A Computational Study on the Ground and Excited States of Nickel

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A Computational Study on the Ground and Excited States of Nickel Silicide George Schoendorff, Alexis R Morris, Emily D. Hu, and Angela K Wilson J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b05661 • Publication Date (Web): 24 Aug 2015 Downloaded from http://pubs.acs.org on August 29, 2015

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The Journal of Physical Chemistry

A Computational Study on the Ground and Excited States of Nickel Silicide

George Schoendorff, Alexis R. Morris, Emily D. Hu, Angela K. Wilson 1 Department of Chemistry and Center for Advanced Scientific Computing and Modeling (CASCaM), University of North Texas, Denton, Texas 76203-5017 ABSTRACT Nickel silicide has been studied with a range of computational methods to

determine the nature of the Ni-Si bond. Additionally, the physical effects that need to be addressed within calculations to predict the equilibrium bond length and bond dissociation energy within experimental error have been determined. The ground

state is predicted to be a 1Σ+ state with a bond order of 2.41 corresponding to a triple bond with weak π bond. It is shown that calculation of the ground state equilibrium geometry requires a polarized basis set and treatment of dynamic

correlation including up to triple excitations with CR-CCSD(T)L resulting in an

equilibrium bond length of only 0.012 Å shorter than the experimental bond length. Previous calculations of the bond dissociation energy resulted in energies that were only 34.8% to 76.5% of the experimental bond dissociation energy. It is shown here

that use of polarized basis sets, treatment of triple excitations, correlation of the valence and subvalence electrons, and a Λ coupled cluster approach is required to obtain a bond dissociation energy that deviates as little as 1% from experiment. KEYWORDS

NiSi, nickel silicide, diatomic, CASSCF, MR-AQCC, CCSD(2)T, CR-CCSD(T)L 1

Author to whom correspondence should be addressed: [email protected]

ACS Paragon Plus Environment


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INTRODUCTION The high efficiency of transition metal silicides in fields involving catalysis

and microelectronic devices make them of importance largely due to their desirable

physical properties including oxidation, resistivity, and stability at high

temperatures. 1-3 This is particularly true for nickel silicide, which is of interest due to its exceptional hardness, low resistivity, and reduced thermal energy. Thus, nickel has the potential of fulfilling many functions within the manufacturing of microelectronics. 4 Although possible treatments for better quality microelectronics with nickel silicide have been proposed, the details of the morphology and electronic structure of nickel silicide remains unknown.

Moreover, the

semiconducting properties of metal silicides are dependent on the Schottky-barrier

heights, a property that is well known to be dependent on the atomic scale structure

at the surface and thus dependent on the local electronic structure of this region. 5-9

A number of recent studies have been performed on nickel silicide in the solid state

using density functional theory where nickel silicide exists as a metalsemiconductor interface or as a small NixSiy cluster.10-12 However, investigation of the fundamental interactions between nickel and silicon with high level ab initio

methods have been lacking to date. To this end, it is beneficial to examine the

simplest nickel silicide system, i.e. the NiSi diatomic, to determine the appropriate computational methods to characterize the ground and excited state properties.

Dissociation energies for group 10 containing diatomic molecules, including

nickel silicide, have been reported via Knudsen effusion cell mass spectrometry and band spectroscopy.

13-15

However, as nickel silicide is of particular interest as a 2


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semiconductor, it is essential to obtain a detailed understanding of the bonding

nature and excited state electronic structure of nickel silicide, and the study of the NiSi diatomic species enables such a detailed understanding of the Ni-Si bond. The earliest study of the NiSi diatomic was a multireference doubles configuration

interaction (MRD CI) study of the ground and low-lying excited states using

nonrelativistic pseudopotentials performed by Haberlandt.

16

It was determined

that the ground state is a doubly bonded 1Σ+ state. This prediction is in agreement with the experimentally determined ground state assignment17 but the computed bond dissociation energy of 43.6 kcal mol-1 accounts for only 58% of the experimental bond dissociation energy of 75 ± 4 kcal mol-1.

Moreover, the

computed ground state equilibrium bond distance of 2.24 Å is 10% shorter than the experimentally determined equilibrium bond distance of 2.032 Å.

18

Another

computational study was performed by Shim et al. using configuration interaction (CI) and complete active space self-consistent field (CASSCF) methods.

19

Shim’s

results were qualitatively similar to those predicted by Haberlandt; the bond

lengths were longer than experiment and the bond dissociation energy was less

than experiment. There was a modest improvement in the computed bond lengths,

i.e. 2.23 Å with CI and 2.14 Å with CASSCF, but the computed bond dissociation energies were even further from experiment, i.e. 26.1 kcal mol-1 and 29.5 kcal mol-1 for CI and CASSCF, respectively.

Modest improvements in the computational results were achieved through

the use of density functional theory (DFT). 18 Calculations on the 1Σ+ ground state

were performed using DFT, and all computed bond lengths were shorter than the 3



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experimental bond length with the computed bond lengths of 2.016 Å, 2.010 Å, and 2.004 Å using the B3LYP, B3PW91, and B3P86 functionals, respectively. While DFT

overbinds NiSi, it exhibits a clear improvement in the prediction of the equilibrium bond distance compared with previously computed bond dissociation energies.

Moreover, the bond dissociation energies obtained with the three functionals employed are 54.2 kcal mol-1, 53.5 kcal mol-1 and 57.4 kcal mol-1 using the B3LYP,

B3PW91, and B3P86 functionals, respectively. However, while this is certainly an

improvement over previous studies, even the best computed bond dissociation accounts for only 76.5% of the experimental bond dissociation energy.

In the present work, multireference and single reference methods are

employed to elucidate the source of the difficulties in earlier studies in determining an accurate equilibrium geometry and bond dissociation energy. Additionally, the low-lying excited state manifold is studied and the electronic structure of the NiSi bond are presented.

COMPUTATIONAL DETAILS Both multireference and single reference calculations on the NiSi diatomic

molecule were performed using the full optimized reaction space (FORS)

20-22

/

compete active space self-consistent field (CASSCF) 23 methods implemented within

the GAMESS quantum chemistry software package. 24 The cc-pVTZ-DK basis set was used for nickel25 and the cc-pV(T+d)Z-DK basis set was used for silicon. 26, 27 Scalar relativistic effects were included via the use of the infinite order two-component method (IOTC) of Barysz et al. 28-31

4


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Multireference calculations were performed with a 10 orbital active space

that spanned the Ni 4s and 3d orbitals and the Si 3s and 3p orbitals. C2v symmetry

was enforced for the multireference calculations and potential energy curves (PECs)

were computed for the lowest energy state in each irreducible representation in

each spin multiplicity considered, i.e. singlet, triplet, quintet, and septet. An intrinsic

localized density analysis (ILDA) was performed at the ground state equilibrium distance.

32, 33

Spectroscopic constants for the ground and excited states were

determined via a Dunham analysis34 using a ninth-order polynomial fit to the ab initio PECs with the isotopes chosen to be 58Ni and 28Si to enable direct comparison with experimental results.

18

The dissociation energy was computed via a

supermolecule approach with an internuclear distance of 8.0 Å.

The bond

dissociation energy also was computed with MR-AQCC35 calculations performed

using the CASSCF natural orbitals with a reduced active space based on the CASSCF natural orbital occupation numbers.

The MR-AQCC calculations correlated all

valence electrons and employed a (6,6) active space with the Ni 3dz2-4s and 3dδ

orbitals in the active space along with the Si 3p orbital set.

The performance of single reference methods for the determination of the

bond length and bond dissociation energy was also tested. The initial Hartree-Fock

reference wavefunction was obtained by reoptimization of the CASSCF natural orbitals. The Maximum Overlap Method (MOM) was employed to ensure that the Hartree-Fock wavefunction corresponded as closely as possible to the leading determinant of the CASSCF wavefunction.

36

The correlated single reference

methods tested were MBPT2, CCSD, and CCSD(T) as well as Λ and completely 5



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renormalized coupled-cluster methods, CCSD(2)T and CR-CCSD(T)L [CR-CC(2,3),A and CR-CC(2,3),D, respectively in GAMESS].

37-40

When computing the bond

dissociation energy with the correlated methods, three levels of correlation were employed. The lowest level of correlation included only the valence electrons in the correlation space, i.e. Ni 4s and 5d and Si 3s and 3p. Another level considered included the valence and subvalence electrons in the correlation space, i.e. Ni 3s, 3p,

4s, and 3d and Si 2s, 2p, 3s, and 3p. Finally, all electrons were correlated in the highest level of correlation. DISCUSSION The ground and low-lying excited states of the NiSi diatomic molecule have

been computed at the CAS(14,10) level of theory. The resulting potential energy

curves are shown in Figure 1. The ground state was determined to be a 1Σ+ state,

which is in agreement with previous studies.

The computed ground state

equilibrium bond length is 2.086 Å which is 0.1 – 0.2 Å shorter than previous predictions with multireference methods19,

41

yet is in better agreement with the

experimentally determined bond length of 2.032 Å.

18

The reason for the

discrepancy between the present result and earlier results is likely due to

differences in the basis set leading to different descriptions of the electronic structure at the ground state minimum. Early studies indicated that the σ bond in NiSi is a result of bond formation between the Ni 4s and Si 3pz orbitals. This is

indeed what is observed in the present study at bond lengths greater than 2.3 Å. This state is well described by the modest basis sets previously employed wherein 6


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the highest angular momentum functions were d functions. 16, 19, 42, 43 However, at

internuclear distances less than 2.3 Å the σ bond in NiSi has a sizeable contribution from the compact Ni 3dz2 orbital.

This bonding motif cannot be described

adequately unless the basis set at least has f polarizing functions available which are

present in the cc-pVTZ-DK basis set used in the present work. This change in electronic structure is clearly evident in the PEC for the 1Σ+ ground state as there is a

shoulder in the PEC. This shoulder is simply the result of a change in binding motif and is analogous to the shoulder observed in the ground state PEC for the chromium dimer. 44, 45

To better understand the nature of the bonding interactions in NiSi, an

intrinsic localized density analysis was performed on the X1Σ+ ground state at the CAS(14,10) equilibrium bond distance of 2.086 Å. The ILDA method allows for a

basis set independent bonding analysis wherein the diagonal elements of the density matrix of the oriented localized quasiatomic molecular orbitals are the

orbital populations and the off-diagonal terms are the bond orders. 32, 33 The results of the ILDA are shown in Table 1. It is clear that the Si 3s and the Ni 3dδ orbitals do

not take part in bonding and can be considered lone pairs. Hybridization occurs between the Ni 3dz2 and the Ni 4s orbitals resulting in two new orbitals, 3dz2-4s and 3dz2+4s. The 3dz2-4s orbital is polarized away from Si such that it is largely non-

bonding in character. The small off-diagonal element in the density matrix, i.e. 0.01, supports this analysis.

The other combination, 3dz2+4s, accumulates electron

density in the internuclear region and forms a σ bond with the Si 3pz orbital for a

contribution to the total bond order of 0.92, as determined from the off-diagonal 7



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elements. The degenerate Ni 3dπ orbitals combine with the Si 3pπ orbitals (i.e. 3px and 3py) to form a degenerate pair of π bonds. The π bonds in NiSi are relatively

weak with each π bond having a bond order of 0.74. Thus, NiSi is a triply bonded

system to a first approximation, yet if the weak π character is accounted for then the total bond order is 2.41. The possibility of π bonding in NiSi has been previously noted, but only one π bond was postulated.

18

The IDLA results suggest that π

bonding plays a greater role than previously thought.

The excited state manifold begins ~10 kcal mol-1 above the ground state at

the ground state equilibrium bond distance.

The ground state remains well-

separated from the excited states until the internuclear distance is stretched to ~3.0 Å. One noticeable feature in the excited state manifold is the shoulder in the b3Φ

state. The reason for the shoulder is similar to what was observed with the X1Σ+ ground state. The σ bond in NiSi is characterized by a large contribution from the Ni 3dz2 orbital at internuclear distances of 2.3 Å or less. However, as the internuclear

distance is increased, the Ni 4s contribution to the σ bond increases in order to maximize orbital overlap. The shoulders are a direct consequence of the large difference in the radial extent of the Ni 3d and 4s orbitals which have radial expectation values, , equal to 0.547 Å and 1.446 Å, respectively. 2.

Spectroscopic constants for the ground and excited states are shown in Table

Spectroscopic constants for the septet states are omitted since the first

appearance of the septet states occurs at energies greater than the computed bond dissociation energy (see Figure 1). The excited state manifold consists of a dense

cluster of states with seven states located within 5 kcal mol-1 of the lowest excited 8


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state (A1Π). It can be seen from both Figure 1 and Table 2 that the ground state

equilibrium bond distance is significantly shorter than the equilibrium bond distances of the excited states with the difference ranging from 0.4 - 0.5 Å. The well

depth of the ground state is reflected in the larger stretching frequency compared with the excited states, yet the ground state stretching frequency remains 100 cm-1

below the experimental value. 18 This indicates that ground state potential well is

too shallow at the CAS(14,10) level of theory. The excited states must be less tightly bound than the ground state, hence the smaller stretching frequencies (< 300 cm-1).

The multireference computational methods employed in this and earlier

studies have been successful in providing a qualitative description of the ground and excited states. However, methods capable of accurately predicting the ground

state equilibrium bond length and bond dissociation energy have been elusive. Shown in Figure 2 are the ground state potential energy curves in the equilibrium

bonding regions computed with a number of single reference methods. Table 3 shows the equilibrium bond distances, the bond dissociation energies, and the

vibrational frequencies associated with the X1Σ+ ground state computed with a range of methods. The single reference methods used included Hartree-Fock and perturbation theory as well as a number of coupled cluster methods including the Λ and CR-CC(2,3) formalisms, i.e. CCSD(2)T and CR-CCSD(T)L, respectively.

The

calculation of the Hartree-Fock reference utilized the CAS(14,10) natural orbitals as the initial orbital guess, and the Maximum Overlap Method (MOM) was employed to

ensure the best possible single reference description of the X1Σ+ ground state. The

resulting Hartree-Fock solution produces a bond length within 0.05 Å of the 9



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experimental result of 2.032 Å. 18 The bond length obtained is closer to experiment

than those computed with the MRD CI or CASSCF with modest basis sets by 0.1 – 0.2

Å. Thus, the quality Hartree-Fock reference is essential for the computation of the bond length even though it still overbinds resulting in a shortened bond length compared with experiment. Correlated methods that formally include up to double

excitations, i.e. MBPT2 and CCSD, also overbind with CCSD producing the shorted bond length Inclusion of triples in the coupled cluster method can help remedy this

problem. CCSD(T) and CCSD(2)T both underbind resulting in a bond length that is 0.037 Å too long when computed with either of these methods. However, CRCCSD(T)L performs the best with a computed bond length only 0.012 Å too short.

Thus both the quality of the Hartree-Fock reference and a treatment of electron

correlation including up to triple excitations are required for accurate computation of the equilibrium bond length.

The bond dissociation energies computed with both multireference and

single reference methods are shown in Table 3. For all methods, the dissociation limit is (3F)Ni + (3P)Si. Despite providing a qualitatively correct description of the

electronic structure, the multireference methods employed are lacking when it comes to the computation of the bond dissociation energy. The CAS(14,10) level of theory results in a bond dissociation energy that is 50 kcal mol-1 lower than the

experimental bond dissociation energy of 75 ± 4 kcal mol-1. 17 Use of MR-AQCC to

capture additional dynamic correlation was also employed to compute the bond dissociation energy, resulting in a dissociation energy of 34.5 kcal mol-1. The 10.4 kcal mol-1 improvement in the bond dissociation energy indicates that dynamic 10


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correlation is certainly important, yet the double excitations from MR-AQCC

treatment still are not sufficient to reproduce the experimental bond dissociation energy.

In addition to multireference methods, the bond dissociation energy was also

computed using correlated single reference methods noted above. In each case,

three levels of electron correlation were tested. First, only the valence electrons

were correlated (Ni 4s and 3d and Si 3s and 3p), then the subvalence also was correlated (Ni 3s, 3p, 4s and 3d and Si 2s, 2p, 3s and 3p), and finally all electrons were correlated.

With all correlated methods used, the additional levels of

correlation stabilize NiSi relative to the dissociation product and hence the computed bond dissociation energy increases with increasing number of electrons

correlated. The two methods that include only double excitations, MBPT2 and

CCSD, exhibit vastly different trends. MBPT2 results in bond dissociation energies over twice the experimental value. This is a situation where perturbation theory is

not appropriate as the perturbation is not a small correction to the Hartree-Fock reference. CCSD outperforms even MR-AQCC, though the bond dissociation energy is

still 35 – 40 kcal mol-1 too low accounting for at best 53.6% of the experimental

bond dissociation energy. CCSD(T) is a modest improvement over CCSD, but the

computed bond dissociation energy is improved only when more than just the

valence electrons are correlated with the best result recovering 60.1% of the experimental bond dissociation energy. The only methods examined that get close to the experimental bond dissociation energy are the Λ and completely

renormalized coupled cluster methods, i.e. CCSD(2)T and CR-CCSD(T)L. Of the two, 11



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though, only CCSD(2)T comes within experimental error, and CCSD(2)T can achieve this result with just the valence electrons correlated. However, an improvement of a

few kcal mol-1 is achieved when the subvalence electrons are correlated resulting in

a bond dissociation energy that is 1.1 kcal mol-1 from the experimental bond

dissociation energy and within the 4 kcal mol-1 experimental error. Correlation of any more of the core does not appreciably improve the computed bond dissociation energy with either CCSD(2)T or CR-CCSD(T)L. CONCLUSION The NiSi diatomic molecule was studied with both multireference and single

reference methods. It was determined that the failure of earlier studies to obtain a ground state bond length in even modest agreement with experiment was the result

of the use of basis sets that were incapable of polarizing the Ni 3d orbitals. Yet, this and all earlier studies are in agreement that the ground state is indeed a 1Σ+ state. It further has been determined that the NiSi molecule is triply bonded, but with weak

π bonds resulting in a total bond order of 2.41. The equilibrium bond length also was computed with a number of single reference methods that relied on Hartree-

Fock references obtained using the CAS(14,10) natural orbitals. It is shown that

reasonable agreement with experiment can be obtained with single reference methods if a good reference wave function is employed. Furthermore, the best agreement with experiment was obtained only when some treatment of triple excitations was included with CR-CCSD(T)L providing the most accurate bond

length.

12


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Until now, computed bond dissociation energies have never come within

experimental error of the experimental value of 75 ± 4 kcal mol-1. It has been shown

herein that a treatment of dynamic electron correlation is essential for the accurate

prediction of the bond dissociation energy. As with the bond length, a treatment of triple excitations is needed, yet triple excitations alone is still insufficient. It is the Λ and completely renormalized coupled cluster formalisms that are required to obtain

bond dissociation energies within 90% of experiment, and only CCSD(2)T produces

a bond dissociation energy within experimental error. Finally, it has been shown

that the best results are obtained when the subvalence electrons are correlated as well as the valence resulting in a bond dissociation energy that is 1.1 kcal mol-1 from experiment and within the 4 kcal mol-1 experimental error.

ACKNOWLEDGEMENTS This material is based upon work supported by the National Science

Foundation under CHE-1362479.

Computing resources were provided by the

Computing and Information Technology Center at the University of North Texas. Additional support was provided by the U.S. Department of Energy (DOE) for the Center for Advanced Scientific Computing and Modeling (CASCaM). The authors would like to thank Aaron C. West and Michael D. Morse for helpful discussions. The authors declare no competing financial interest. REFERENCES

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20. Ivanic, J. Direct configuration interaction and multiconfigurational selfconsistent-field method for multiple active spaces with variable occupations. I. Method. J. Chem. Phys. 2003, 119, 9364-9376. 21. Ivanic, J. Direct configuration interaction and multiconfigurational selfconsistent-field method for multiple active spaces with variable occupations. II. Application to oxoMn(salen) and N2O4. J. Chem. Phys. 2003, 119, 9377-9385. 22. Ruedenberg, K.; Sundberg, K. R. In Quantum Science; Calais, J.-L., Goscinski, O., Lindenberg, J.;,Öhrm, Y., Eds.; Plenum: New York, 1976; pp 505-515. 23. Seigbahn, P.; Heiberg, A.; Roos, B.; Levy, B. A comparison of the super-CI and the Newton-Raphson scheme in the complete active space SCF method. Phys. Scr. 1980, 21, 323-327. 24. Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. J.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; Windus, T. L.; Dupuis, M.; Montgomery Jr., J. A. General atomic and molecular electronic structure system. J. Comput. Chem. 1993, 14, 1347-1363. 25. Balabanov, N. B.; Peterson, K. A. Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc-An. J. Chem. Phys. 2005, 123, 064107/1-15. 26. Dunning Jr., T. H.; Peterson, K. A.; Wilson, A. K. Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited. J. Chem. Phys. 2001, 114, 9244-9253. 27. de Jong, W. A.; Harrison, R. J.; Dixon, D. A. Parallel Douglas-Kroll energy and gradients in NWChem: Estimating scalar relativistic effects using Douglas-Kroll contracted basis sets. J. Chem. Phys. 2001, 114, 48-53. 28. Barysz. M.; Sadlej, A. J. Infinite-order two-component theory for relativistic quantum chemistry. J. Chem. Phys. 2002, 116, 2696-2704. 29. Kedziera, D.; Barysz, M.; Sadlej, A. J. Two-component relativistic methods for the heaviest elements. J. Chem. Phys. 2004, 121, 6719-6727. 30. Kedzeira, D.; Barysz, M.; Sadlej, A. Expectation values in spin-averaged DouglasKroll and infinite-order relativistic methods. Struct. Chem. 2004, 15, 369-377. 31. Barysz. M.; Mentel, L.; Leszczynscki, J. Recovering four-component solutions by the inverse transformation of the infinite-order two-component wave funvetions. J. Chem. Phys. 2009, 130, 164114/1-7. 32. Ivanic, J.; Atchity, G. J.; Ruedenberg, K. Intrinsic local constituents of molecular electronic wave functions. I. Exact representation of the density matrix in terms of chemically deformed and oriented atomic minimal basis set orbitals. Theor. Chem. Acc. 2008, 120, 281-294. 33. Ivanic, J.; Ruedenberg, K. Intrinsic local constituents of molecular electronic wave functions. II. Electronic structure analyses in terms of intrinsic oriented quaiatomic molecular orbitals for the molecules FOOH, H2BH2BH2, H2CO and the isomerization HNO → NOH. Theor. Chem. Acc. 2008, 120, 295-305. 34. Dunham, J. L. The energy levels of a rotating vibrator. Phys. Rev. 1932, 41, 721731. 35. Szalay, P. G. In Bartlett, R. J., Ed.; Modern ideas in coupled-cluster methods; World Scientific: Singapore, 1997; pp 81-123. 15



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36. Gilbert, A. T. B.; Besley, N. A.; Gill, P. M. W. Self-consistent field calculations of excited states using the maximum overlap method (MOM). J. Phys. Chem. A 2008, 112, 13164-13171. 37. Gwaltney, S. R.; Head-Gordon, M. A second-order perturbative correction to the coupled-cluster singles and doubles method: CCSD(2). J. Chem. Phys. 2001, 115, 2014-2021. 38. Piecuch, P.; Kowalski, K.; Pimienta, I. S. O.; Fan, P.-D.; Lodriguito, M.; McGuire, M. J.; Kucharski, S. A.; Kuś, T.; Musial, M.; Method of moments of coupled-cluster equations: A new formalism for designing accurate electronic structure methods for ground and excited states. Theor. Chem. Acc. 2004, 112, 349-393. 39. Piecuch, P.; Kucharski, S. A.; Kowalski, K.; Musial, M. Efficient computer implementation of the renormalized coupled-cluster methods: The R-CCSD[T], RCCSD(T), CR-CCSD[T], and CR-CCSD(T) approaches. Comput. Phys. Commun. 2002, 149, 71-96. 40. Kowalski, K.; Piecuch, P. The method of moments of coupled-cluster equations and the renormalized CCSD[T], CCSD(T), CCSD(TQ), and CCSDT(Q) approaches. J. Chem. Phys. 2000, 113, 18-35. 41. Haeberlen, O. D.; Roesch, N. A scalar-relativistic extension of the linear combination of Gaussian-type orbitals local density functional methods: Application to AuH, AuCl and Au2. Chem. Phys. Lett. 1992, 199, 491-496. 42. Veillard, A. Gaussian basis set for molecular wavefunctions containing secondrow atoms. Theor. Chim. Acta 1968, 12, 405-411. 43. Wachters, A. J. H. Gaussian basis set for molecular wavefunctions containing third-row atoms. J. Chem. Phys. 1970, 52, 1033-1036. 44. Casey, S. M.; Leopold, D. G. Negative ion photoelectron spectroscopy of Cr2. J. Phys. Chem. 1993, 97, 816-830. 45. Brunda, M.; Gagliardi, L.; Roos, B. O. Analyzing the chromium-chromium multiple bonds using multiconfigurational quantum chemistry. Chem. Phys. Lett. 2009, 471, 1-10.

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TABLES AND FIGURES Figure 1. Ground and excited state potential energy curves for NiSi computed at the CAS(14,10) level of theory. The lowest lying singlet, triplet, quintet, and septet states are shown with the ground state being a 1Σ+ state.

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Table 1. Populations and bond orders of each oriented localized molecular orbital optimized for the X1Σ+ ground state. The bond orders listed for each localized orbital correspond to the bond order of the resulting molecular orbital, e.g. the Ni 3dz2+4s and Si 3pz orbitals combine to form a molecular orbital with a bond order of 0.92. Orbital Population 3dδ 1.99 3dδ 1.99 Ni 3dz2-4s 1.95 3dπ 1.23 3dπ 1.23 3dz2+4s 0.97 3s 1.99 Si 3pz 1.15 3px 0.78 3py 0.78 Total Bond Order

Bond Order 0.00 0.00 0.01 0.74 0.74 0.92 0.01 0.92 0.74 0.74 2.41

Table 2. Spectroscopic constants for singlet, triplet, and quintet states. The equilibrium bond lengths are from ab initio calculations while the remaining constants were obtained by a Dunham analysis with a ninth order polynomial fit to the CAS(14,10) data. X1Σ+ A1Π a3Σ+ b3Φ C1Φ c3Σd5Δ e5Π

re (Å) 2.086 2.434 2.466 2.551 2.567 2.555 2.534 2.546

ωe (cm-1) 366.1 269.9 205.4 211.9 244.4 258.4 257.7 211.1

ωexe (cm-1) 6.66 2.02 2.58 3.29 2.35 6.17 3.10 2.13

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Be (cm-1) 0.2038 0.1494 0.1491 0.1633 0.1358 0.1428 0.1392 0.1402


αe (cm-1) 0.00286 0.00016 0.00344 0.00288 0.00128 0.00194 0.00119 0.00206

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Figure 2. Equilibrium region of the X1Σ+ ground state of NiSi for a variety of single reference methods. The reference state corresponds to a triple bond with the Si 3s and the Ni 3dδ orbitals constrained to be doubly occupied.

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Table 3. Molecular constants for the X1Σ+ ground state of NiSi. The dissociation products are (3F)Ni + (3P)Si. For the single reference methods, dissociation energies are computed first with three levels of correlation. The smallest correlation space includes only the valence electrons, the next larger correlation space includes the valence and subvalence electrons, and finally the largest correlation space includes all electrons. re (Å) CAS(14,10) MR-AQCC(6,6) MBPT2 CCSD CCSD(T) CCSD(2)_T CR-CCSD(T)_L Experiment a Ref. 10; b Ref. 9

2.086 --1.999 1.970 2.059 2.059 2.020 2.032a

De (kcal mol-1) ωe (cm-1) Valence Valence + All Subvalence Correlated 24.1 366 34.5 --156.1 186.5 187.2 609 36.4 39.7 40.2 556 24.7 43.4 45.1 418 71.0 76.1 76.7 458 63.9 68.6 69.2 --75 ± 4b 467.43a

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A Computational Study on the Ground and Excited States of Nickel

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