Introduction to Computational Quantum Chemistry Lesson 6: Frequency calculations and IR spectra Martin Novák (NCBR) Frequency calculations October 3, 2017 1 / 24 Frequency calculations Hessian matrix eigenvalues Second derivatives with respect to molecular geometry All positive values (curvature) - local minimum Imaginary (negative) values - “nth order saddle point” H(f) =        ∂2f ∂x2 1 ∂2f ∂x1∂x2 · · · ∂2f ∂x1∂xn ∂2f ∂x1∂x2 ∂2f ∂x2 2 · · · ∂2f ∂x2∂xn ... ... ... ... ∂2f ∂xn∂x1 ∂2f ∂xn∂x2 · · · ∂2f ∂x2 n        If optimizer finds saddle point instead of a minimum, move atoms “in vibration’s direction” Martin Novák (NCBR) Frequency calculations October 3, 2017 2 / 24 IR spectroscopy Uses infrared electromagnetic radiation Excites vibrational states Molecular dipole must change during excitation Energy reported in cm−1 (wavenumbers) Typical range of experiment is 400-4000 cm−1 Martin Novák (NCBR) Frequency calculations October 3, 2017 3 / 24 Wavenumber Wavenuber states how many waves (amplitudes) of the radiation is in one centimeter Therefore higher wavenumber equals to higher energy radiation E = hν = hc λ (1) ˜ν = 1 λ (2) ˜ν = E hc (3) Martin Novák (NCBR) Frequency calculations October 3, 2017 4 / 24 Normal modes of vibrations Two types of molecular vibrations: Stretching Bending Molecule of N-atoms has 3N − 6 degrees of freedom (non-linear) 3N − 5 degrees of freedom (linear) Water: CO2 Martin Novák (NCBR) Frequency calculations October 3, 2017 5 / 24 Characteristic frequencies Bending is less demanding than stretching Group Type Value Intensity -O-H (HB) Stretch 3200-3600 Strong, broad -O-H (Free) Stretch 3500-3700 Strong, sharp -C-H Stretch 2850-3000 Strong -C-H Bend 1350-1480 Variable =C-H Stretch 3010-3100 Medium =C-H Bend 675-1000 Strong C=O Stretch 1670-1820 Strong C=C (alkene) Stretch 1620-1680 Variable C=C (aromatic) Stretch 1400-1600 Medium-Weak Martin Novák (NCBR) Frequency calculations October 3, 2017 6 / 24 Stretching vibrations Simplest approximation: Atoms connected with springs Hook’s law: Frequency of vibration is given by mass and force constant ˜ν = 1 2πc k m (4) E = 1 2 kx2 (5) Energy is quantized E = (n + 1/2)hν (6) Martin Novák (NCBR) Frequency calculations October 3, 2017 7 / 24 Selection rules Photon has energy hν Transitions to next energy levels Overtones: Transitions to further levels (less intensive) Combination bands: 2 or more simultaneous excitations ΔΕ = hν ZPV Martin Novák (NCBR) Frequency calculations October 3, 2017 8 / 24 Beyond harmonic oscilator Bonded atoms behave as anharmonic oscilators This causes the higher energy levels to be closer For diatomic oscilator: ˜ν = 1 2πc f(m1 + m2) m1m2 (7) where f is the force constant of the bond Martin Novák (NCBR) Frequency calculations October 3, 2017 9 / 24 Task: Calculate the absorption energy (in wavenumbers) for following groups: C-H, C=O and C≡N Use these force constants: Single bond: f = 5 · 105 dyn · cm−1 Double bond: f = 10 · 105 dyn · cm−1 Triple bond: f = 15 · 105 dyn · cm−1 1dyn = 1g · cm · s−2 Compare them to typical experimental values: C-H: 2850-3000 C=O: 1670-1820 C≡N: 2000-2300 Martin Novák (NCBR) Frequency calculations October 3, 2017 10 / 24 Harmonic vs. Anharmonic oscilator Harmonic: Quadratic potential: V (r) = k(r − r0)2 Anharmonic: Morse potential: V (r) = De(1 − e−a(r−r0) )2 Scaling factors for various levels of theory available in literature Merrick, J.P. et al. J. Phys. Chem. A 2007, 111, 11683. De Martin Novák (NCBR) Frequency calculations October 3, 2017 11 / 24 Tasks: Perform following calculations: Use Gaussian for optimization of CH3F, CH3 79 Br and, CH3 81 Br Harmonic and anharmonic frequency calculations Use Def2-SVPD basis set Run the calculations in serial Run everything using batch system Martin Novák (NCBR) Frequency calculations October 3, 2017 12 / 24 Custom basis sets Keyword gen instead of basis set specification EMSL Basis Set Exchange: https://bse.pnl.gov/bse/portal Select desired atoms and basis set Specify “Gaussian94” format Put the basis set after molecular specification BE AWARE Missing atomic basis set → WARNING Extra atomic basis set → ERROR Martin Novák (NCBR) Frequency calculations October 3, 2017 13 / 24 Serial Gaussian jobs Use this syntax: job1 blank line - -link1- - job2 blank line Logfiles are appended into 1 huge file Everything goes well: Normal termination of Gaussian 09 at Tue Jul 1 04:34:16 2014. Martin Novák (NCBR) Frequency calculations October 3, 2017 14 / 24 Gaussian resources %chk=checkpoint.chk %nprocshared=ncpu %mem=memory How to find out available resources: pnodes Martin Novák (NCBR) Frequency calculations October 3, 2017 15 / 24 Gaussian resources Martin Novák (NCBR) Frequency calculations October 3, 2017 15 / 24 Evaluation of results Thermodynamic corrections to electronic energy Frequencies can be visualized from logfile in GaussView Anharmonic vibrations are generally closer to experiment but require much more resources Calculate the RMSD of vibrations using the prepared scripts Structure of result.dat: Sort the frequencies from lowest to highest wavenumber One number per line Group the degenerate modes together (calculate average) Average the CH3 79 Br and CH3 81 Br results awk -f script.awk result.dat Martin Novák (NCBR) Frequency calculations October 3, 2017 16 / 24 Experimental spectra of CH3F Martin Novák (NCBR) Frequency calculations October 3, 2017 17 / 24 Experimental spectra of CH3Br Martin Novák (NCBR) Frequency calculations October 3, 2017 18 / 24 Turbomole Developed at University of Karlsruhe and Forschungszentrum Karlsruhe GmbH More UNIX-like approach to solve problems: Several independent modules x2t and t2x define dscf jobex aoforce RI and MARIJ approximations of Coulombic terms in DFT → insanely fast code (not for hybrids) Martin Novák (NCBR) Frequency calculations October 3, 2017 19 / 24 Workflow Build a molecule and save it in xyz format x2t molecule.xyz > coord define Interactive program Prepares the control file containing all job specifications Basis sets and initial guess jobex Performs optimization of geometry aoforce Runs frequency calculations Cannot do anharmonic frequencies Martin Novák (NCBR) Frequency calculations October 3, 2017 20 / 24 define First two items can be skipped Molecular geometry: a coord Reads in the geometry ired Generates internal coordinates * Proceed to next stage Basis set: b all def2-SVP Assign this basis set to all atoms * Proceed to next stage Method eht Perform initial guess from Extended Hückel Theory Accept all defaults Martin Novák (NCBR) Frequency calculations October 3, 2017 21 / 24 define - cont. Method dft Enter the DFT submenu on Use DFT func b-lyp Select the functional grid m5 Increase the gridsize to m5 * Exit the submenu ri Enter the RI submenu m Assign memory for RI 2000 As much as possible on Use RI * Exit the submenu dsp Use dispersion correction on Use Grimme D3 correction * Exit the submenu marij Multipole-Accelerated RI-J * End the define session Martin Novák (NCBR) Frequency calculations October 3, 2017 22 / 24 Turbomole job For running TM in parallel mode use the parallel build module add turbomole:7.02:x86_64:para Infinity selects it by default if ncpu > 1 mnovak@wolf #!/usr/bin/env infinity-env module add turbomole:7.02 jobex -ri -c 1024 > dft.out aoforce > freq.out Martin Novák (NCBR) Frequency calculations October 3, 2017 23 / 24 Turbomole output File Contens dft.out Optimization procedure energy Energies of steps gradient Gradients of steps mos Molecular orbitals freq.out Output from aoforce program Martin Novák (NCBR) Frequency calculations October 3, 2017 24 / 24