Simulation of infrared and Raman spectra

Transcription

1 Simulation of infrared and Raman spectra, 1 Bernard Kirtman, 2 Michel Rérat, 3 Simone Salustro, 1 Marco De La Pierre, 1 Roberto Orlando, 1 Roberto Dovesi 1 1) Dipartimento di Chimica, Università di Torino and NIS 2) Dept. of Chemistry and Biochemistry, University of California, Santa Barbara 3) Equipe de Chimie Physique, Université de Pau, France Today s menu 1

2 Today s menu Appetizer Today s menu Appetizer Main course - Theory 2

3 Today s menu Appetizer Main course - Theory Cheese - From theory to experiment Today s menu Appetizer Main course - Theory Cheese - From theory to experiment Dessert - Some simulated spectra 3

4 Today s menu Appetizer Main course - Theory Cheese - From theory to experiment Dessert - Some simulated spectra Coffee 1. The Appetizer 4

5 Mg3Al2Si3O12 Cubic, 80 atoms in the unit cell Raman spectrum, a long story Hofmeister et al

6 Hofmeister et al All 25 Raman active modes were assigned Experiment Simulation 6

7 Chaplin et al Method: Classical dynamics Experiment Simulation 7

8 Kolesov and Geiger

9 Experiment Simulation To be continued... 9

10 2. Main Course - Theory A little bit of history CRYSTAL95 CRYSTAL98 Energy, electronic structure 10

11 A little bit of history CRYSTAL95 CRYSTAL98 Energy, electronic structure CRYSTAL03 Geometry optimization A little bit of history CRYSTAL95 CRYSTAL98 Energy, electronic structure CRYSTAL03 CRYSTAL06 Geometry optimization Frequencies (peak positions), infrared intensities (numerical) 11

12 A little bit of history CRYSTAL95 CRYSTAL98 Energy, electronic structure CRYSTAL03 CRYSTAL06 CRYSTAL09 Geometry optimization Frequencies (peak positions), infrared intensities (numerical) Polarizabilities A little bit of history CRYSTAL95 CRYSTAL98 Energy, electronic structure CRYSTAL03 CRYSTAL06 CRYSTAL09 Geometry optimization Frequencies (peak positions), infrared intensities (numerical) Polarizabilities CRYSTAL14 Raman Intensities 12

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14 IR and non-resonant Raman intensities Born Charges (IR intensities): derivative of the dipole moment = electric field = Atomic displacement IR and non-resonant Raman intensities Born Charges (IR intensities): derivative of the dipole moment In CRYSTAL06 through Wannier functions: numerical derivatives in direct space = electric field = Atomic displacement 14

15 IR and non-resonant Raman intensities Born Charges (IR intensities): derivative of the dipole moment In CRYSTAL06 through Wannier functions: numerical derivatives in direct space In CRYSTAL09 through Berry Phase: numerical derivatives in reciprocal space = electric field = Atomic displacement IR and non-resonant Raman intensities Born Charges (IR intensities): derivative of the dipole moment We want analytical derivatives = electric field = Atomic displacement 15

16 IR and non-resonant Raman intensities Born Charges (IR intensities): derivative of the dipole moment Within Placzeck approximation, Raman tensor elements are defined as: = electric field = Atomic displacement IR and non-resonant Raman intensities Born Charges (IR intensities): derivative of the dipole moment Within Placzeck approximation, Raman tensor elements are defined as: We want analytical derivatives = electric field = Atomic displacement 16

17 External electric field in periodic systems This operator is not consistent with the periodic boundary conditions, it is not bound and breaks the translational invariance of the system. External electric field in periodic systems This operator is not consistent with the periodic boundary conditions, it is not bound and breaks the translational invariance of the system. 17

18 External electric field in periodic systems This operator is not consistent with the periodic boundary conditions, it is not bound and breaks the translational invariance of the system. Derivative in k: a lot of problems! We want analytical derivatives The Omega operator is the matrix representation of the field operator in AO basis At zero field: 18

19 The Omega operator is the matrix representation of the field operator in AO basis At zero field: Imaginary diagonal elements undefined: must be avoided! Mixed derivatives of total energy 19

20 Mixed derivatives of total energy If we differentiate this w.r.t. atomic displacements we get Mixed derivatives of total energy If we differentiate this w.r.t. atomic displacements we get This is not good. We want to avoid to solve perturbation equations for the atomic displacements. 20

21 Mixed derivatives of total energy Much better to start from here Where we introduce the eigenvalue-weighted density matrix Because : occupation matrix since Mixed derivatives of total energy Much better to start from here! Also note that the density matrix inside the Fock operator is not differentiated with respect to displacements Only gradients of the integrals are needed 21

22 Moving on: we differentiate once w.r.t. field Taken at zero field, this is the expression for the IR intensity. Note the derivative of DW. Moving on: we differentiate once w.r.t. field Taken at zero field, this is the expression for the IR intensity. Note the derivative of DW. The diagonal elements of are undefined, but it appears in two places with opposite sign. Diagonal blocks cancel out! 22

23 Let us differentiate once more w.r.t. field Things get more complicated Again, it can be demonstrated that the diagonal blocks of vanish. The same is true for Raman intensities We reformulate the previous expression as 23

24 Raman intensities We reformulate the previous expression as Virt-occ block of appears only in that is inside What must be computed: 1) One CPHF calculation 2) One CPHF2 calculation (only for Raman) 3) Integral gradients at the equilibrium geometry. IR and Raman tensors are built assembling all these ingredients and then contracted with eigenmodes. 24

25 IR 25

26 IR Raman 26

27 Raman Effect of computational parameters: shrinking factor 27

28 Effect of computational parameters: shrinking factor Not an important parameter. Usual values are fine. Effect of computational parameters: TOLINTEG 28

29 Effect of computational parameters: TOLINTEG Some dependence upon TOLINTEG. Usual values are fine for comparison with experiments 3. Cheese - from theory to experiment 29

30 Raman intensities - single crystal Raman intensities - powder Tensor invariants are obtained averaging the Raman directional intensities 30

31 4. Dessert - simulated spectra CRYSTAL input: very simple FREQCALC INTENS INTRAMAN INTCPHF END END END 31

32 CRYSTAL input: very simple FREQCALC INTENS INTRAMAN INTCPHF END END END CPHF input block CRYSTAL input: very simple FREQCALC INTENS INTRAMAN INTCPHF END IRSPEC END RAMSPEC END END END Optional generation of spectra profiles 32

33 Theory Vs Experiment: alpha-sio2 EXP: Handbook of Minerals Raman Spectra database of Lyon ENS Frequency cm -1 Garnets are important rock-forming silicates : Mg3Al2Si3O12 33

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42 - general considerations Some modes, though Raman active by symmetry considerations, have nearly zero intensity. Assignment of experimental peaks is widely guided by experience Experimental=Kolesov (2000) 42

43 Three other examples Jadeite NaAlSi2O6 Calcite CaCo3 UiO-66 Jadeite Experimental spectrum from rruff database 43

44 Jadeite 44

45 Calcite Calcite Thanks to C. Carteret (Nancy) 45

46 Calcite Theory Experiment Thanks to C. Carteret (Nancy) UiO-66 Metal-Organic Framework More than 90 Raman-active modes Exp. Spectrum: S. Bordiga and F. Bonino 46

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48 UiO-66 Metal-Organic Framework UiO-66 Metal-Organic Framework 48

49 5. Coffee - Conclusions Conclusions Infrared and Raman spectra can be now fully simulated with CRYSTAL A new formalism based on CPHF has been implemented Since all derivaties are performed analytically, the method is efficient and stable with respect to computational parameters Comparison with experiments is very good 49

50 Acknowledgments Development B. Kirtman M. Rérat R. Orlando R. Dovesi Testing and applications M. De La Pierre R. Demichelis S. Salustro More information L. Maschio, B. Kirtman, R. Orlando, and M. Rèrat Ab initio analytical infrared intensities for periodic systems through a coupled perturbed Hartree-Fock/Kohn-Sham method J. Chem. Phys. 137, (2012) L. Maschio, B. Kirtman, M. Rèrat, R. Orlando, and R. Dovesi Ab initio analytical Raman intensities for periodic systems through a coupled perturbed Hartree- Fock/Kohn-Sham method I: theory. J. Chem. Phys. 139, (2013) L. Maschio, B. Kirtman, M. Rèrat, R. Orlando, and R. Dovesi Ab initio analytical Raman intensities for periodic systems through a coupled perturbed Hartree- Fock/Kohn-Sham method II: validation and comparison with experiments. J. Chem. Phys. 139, (2013) L. Maschio, B. Kirtman, S. Salustro, C.M.Zicovich-Wilson, R. Orlando, and R. Dovesi The Raman spectrum of garnet. A quantum mechanical simulation of frequencies, intensities and isotope shifts. J. Phys. Chem. A 117 (14), (2013) 50

51 Thank you all for your attention! 51