simulation of ir and raman spectra of crystals
TRANSCRIPT
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Lorenzo Maschio,1 Bernard Kirtman,2 Michel Rérat,3 Simone Salustro,1
Marco De La Pierre,1 Roberto Orlando,1 Roberto Dovesi1
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
Simulation of infrared and Raman
spectra
Today’s menu
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Appetizer
Today’s menu
Appetizer
Main course - Theory
Today’s menu
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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
Today’s menu
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Appetizer
Main course - Theory
Cheese - From theory to experiment
Dessert - Some simulated spectra
Today’s menu
Coffee
1. The Appetizer
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Mg3Al2Si3O12
Cubic,
80 atoms in the
unit cell
Pyrope
Raman
spectrum,
a long story
Hofmeister et al. 1991
Pyrope
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Hofmeister et al. 1991
All 25 Raman active
modes were assigned
Pyrope
Simulation
Experiment
Pyrope
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Chaplin et al. 1998
Method:
Classical dynamics
Pyrope
Simulation
Experiment
Pyrope
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Pyrope
Kolesov and Geiger 2000
Pyrope
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Simulation
Experiment
Pyrope
Pyrope
To be continued...
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2. Main Course - Theory
A little bit of history
CRYSTAL95
CRYSTAL98 Energy, electronic structure
Lorenzo Maschio [email protected]
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CRYSTAL95
CRYSTAL98
CRYSTAL03
Energy, electronic structure
Geometry optimization
Lorenzo Maschio [email protected]
A little bit of history
CRYSTAL95
CRYSTAL98
CRYSTAL03
CRYSTAL06
Energy, electronic structure
Geometry optimization
Frequencies (peak positions),
infrared intensities (numerical)
Lorenzo Maschio [email protected]
A little bit of history
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CRYSTAL95
CRYSTAL98
CRYSTAL03
CRYSTAL06
Energy, electronic structure
Geometry optimization
CRYSTAL09 Polarizabilities
Lorenzo Maschio [email protected]
A little bit of history
Frequencies (peak positions),
infrared intensities (numerical)
CRYSTAL95
CRYSTAL98
CRYSTAL03
CRYSTAL06
CRYSTAL14
Energy, electronic structure
Geometry optimization
CRYSTAL09 Polarizabilities
Raman Intensities
A little bit of history
Frequencies (peak positions),
infrared intensities (numerical)
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IR and non-resonant Raman intensities
= electric field
= Atomic displacement
Lorenzo Maschio [email protected]
Born Charges (IR intensities): derivative of the dipole moment
IR and non-resonant Raman intensities
= electric field
= Atomic displacement
Lorenzo Maschio [email protected]
In CRYSTAL06 through Wannier functions:
numerical derivatives in direct space
Born Charges (IR intensities): derivative of the dipole moment
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In CRYSTAL09 through Berry Phase:
numerical derivatives in reciprocal space
IR and non-resonant Raman intensities
Born Charges (IR intensities): derivative of the dipole moment
= electric field
= Atomic displacement
Lorenzo Maschio [email protected]
In CRYSTAL06 through Wannier functions:
numerical derivatives in direct space
IR and non-resonant Raman intensities
= electric field
= Atomic displacement
Lorenzo Maschio [email protected]
We want analytical derivatives
Born Charges (IR intensities): derivative of the dipole moment
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Within Placzeck approximation, Raman tensor elements are defined as:
= electric field
= Atomic displacement
Lorenzo Maschio [email protected]
IR and non-resonant Raman intensities
Born Charges (IR intensities): derivative of the dipole moment
= electric field
= Atomic displacement
We want analytical derivatives
Lorenzo Maschio [email protected]
IR and non-resonant Raman intensities
Within Placzeck approximation, Raman tensor elements are defined as:
Born Charges (IR intensities): derivative of the dipole moment
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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
Lorenzo Maschio [email protected]
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.
Lorenzo Maschio [email protected]
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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!
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We want analytical derivatives
The Omega operator
Lorenzo Maschio [email protected]
At zero field:
is the matrix representation of the field operator in AO basis
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The Omega operator
Lorenzo Maschio [email protected]
At zero field:
Imaginary diagonal elements undefined: must be avoided!
is the matrix representation of the field operator in AO basis
Mixed derivatives of total energy
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If we differentiate this w.r.t. atomic displacements we get
Mixed derivatives of total energy
Lorenzo Maschio [email protected]
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.
Mixed derivatives of total energy
Lorenzo Maschio [email protected]
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Much better to start from here
Because
Where we introduce the eigenvalue-weighted density matrix
Mixed derivatives of total energy
since
: occupation matrix
Mixed derivatives of total energy
Also note that the density matrix inside the Fock operator is not
differentiated with respect to displacements
Only gradients of the integrals are needed
Much better to start from here!
Lorenzo Maschio [email protected]
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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
Lorenzo Maschio [email protected]
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
The diagonal elements of are undefined, but it appears in two
places with opposite sign. Diagonal blocks cancel out!
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Things get more complicated
Again, it can be demonstrated that the diagonal blocks of
vanish. The same is true for
Let us differentiate once more w.r.t. field
Lorenzo Maschio [email protected]
Raman intensities
Lorenzo Maschio [email protected]
We reformulate the previous expression as
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Raman intensities
that is inside
Virt-occ block of appears only in
Lorenzo Maschio [email protected]
We reformulate the previous expression as
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.
What must be computed:
Lorenzo Maschio [email protected]
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IR
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IR
Raman
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Raman
Effect of computational parameters: shrinking factor
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Effect of computational parameters: shrinking factor
Lorenzo Maschio [email protected]
Not an important parameter. Usual values are fine.
Effect of computational parameters: TOLINTEG
Lorenzo Maschio [email protected]
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Effect of computational parameters: TOLINTEG
Lorenzo Maschio [email protected]
Some dependence upon TOLINTEG. Usual values are fine for
comparison with experiments
3. Cheese - from theory to experiment
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Raman intensities - single crystal
Lorenzo Maschio [email protected]
Raman intensities - powder
Lorenzo Maschio [email protected]
Tensor invariants are obtained averaging the Raman
directional intensities
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4. Dessert - simulated spectra
FREQCALC
INTENS
INTRAMAN
INTCPHF
END
END
END
CRYSTAL input: very simple
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FREQCALC
INTENS
INTRAMAN
INTCPHF
END
END
END
CRYSTAL input: very simple
CPHF input block
FREQCALC
INTENS
INTRAMAN
INTCPHF
END
IRSPEC
END
RAMSPEC
END
END
END
CRYSTAL input: very simple
Optional generation of spectra profiles
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Theory Vs Experiment: alpha-SiO2
EXP: Handbook of Minerals Raman Spectra database of Lyon ENS
Frequency cm-1
Lorenzo Maschio [email protected]
Garnets are important
rock-forming silicates
Pyrope:
Mg3Al2Si3O12
Pyrope
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Pyrope
Pyrope
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Pyrope
Pyrope
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Pyrope
Pyrope
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Pyrope
Pyrope
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Pyrope
Pyrope
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Pyrope
Pyrope
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Pyrope
Pyrope
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Pyrope
Pyrope
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Some modes, though Raman active by symmetry
considerations, have nearly zero intensity.
Assignment of experimental peaks is widely
guided by experience
Pyrope - general considerations
Lorenzo Maschio [email protected]
Experimental=Kolesov (2000)
Pyrope
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Three other examples
Jadeite NaAlSi2O6
Calcite CaCo3
UiO-66
Jadeite
Experimental spectrum from rruff database
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Jadeite
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Calcite
Thanks to C. Carteret (Nancy)
Calcite
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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
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UiO-66 Metal-Organic Framework
UiO-66 Metal-Organic Framework
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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
Lorenzo Maschio [email protected]
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Acknowledgments
B. Kirtman
M. Rérat
R. Orlando
R. Dovesi
M. De La Pierre
R. Demichelis
S. Salustro
Development
Testing and applications
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, 204113 (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, 164101 (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, 164102 (2013)
L. Maschio, B. Kirtman, S. Salustro, C.M.Zicovich-Wilson, R. Orlando, and R.
Dovesi“ The Raman spectrum of Pyrope garnet. A quantum mechanical simulation of
frequencies, intensities and isotope shifts.“
J. Phys. Chem. A 117 (14), 11464-11471 (2013)
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Thank you all for your attention!