond is not severely affected by the formation of the HScO molecule. The same is true for the Sc-O frequencies: 925 and 530 cm-1 in HScO (see Table 5) vs 976 and 580 cm-1 in free ScO.18 Finally, r e(H-ScO) ≈ 2.0 Å for all states; this is much larger than the bond length in the free hydride 4441



Figure 3. MRCI potential energy profiles for the oblique approach of H to ScO (the H-Sc-O angle is set to 128). The energies are shifted up by 835 a.u.

re(Sc-H; X1Σþ) = 1.775 Å.36 However, De(H-ScO) ≈ 55 kcal/mol, which is practically equal to that of ScH, De(ScH) = D0(ScH) þ 1/2ωe(ScH) = (47.5 ( 2.0) kcal/mol þ800 cm-1 (see Table 3) = 50 ( 2 kcal/mol. Unfortunately, the calculated bending frequencies of 1Σþ and one component of 1Π are imaginary, indicating that these are not real minima (see below). Additionally, the bending frequencies of the remaining states are relatively low (50-150 cm-1), raising questions about their stability. To determine their stability conclusively, more accurate calculations are needed. The first three electronic states of ScO (X2Σþ, A0 2Δ, and A2Π) form a triple bond with a remaining σ, δ, or π electron defining the symmetry of the wave function.18 The ground state of ScO should lead to linear HScO as its lowest minimum, because it is not expected to break its triple bond to provide a bent HScO structure. On the other hand, the π or δ electrons of the excited states of ScO could permit the formation of bent HScO. In Figure 3 we show the potential energy curves (PEC) for an oblique attack of H(2S) on ScO in its first three electronic states at an angle of 128, which is the equilibrium angle of the ground PEC; see Table 6. The dashed lines in Figure 3 show the “expected” diabatic PECs, while the actual curves are depicted with solid lines. The result of the oblique attack is ~1A0 and A ~1A0 . We studied the formation of two 1A0 HScO states, X the former extensively, and our numerical findings are included in Table 6. However, we were not able to determine the optimum ~1A0 due to convergence issues. The equilibrium structure of A ~1A0 at the C-RCCSD(T) level is re(HSc-O) geometry of X =1.678 Å, re(H-ScO) = 1.932 Å, and φ(H-Sc-O) = 123.0. It is interesting that the bond length of 1.678 Å is very similar to the bond length of ScO in the A2Π state.18 The computed ωe values of the H-ScO and HSc-O bonds are 1417-1427 and 942-946 cm-1 (see Table 6), while the corresponding anharmonicities are found to be 43 and 8 cm-1. As in the case of ScOH, the last values are similar to the anharmonicities of the = 44 cm-1 and 2ωexScO = ScH and ScO molecules [2ωexScH e e -1 7.2 cm at the RCCSD(T) level]. Our RCCSD(T) anharmonic

ARTICLE

frequencies then are 1427 - 43 = 1384 and 942 - 8 = 934 cm-1, which are now closer to the experimental values of 1391.1 and 922.3 or 922.4 cm-1.1,2 The vibrational frequency near ωe ≈ 335 cm-1, or 315 cm-1 after accounting for the anharmonicity, has not been measured experimentally yet. To summarize, we located five stable minima for linear ScOH, one stable minimum for bent HScO, and seven linear HScO structures of rather questionable stability. To show all of them together, we constructed PECs with respect to the H-Sc-O angle (see Figure 4). Small angles correspond to the stable ScOH structures, whereas angles close to 180 correspond to HScO. Figure 4 shows that linear HScO(1Σþ) is indeed not a minimum, since its bending leads to X~1A0 . The same holds true for B~1Π, the ~1A0 (Convergence problems A0 component of which leads to A prevented us from constructing full PECs other than that of the ground state). We note that the A0 and A00 components (in the Cs point group) of the Π, Δ, and Φ states of ScOH remain practically degenerate upon bending. The two real minima of the ground-state potential energy surface are connected through a transition state TS (a first-order saddle point). The geometry and frequencies of TS are listed in Table 6. The Sc-O-H angle is 70, denoting that it results from the near-perpendicular attack of OH toward Sc. The relative energies of the three geometrical configurations in question (the two minima and TS) depend on the level of theory employed. The energy barrier from ScOH to HScO, for instance, is 33.5 kcal/mol at the MRCI level, 37.0 kcal/mol at the MRCIþQ level, and 41.1 kcal/mol at the RCCSD(T) level. Considering the last two numbers to be more accurate, we suggest a barrier height of 39 ( 2 kcal/mol, which is 10 kcal/mol larger than that obtained earlier through density-functional approximations (see Table 1). The energy difference between the two minima is 0.2 kcal/mol at the MRCIþQ level, 3.9 kcal/mol at the RCCSD(T) level, -4.9 kcal/ mol at the C-MRCIþQ level, and 0.6 kcal/mol at the C-RCCSD(T) level, where positive values indicate that ScOH is preferred. If we take into account the ZPEs of the isomers, then the MRCIþQ, C-MRCIþQ, and C-RCCSD(T) calculations show that HScO lies lower than ScOH, since its ZPE is on average 3.3 kcal/mol smaller. However, due to the small energy difference combined with the high interconversion barrier, HScO and ScOH are both observable experimentally. For example, Zhang et al.1 noted that “The ScOH molecule undergoes photoinduced rearrangement to the HScO molecule”. The energy difference between linear and bent HScO stationary points ranges from 3.8 to 7.3 kcal/mol, depending on the computational level. This energy difference constitutes the energy barrier for the hydrogen atom to “wag” around scandium. The bending frequency ωδe of HScO is about 335 cm-1 (Table 6); thus, the first vibrational level related to bending is approximately 0.5 kcal/mol higher than the equilibrium energy. The latter value is indeed small compared to the wagging barrier of at least 3.8 kcal/mol. Hence, the HScO molecule is trapped in one of the two possible bent (identical) minima. Except for the ground potential energy surface, we were not able to construct full curves. However, Figure 4 illustrates that transitions from the ScOH species to the HScO species are not expected, since transition states are not manifested even as high as 80 kcal/mol above the corresponding ScOH minima. Finally, we report the dipole moments of the linear and bent species. The polarity in ScO, ScH, and OH can be fairly represented as þSc-O-, þSc-H-, and -O-Hþ, respectively. Therefore, we expect that the þSc-O--Hþ and -H-Scþ-O4442



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Table 6. Results for Linear HScO from the Current Work. Total Energies E, Bond Lengths re, H-Sc-O Angles Oe, Harmonic Frequencies ωe, and Excitation Energies Te -E (a.u.)

Method

re(HSc-O) (Å)

re(H-ScO) (Å)

φe (deg)

ωe (cm-1)

Te (cm-1)

~1A0 X MRCI

835.613320

1.695

1.936

128.2

1417, 946, 335

0.0

MRCIþQ C-MRCI

835.622623 835.918735

1.700 1.667

1.934 1.902

127.7 123.9

1422, 945, 336

0.0 0.0

C-MRCIþQ

835.964627

1.672

1.901

123.1

RCCSD(T)

835.620736

1.710

1.932

128.1

C-RCCSD(T)

835.974748

1.678

1.900

123.0

0.0 1427, 942, 332

0.0 0.0

TS (1A0 ) a

a

MRCI

835.551952

1.739

1.871

49.2

1464, 907, 1326i

13 469

MRCIþQb

835.564008

1.739

1.871

49.2

1504, 908, 1217i

12 865

RCCSD(T)

835.561520

1.753

1.870

49.5

1468, 908, 1296i

12 996

Transition state. b MRCI geometry is used.

species have rather small dipole moments, due to the cancellation of the in situ bond dipoles. However, when HScO bends, then the two in situ bond dipoles act additively. In accord with this expectation, the calculated RCCSD(T) dipole moments are 1.07, 1.01, and 5.93 D for linear ScOH, linear HScO, and bent HScO, ~-state. The angle between the dipole respectively, in the X moment vector and the Sc-O bond, in the case of bent HScO, is 54. Indeed, in the last case the Mulliken atomic charge on Sc is þ1.1, exactly the sum of its charges in the ground states of Sc-H (qSc = þ0.3) and Sc-O (qSc = þ0.8). The dipole moments are also very small for the remaining linear ScOH or HScO minima studied. The ~a3Δ and ~b3Π states of ScOH have dipole moments equal to 0.62 and 0.32 D at the RCCSD(T) level of theory, ~1Π have dipoles of ~1Δ and B whereas the corresponding singlets A 0.22 and 1.51 D at the MRCIþQ level, respectively. The dipole moment values in all excited states of HScO range from 0.2 to 0.4 D. 5.2. ScOHþ and HScOþ. When one electron is removed, ScOHþ structures stabilize more than HScOþ structures, as already mentioned in section 2. This can be attributed to the fact that the electron is removed from the metal center in the case of ScOH, whereas in the other case the electron is removed from the H-ScO bond. Thus, the ionic picture of ScOHþ is close to Sc2þOH-, while the H-ScO bond weakens substantially upon ionization to HScOþ (see below). The ground state of Sc2þ is a 2D(3d1) state, with its first excited state 2S(4s1) lying 3.15 eV higher.42 These two atomic states, 2D and 2S, upon interacting with OH-(X1Σþ), yield four molecular states of 2Δ, 2Π, 2Σþ, and 2Σþ symmetry, respectively. This is exactly the case with the first four electronic states studied. Their Mulliken atomic charges on Sc range between þ1.4 and þ1.6 and on O between -0.67 and -0.80; the hydrogen atom is slightly positive. The CI vectors of the four states in question are given by (omitting the 1σ2 through 6σ2 and 1π42π4 inner electrons) ~ Δæ 0:96j7σ 8σ 3π 1δ æ jX 2

2

2

4

1

~ Σþ æ 0:89j7σ2 8σ 2 9σ1 3π4 æ - 0:32j7σ2 8σ 2 10σ1 3π4 æ jA 2

~ Πæ 0:96j7σ2 8σ 2 3π4 4π1 æ jB 2

~ Σþ æ 0:89j7σ2 8σ 2 10σ 1 3π4 æ þ 0:32j7σ 2 8σ2 9σ 1 3π4 æ jC 2

Figure 4. MRCIþQ potential energy profiles for the O-Sc-H bend. Small angles correspond to the ScOH isomer, while angles close to 180 correspond to HScO. The A0 components are depicted with open circles and the A00 components with closed circles. The plot shows the minimum energy for a given value of φ for each state; at each φ, the H-Sc and Sc-O bond lengths have been varied to locate the minimum (where possible). The configuration Sc-H-O is not considered.

The 1δ and 4π molecular orbitals are essentially the 3dδ and 3dπ atomic orbitals of Sc, while the 9σ and 10σ orbitals are largely composed of scandium atomic orbitals as follows 9σ 0:88ð3d0 Þ þ 0:32ð4sÞ þ 0:21ð4pσ Þ 10σ - 0:41ð3d0 Þ þ 0:80ð4sÞ - 0:21ð4pσ Þ Apparently the two 2Σþ states originating from Sc2þ(2D; 3dσ) and Sc2þ(2S; 4s) are mixed. The Mulliken populations on 4s and ~2Σþ) and 4s0.413dσ0.52 (C ~2Σþ). For the 3dσ are 4s0.633dσ0.61 (A remaining two states, the 4s scandium atomic orbital is practically empty, as expected since these states originate from Sc2þ(2D;3d1). For all four states, we give geometries, binding energies, harmonic frequencies, and energy separations in Table 7, while the [Sc-OH]þ PECs are shown in Figure 5. As found for ScOH, in all of the states that we studied re(ScO-H) is almost equal to the bond length in free OH or OH- (0.96 Å). 4443



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Table 7. Results for Linear ScOHþ from the Current Work. Total Energies E, Bond Lengths re, Binding Energies De, Harmonic Frequencies ωe, and Excitation Energies Te Method

-E (a.u.)

re(Sc-OH) (Å)

re(ScO-H) (Å)

De(Scþ-OH) (kcal/mol)a

ωe (cm-1)b

Te (cm-1)

~2Δ X MRCI

835.393363

1.842

0.956

120.7

3939, 752, 425

0.0

MRCIþQ C-MRCI

835.399044 835.683790

1.842 1.820

0.956 0.955

118.5 117.4

3940, 751, 409 3926, 776, 420

0.0 0.0

C-MRCIþQ

835.728540

1.818

0.953

119.4

3916, 771, 415

0.0

RCCSD(T)

835.397324

1.857

0.955

117.7

3964, 758, 428

0.0

C-RCCSD(T)

835.746232

1.813

0.954

121.0

3967, 781, 413

0.0

~2Σþ A MRCI

835.381299

1.777

0.960

113.4

3879, 804, 444

2648

MRCIþQ

835.389884

1.778

0.961

112.9

3878, 816, 435

2010

RCCSD(T)

835.390152

1.789

0.960

113.2

3898, 822, 443

1574

C-RCCSD(T)

835.739087

1.759

0.961

116.5

3877, 825, 450

1568

~2Π B MRCI

835.359322

1.881

0.953

99.6

3966, 731, 480

7471

MRCIþQ

835.372428

1.870

0.955

102.0

3967, 730, 482

5842

RCCSD(T)

835.371421

1.894

0.954

101.4

3973, 722, 495

5685

C-RCCSD(T)

835.717632

1.854

0.954

103.1

3965, 739, 457

6277

~2Σþ C MRCI

835.329109

1.861

0.963

80.4

MRCIþQ

835.341988

1.870

0.963

82.7

RCCSD(T)

835.343158

1.874

0.964

83.7

14 102 12 522 3765, 739, 545

11 888

With respect to ground-state fragments: Scþ(3D) þ OH(X2Π). b The first two numbers correspond to the O-H and Sc-O stretching modes, whereas the third value corresponds to the doubly degenerate bending mode. a

Experimentally, both Sc-OHþ and ScO-Hþ binding energies for the ground state are available (see Table 2). At our highest level of calculation, C-RCCSD(T), we found D e(Sc-OHþ) = 121.0 kcal/mol and D e(ScO-Hþ) = 65.3 kcal/mol, and after considering the ZPEs we obtain D0(Sc-OHþ) = De(Sc-OHþ) - ZPE(ScOHþ) þ ZPE(OH) = 118.9 kcal/mol and D0(ScO-Hþ) = De(ScO-Hþ) ZPE(ScOHþ) þ ZPE(ScOþ; X1Σþ)18 = 59.4 kcal/mol. Both values are in complete agreement with experiment, D0(Sc-OHþ) = 119.2 ( 2 kcal/mol and D0(ScO-Hþ) = 58 ( 2 kcal/mol.12 ~2Δ state, we see Concerning the Sc-OHþ bond length in the X again that core correlation at the MRCI and CC levels reduces it considerably. Our suggested value is 1.815 Å, in reasonable agreement with previous theoretical results (see Table 2). Vibrational frequencies are reported here for the first time (see Table 7). ~2Π, and C ~2Σþ, The remaining three electronic states, A~2Σþ, B -1 are located 1500-2000, ∼6000, and ∼12 000 cm above X~2Δ. ~2Σþ 17.2 kcal/ Note that a previous theoretical study located A -1 2 13 ~ mol or ∼6000 cm above X Δ. In close analogy, the first two excited states of ScFþ are of 2Σþ and 2Π symmetry as well, lying at about 3000 and 5500 cm-1 above the ground state.19 Compared to re(Sc-Fþ), the re(Sc-OHþ) values are consistently larger by 0.01 Å: 1.81 (1.80), 1.76 (1.75), and 1.85 (1.84) Å for the 2Δ, 2Σþ, and 2Π states, respectively. A similar trend is followed for the Sc-X stretching frequencies with X = OH or F: those having X = OH are 25 cm-1 higher, on average. The electronic states of linear HScOþ can be obtained from those of HScO by removing one electron from the H-ScO bond. In this way, the 2Σþ, 2,4(Π,Φ), and 2,4Δ states are

Figure 5. MRCI potential energy profiles for the linear approach of Scþ to OH. The energies are shifted up by 835 a.u.

produced from the 1Σþ, 1,3(Π,Φ), and 1,3Δ states of the neutral species. As a result, the energy differences between the cation’s excited electronic states and its ground state nearly match the energy differences for the corresponding states of the neutrals and their ground states: approximately 26 000 cm-1 for the (Π,Φ) states and 28 000 cm-1 for the Δ states. Alternatively, these states can be viewed as arising from the weak attachment of 4444



ARTICLE

Table 8. Results for Linear HScOþ from the Current Work. Total Energies E, Bond Lengths re, Binding Energies De, Harmonic Frequencies ωe, and Excitation Energies Te Method

-E (a.u.)

re(HSc-O) (Å)

re(H-ScO) (Å)

De(H-ScOþ) (kcal/mol)a

Te (cm-1)

2 þ

Σ

MRCI

835.296573

1.642

2.707

2.8

0.0

MRCIþQ RCCSD(T)

835.301981 835.298008

1.646 1.658

2.684 2.674

2.9 3.0

0.0 0.0

4

Π

MRCI

835.178515

1.939

2.660

3.4

25 911

MRCIþQ

835.183647

1.946

2.656

3.5

25 971

Φ

4

MRCI

835.178456

1.939

2.660

3.4

25 924

MRCIþQ

835.183518

1.952

2.647

3.4

26 000

2

Π

MRCI

835.178023

1.937

2.711

3.1

26 019

MRCIþQ

835.183140

1.937

2.704

3.2

26 083

Φ

2

MRCI

835.177989

1.938

2.712

3.1

26 026

MRCIþQ

835.183069

1.938

2.706

3.2

26 098

Δ

2

MRCI

835.169524

1.840

2.534

4.2

27 884

MRCIþQ

835.174602

1.840

2.531

4.4

27 956

Δ

4

a

MRCI

835.168357

1.843

2.686

3.5

28 140

MRCIþQ

835.173365

1.843

2.682

3.6

28 228

RCCSD(T)

835.171491

1.858

2.672

3.5

27 767

With respect to their adiabatic fragments, see text.

Figure 6. MRCI potential energy profiles of the [O-Sc-H]þ bend. Small angles correspond to the ScOHþ conformation, while angles near 180 correspond to HScOþ. The A0 components are depicted with open circles and the A00 components with closed circles. The plot shows the minimum energy for a given value of φ for each state; at each φ, the HSc and Sc-O bond lengths have been varied to locate the minimum (where possible). The configuration Sc-H-O is not considered.

3.0-4.0 kcal/mol and an Sc-H bond length of ∼2.7 Å for all of the states studied (see Table 8). We calculated ωe values only for the ground state of HScOþ. At the MRCI (MRCIþQ) levels we obtained 973 (969), 371 (352), and 81i (78i) cm-1. The imaginary value of this last frequency indicates that the linear HScOþ structure is not a real minimum. Hence, we constructed the profiles of the [Sc,O,H]þ potential energy surfaces with respect to the H-Sc-O angle (Figure 6). Indeed, the energy of the ground-state curve drops slightly as the angle decreases from 180 (linear HScOþ). After a shallow minimum at about 80, the energy plummets by 60.7 kcal/mol to the energy of the X~2Δ state of linear ScOHþ, at the MRCI level, by 60.9 kcal/mol at the MRCIþQ level, and by 62.3 kcal/mol at the RCCSD(T) level. The same energy difference was found to be 91.9 kcal/mol by Tilson and Harrison.13 Moving in the opposite direction, from 0 to 180, the A0 and A00 components of X~2Δ remain degenerate until 30, whereas the two components of B~2Π are separated slightly, even for small angles. In the case of [Sc,O,H]þ we did not examine bent structures connected to linear HScOþ for two reasons. First, they seem to lie at least 60 kcal/mol above the global minimum, and second, excitations from the ground state to these structures are FranckCondon forbidden.

a H(2S) to the first seven electronic states of ScOþ. Since no σ electrons exist in these states of ScOþ, only a σ dative half bond HfScO may form. The result is an Sc-H bond strength of

6. SUMMARY The present study is the first systematic ab initio work on the [Sc,O,H]0,þ species. Using MRCI and CC methodologies with 4445


The Journal of Physical Chemistry A large basis sets, we explored the potential energy surfaces of the ground states and several excited states of both the neutral and the cationic species. We found that the linear ScOH0,þ configurations present behavior similar to that of the isoelectronic ScF0,þ, revealing an ionic ScþOH- and Sc2þOH- character. The linear HScO0,þ states come from the covalent or dative interaction of H(2S) and the appropriate ScO0,þ electronic states. For the neutral species, we also examined the oblique approach of H(2S) to ScO, locating a stable bent HScO structure. The absolute energies of both linear isomers, ScOH and HScO, and the bent isomer have been found to be nearly equal, rendering the ground-state potential energy surface extremely complicated but for that reason interesting. The linear ScOH and the bent HScO structures are the ground states, separated by a barrier of about 40 kcal/mol. For the excited states the situation is simpler, with the linear ScOH configurations being more stable. For a total of 14 stationary points on the potential surfaces, in this work we have given geometries, binding energies, energy gaps, and (for most of the stationary points) vibrational frequencies. For the ground state, we also reported dipole moments. As far as the cation is concerned, we studied extensively the ground and first three excited states of the linear ScOHþ conformation. The linear and bent HScOþ structures have relatively high excitation energies, and they are Franck-Condon inaccessible. For all of the species and states studied, the agreement between our results and existing experimental results is very good. However, extensive spectroscopic studies such as those of the isovalent YOH molecule9 have not yet been reported for the lighter, scandium-containing species. We hope that our results will be useful in future spectroscopic work.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This material is based upon work supported by the National Science Foundation under grant no. 0708496. We thank Professor James F. Harrison, Michigan State University, and Professor Aristides Mavridis, National and Kapodistrian University of Athens, for their valuable comments on the manuscript. ’ REFERENCES (1) Zhang, L.; Dong, J.; Zhou, M. J. Phys. Chem. A 2000, 104, 8882. (2) Andrews, X.; Wang, L. J. Phys. Chem. A 2006, 110, 1850. (3) Zhou, M.; Zhang, L.; Dong, J.; Qin, Q. J. Am. Chem. Soc. 2000, 122, 10680. (4) Jacox, M. E. J. Phys. Chem. Ref. Data 2003, 32, 1. (5) Andrews, X.; Wang, L. J. Phys. Chem. A 2006, 110, 10409. (6) Andrews, X.; Wang, L. J. Phys. Chem. A 2006, 110, 10035. (7) Park, M.; Hauge, R. H.; Margrave, J. L. High Temp. Sci. 1988, 25, 1. (8) Trkula, M.; Harris, D. O. J. Chem. Phys. 1983, 79, 1138; Jarman, C. N.; Fernando, W. T. M. L.; Bernath, P. F. J. Mol. Spectrosc. 1990, 144, 286; ibid. 1991, 145, 151; Tao, C.; Mukarakate, C.; Reid, S. A. Chem. Phys. Lett. 2007, 449, 282; Kauffman, J. W.; Hauge, R. H.; Margrave, J. L. J. Phys. Chem. 1985, 89, 3541; Whitham, C. J.; Ozeki, H.; Saito, S. J. Chem. Phys. 1999, 110, 11109; ibid 2000, 112, 641. (9) Adam, A. G.; Athanassenas, K.; Gillett, D. A.; Kingston, C. T.; Merer, A. J.; Peers, J. R. D.; Rixon, S. J. J. Mol. Spectrosc. 1999, 196, 45;

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First-Principles Calculations of the Electronic and ... - ACS Publications

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