Vibronic Perturbations in the Electronic Spectrum of Magnesium Carbide Phalgun Lolur*, Richard Dawes*, Michael Heaven + *Department of Chemistry, Missouri S&T, Rolla, MO. + Department of Chemistry, Emory University, Atlanta, GA.

Motivation Magnesium – a high performance material Interest in covalent bonding characteristics of IIA group metals –ns 2 configuration Challenge for ab initio theory models –Multi-configurational, multiple states in the energy range of interest Provide predictions for experimentalists –Comparison with the valence iso- electronic BeC system 2

Resonantly enhanced multiphoton ionization (REMPI) spectrum for BeC 3 Barker et al. J. Chem. Phys. 137, (2012) T: 3 3 Π - X 3 Σ − Q: 1 5 Π Σ −

Outline 1.Potential Energy Curves  Molecular states from atomic states 2.Diabatic transformation of adiabats  Vibronic states  Spectroscopic constants and lifetime of states. 3.Results and Conclusions 4

Magnesium – Atomic States 5 Source:

Carbon – Atomic States 6 Source:

Combining Mg ( 1 S, 3 P) + C ( 3 P, 1 D) in C 2V Symmetry MOLPRO was used to calculate the energies of these states Combining the states (with a cut off at 44,000 cm -1 ), – 1 (5A 1 +3B 1 +3B 2 +4A 2 ) – 3 (9A 1 +10B 1 +10B 2 +10A 2 ) – 5 (2A 1 +2B 1 +2B 2 +4A 2 ) 7

DW-AE-MRCI/CBS(3,4,5) R (Å) Energy (cm -1 ) Mg ( 1 S) + C ( 3 P) 3Σ-3Σ- 1 3 Π 2 3 Π 5Π5Π 4 3 Π 5Σ-5Σ- 3 3 Π cm -1 (21890 cm -1 ) cm -1 (32053 cm -1 ) Experimental atomic gaps from NIST are mentioned in parenthesis. Each state was individually optimized using dynamic weighting schemes. 8

Dynamic weighting in BeOBe 9 f(  E)  2/((exp(-  *  E)+ exp(  *  E))^2)

PECs of the triplet states 10 Mg ( 1 S) + C ( 3 P) 3Σ-3Σ- 1 3 Π 2 3 Π 3 3 Π 4 3 Π Mg ( 3 P) + C ( 3 P) Mg ( 3 P) + C ( 1 D) Strong coupling between states Diabatization of adiabats R (Å) Energy (cm -1 ) NACME COUPLING GAUSSIAN MODEL COUPLING

Electronic states of MgC 11 Mg ( 1 S) + C ( 3 P) 3Σ-3Σ- 1 3 Π 2 3 Π 3 3 Π 4 3 Π Mg ( 3 P) + C ( 3 P) Mg ( 3 P) + C ( 1 D) R (Å) Energy (cm -1 ) R (Å) 3Σ-3Σ- 1 3 Π 2 3 Π 3 3 Π 4 3 Π

Comparison of BeC and MgC electronic states 12 BeC MgC

Calculating the vibrational levels using the sine-DVR method V + T d T nd 13

Calculated vibrational levels on the X 3 Σ - electronic ground state vE(v)E(v)-E(0) (cm -1 )

Calculating the vibronic states on 4 3 Π states V1V1 V2V2 V3V3 V4V4 V 21 V 32 V 43 V 12 V 23 V 34 T1T1 T1T1 T2T2 T2T2 T3T3 T3T3 T4T4 T4T4 V 21 = V 12 V 32 = V 23 V 43 = V 34 V 31 = V 13 V 42 = V 24 V 1 = V Π1 +V rot – i*U The complex part of the eigenvalues relate to the width of states Franck Condon Factors from the ground state were computed. V 31 V 42 V 13 V 24 CAP 15

Favorable states for observation 16 LevelE(n)E(n)-ZPE(GS)1 3 Π %2 3 Π %3 3 Π %4 3 Π % ( )- 1/2 WidthFC (cm -1 ) (Å) (cm -1 ) E E E R (Å) Energy (cm -1 ) R (Å)

InteractionInteraction between states Uncoupled 4 3 Π Diabatic calculation Uncoupled 4 3 Π Adiabatic calculation Coupled four- state 3 Π Diabatic calculation (cm -1 ) R (Å) Energy (cm -1 ) 41 %58 % % 4 3 Π - 99 %

Strongly mixed states still favorable for observation 18 LevelE(n)E(n)-ZPE(GS)1 3 Π %2 3 Π %3 3 Π %4 3 Π % ( )- 1/2 WidthFC (cm -1 ) (Å) (cm -1 ) E E E E The above states have a significant level of mixing and narrow widths and Franck-Condon (FC) factors greater than 0.05

States with a significant level of mixing and FCFs more than R (Å) Energy (cm -1 ) R (Å) Energy (cm -1 ) R (Å) Energy (cm -1 ) R (Å) Energy (cm -1 )

Spectroscopic constants  Ground state ZPE = cm -1, ω e = cm -1, ω e χ e = 4.76 cm -1  38 vibrational levels were identified on the ground state  94 vibrational levels were identified on the coupled Π states up to cm StateReRe R0R0 DeDe BD (Å) (cm -1 ) X 3 Σ E Π E Π E Π E Π E-06

Conclusions Development of robust schemes to construct global potential energy surfaces –Compute all molecular states from first principles including all energetically relevant atomic states on an equal footing Calculate ro-vibrational states with predictive spectroscopic accuracy –Explain and Predict Spectra 21

Acknowledgements Dawes Research group: Richard Dawes Moumita Majumder Steve Ndengue Spencer Norman Andrew Powell Collaborator: Michael Heaven, Emory Department of Chemistry, Missouri S&T 22