1 Calculating Spectroscopic Properties With DFT Using
2 A (very) Brief Introduction to DFTFoundation of DFT: Ψ0(r1,r2,r3…rn) = ρ(r) Ψ0(r1,r2,r3…rn) ρ(r) Easier to Calculate Not obvious how to turn density to energy of system E = E[ρ] Expensive to Calculate Simple to relate to Energy of the system HΨ0 = EΨ0 Functional = function which takes a function as input Problem: converting a given density into the energy of the system
3 A (very) Brief Introduction to DFTE[ρ] = kinetic energy + electron-electron interaction + external potential E[ρ] = T[ρ]+ Vee[ρ] + Vext[ρ] kinetic energy: Hard to calculate for n electrons interacting Kohn-Sham: Use fictitious non-interacting electrons T[ρ] = Tks[ρ] + Tc[ρ] Tks is Kohn-Sham K.E. Tc is what is missing compared to ‘real system’ external potential : Vext[ρ] = 𝑉 𝑟 ρ 𝑟 𝑑 𝑟 3 electron-electron interaction: Coulomb + exchange interaction Vee[ρ] = J[ρ] + Vx [ρ] J[ρ] is the Coulomb interaction Vx [ρ] is other interactions not included in Coulomb
4 A (very) Brief Introduction to DFTE[ρ] = kinetic energy + electron-electron interaction + external potential E[ρ] = T[ρ]+ Vee[ρ] + Vext[ρ] kinetic energy: Hard to calculate for n electrons interacting Kohn-Sham: Use fictitious non-interacting electrons T[ρ] = Tks[ρ] + Tc[ρ] Unknown Tks is Kohn-Sham K.E. Tc is what is missing compared to ‘real system’ external potential : Vext[ρ] = 𝑉 𝑟 ρ 𝑟 𝑑 𝑟 3 electron-electron interaction: Coulomb + exchange interaction Vee[ρ] = J[ρ] + Vx [ρ] Unknown J[ρ] is the Coulomb interaction Vx [ρ] is other interactions not included in Coulomb
5 A (very) Brief Introduction to DFTGroup unknown quantities into: Exc[ρ] = Tc[ρ] + Vx [ρ] This is the Exchange-Correlation Functional The exact form is not known So we go to the Functional Zoo! And pick what works the best Note: Several different classes of functionals exist
6 A (very) Brief Introduction to DFTWhen doing a DFT calculation you must: 1.) Pick your functional 2.) Pick your basis set If you are not sure look through the literature and see what has been used on similar systems to what you are studying Common functionals in our field: B3LYP, PBE, BP86 Common basis sets in our field: Pople (6-311g), Ahlrichs (def2-tzvp), LANL2dz Effective core potential All Electron
7 Single Point CalculationInput File Anatomy: Single Point Calculation comment line Basis Set Convergence Criteria # An Example Input ! UKS B3LYP def2-TZVP TightSCF * xyz 0 5 Fe 0 0 0 * keyword line Open shell calculation DFT functional Multiplicity Tells Orca to expect Cartesian coordinates Charge Coordinate Block Output orbitals are stored in .gbw file
8 Single Point CalculationInput File Anatomy: Single Point Calculation Run Orca in Parallel # An Example Input ! UKS B3LYP def2-TZVP TightSCF PAL4 %scf MaxIter 1500 End * xyz 0 5 Fe 0 0 0 * Options Block
9 Geometry OptimizationInput File Anatomy: Geometry Optimization ! B3LYP def2-TZVP TightSCF Opt * xyz 0 5 -Coordinates- * Tells Orca to perform a geometry optimization *Possible with appropriate keywords to add dispersion correction (needed for non covalent interactions), relativistic effects, or constrain some metric of the geometry (i.e. a bond length)
10 Geometry OptimizationInput File Anatomy: Geometry Optimization ! B3LYP def2-TZVP TightSCF Opt * xyz 0 5 -Coordinates- * Tells Orca to perform a geometry optimization How do you know you have converged to a ground state geometry? 1.) Run TDDFT calculation and make sure all transition energies are positive 2.) Calculate vibrational modes and make sure there are no imaginaries
11 Speeding Up A CalculationInput File Anatomy: Speeding Up A Calculation Use the Resolution of the Identity approximation (RI) aka density fitting ‡ ! BP86 RI def2-TZVP def2-TZVP/J TightSCF Opt * xyz 0 5 -Coordinates- * Tells Orca to use RI Auxiliary Basis Set Required for RI /J = approximates Coulomb integrals ‡ Note the change in functional: RI only valid for functionals with no HF exchange!
12 Speeding Up A CalculationInput File Anatomy: Speeding Up A Calculation Use the Resolution of the Identity approximation (RI) aka density fitting ! B3LYP RIJCOSX def2-TZVP def2-TZVP/J TightSCF Opt * xyz 0 5 -Coordinates- * Tells Orca to use RI for the Coulomb part (J) and Chain of Spheres (COS) for exchange (X) This may seem tedious and there are a lot of options but the speed up is worth it and only costs small errors in the final answer
13 Speeding Up A CalculationInput File Anatomy: Speeding Up A Calculation Use smaller basis set on some atoms ! BP86 RI def2-TZVP def2-TZVP/J TightSCF Opt %basis newgto h "def2-SVP" end newauxgto h "def2-SVP/J" end end * xyz 0 5 -Coordinates- * You can specify both a new basis and auxiliary basis function for an atom
14 Mossbauer Parameters ! UKS B3LYP def2-TZVP TightSCF Grid5 NoFinalGrid SlowConv %method SpecialGridAtoms 26 SpecialGridIntAcc 7 end %basis NewGTO 26 "CP(PPP)" end NewGTO 1 "def2-SV(P)" end NewGTO 6 "def2-SV(P)" end *xyz 0 5 -Coordinates- * %eprnmr nuclei = all Fe {rho, fgrad} Tells Orca you expect a slow scf convergence Tells Orca to be accurate with Fe integrals Adjusts integration accuracy. recommended in the manual Calculates electron density at Fe Calculates electric field gradient
15 Mossbauer Parameters Quadrupole SplittingEFG Components and orientation ΔEq
16 Mossbauer Parameters Isomer ShiftIsomer shift can not be calculated directly: It is a relative quantity Use calibration curves from Neese’s group to turn density into isomer shift Romelt, M.; Ye, S.; Neese, F. Inorg Chem 2009, 48 Electron Density at Nucleus
17 g-Tensor ! UKS B3LYP def2-TZVP TightSCF SOMF(1X) *xyz 0 5-Coordinates- * %eprnmr gtensor true end Tells Orca to consider SOC
18 Absorption Spectroscopy/TDDFT! B3LYP RIJCOSX def2-TZVP def2-TZVP/J Grid5 FinalGrid6 TightSCF %tddft nroots 10 maxdim 70 DoNTO true End *xyz 0 5 -Coordinates- * Number of transitions to calculate 5-10 times the number of roots Tells Orca to calculate Natural Transition Orbitals This is optional but can be helpful
19 Absorption Spectroscopy/TDDFT TD-DFT/TDA EXCITED STATES STATE 3: E= au eV cm**-1 108b -> 118b : (c= ) 108b -> 119b : (c= ) 112b -> 118b : (c= ) 112b -> 119b : (c= ) 112b -> 121b : (c= ) 112b -> 124b : (c= ) 112b -> 134b : (c= ) STATE 9: E= au eV cm** b -> 113b : (c= ) Output orbitals are stored in .gbw file NTO stored in .nto file
20 Absorption Spectroscopy/TDDFTCalculated spectrum was created using orca_mapspc
21 Absorption Spectroscopy/TDDFTNTO visualization
22 Absorption Spectroscopy/TDDFTNTO visualization
23 Broken Symmetry DFT ! UKS TPSS RI SVP SVP/J! Grid4 NoFinalGrid TightSCF %scf FlipSpin 1 FinalMs 0 end *xyz 4 7 O Mn O Mn … * Tells Orca to flip spin on nucleus 1 Counting starts at 0 MnIV - - MnIV Final total spin
24 Broken Symmetry DFT ------------------------------------------BROKEN SYMMETRY MAGNETIC COUPLING ANALYSIS S(High-Spin) = 3.0
25 Broken Symmetry DFT --------------------------UHF CORRESPONDING ORBITALS Transforming orbitals done Choosing virtual orbitals in the orth. comp done Orbital Overlap(*) 0: 1: 2: 3: ………………. 65: 66: 67: 68: 69: 70: Looking for overlap much less than unity These are the magnetic orbitals
26 π Super Exchange PathwayBroken Symmetry DFT Magnetic Orbitals α Magnetic Orbitals β Magnetic Orbitals π Super Exchange Pathway
27 The Orca Input Library