Introduction to Computational Quantum Chemistry Lesson 6: Frequency calculations and IR spectra Martin Novák (NCBR) Frequency calculations 21. října 2014 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" a2f ... d\f i dxi&X2 dx\dxn &± ... 92f dx\ dx2dx„ a2f ... §tf 8xndx2 dx\ _ • If optimizer finds saddle point move atoms "in vibration's direction" d2f dx'j ď2/ dxidx2 a2.f ßxndxi Martin Novák (NCBR) 4D^ 4J» J ^)C\CV Frequency calculations 21. října 2014 2 / 24 IR spectroscopy • Uses infrared electromagnetic radiation • Excites vibrational states • Molecular dipole must change during excitation • Energy reported in cmr1 (wavenumbers) • Typical range of experiment is 400-4000 cm 1 □ ^ UV light from the Sur Martin Novák (NCBR) 4D^ 4J» S ^)C\CV Frequency calculations 21. října 2014 3 / 24 Wavenumber • Wavenuber states how many waves (amplitudes) of the radiation is in one centimeter • Therefore higher wavenumber equals to higher energy radiation ^ , he E = hv=— (1) A he Martin Novák (NCBR) 4D^ 4J» S ^)C\CV Frequency calculations 21. října 2014 4 / 24 Normal modes of vibrations • Two types of molecular vibrations: • Stretching • Bending • Molecule of TV-atoms has • 3N — 6 degrees of freedom (non-linear) • 3N - 5 degrees of freedom (linear) • Water: Y V V symmetrical stretching asvmmetiic.il slieltlnlit co2 iisymniird'k'iil slirkhi us Martin Novák (NCBR) cissoring (bending in and oui l>I" the pkine •>( the paper) svmillrUkal Sil fli.lii [l.y Frequency calculations e ihciklum in llie pi,uie -.if the |',i|'er) 21. října 2014 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=0 Stretch 1670-1820 Strong C=C (alkene) Stretch 1620-1680 Variable C=C (aromatic) Stretch 1400-1600 Medium-Weak Martin Novák (NCBR) 4D^ 4J» J ^)C\CV Frequency calculations 21. října 2014 6 / 24 Stretching vibrations • Simplest approximation: Atoms connected with springs • Hook's law: Frequency of vibration is given by mass and force constant * = ^-<ß (4) 2tvc V m E = hx2 (5) • Energy is quantized E = (n + l/2)hv (6) Martin Novák (NCBR) Frequency calculations 21. října 2014 7 / 24 Selection rules • Photon has energy hv • Transitions to next energy levels • Overtones: Transitions to further levels (less intensive) • Combination bands: 2 or more simultaneous excitations AE = hu ZPV Martin Novák (NCBR) 4D^ 4J» J ^)C\CV Frequency calculations 21. října 2014 8 / 24 Beyond harmonic oscilátor • Bonded atoms behave as anharmonic oscilators • This causes the higher energy levels to be closer • For diatomic oscilátor: ~ _ _j_ / f{mi + m2) 2-kc V 17111712 • where • f is the force constant of the bond Martin Novák (NCBR) 4D^ 4J» J ^)C\CV Frequency calculations 21. října 2014 9 / 24 Task: • Calculate the absorption energy (in wavenumbers) for following groups: • C-H, C=0 and C=N • Use these force constants: • Single bond: / = 5 • 105dyn ■ cmr1 • Double bond: / = 10 • 105dyn ■ cmr1 • Triple bond: / = 15 • 105dyn ■ cm~x • ldyn = lg ■ cm ■ s~2 • Compare them to typical experimental values: • C-H: 2850-3000 • C=0: 1670-1820 • C=N: 2000-2300 Martin Novák (NCBR) 4D^ 4J» S ^)C\CV Frequency calculations 21. října 2014 10 / 24 Harmonic vs. Anharmonic oscilátor Harmonic: C • V(r) = k(r — r0)2 Anharmonic: Morse potential: • V(r) = De(l - e-• WARNING • Extra atomic basis set ->• ERROR Martin Novák (NCBR) 4D^ 4J» J ^)C\CV Frequency calculations 21. října 2014 13 / 24 Serial Gaussian jobs • Use this syntax: job1 blank line - -linkl- -job2 blank line 9 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) 4D^ 4J» J ^)C\CV Frequency calculations 21. října 2014 14 / 24 Gaussian resources • %chk=checkpoint.chk • %nprocshared=ncpu • %mem=memory • How to find out available resources: • System monitor • cat/proc/cpuinfo # Prints all available cores • top# Available memory Martin Novák (NCBR) 4D^ 4J» J ^)C\CV Frequency calculations 21. října 2014 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 79Br and CH3 81Br results • awk-fscript.awkresult.dat Martin Novák (NCBR) Frequency calculations 21. října 2014 16 / 24 Experimental spectra of CH3F ro ro tu CC 0.8 - 0.6 - ~ 0.4 - 0.2 - CH3F INFRARED SPECTRUM 1000 3000 2000 Wavenumber (cm-1) NIST Chemistry WebBook (http://webbook.nist.gov/chemistry) Martin Novák (NCBR) Frequency calculations 21. října 2014 "O ^ C* 17/24 Experimental spectra of CH3Br res ro CD > tu cc CH3Br INFRARED SPECTRUM NIST 3000 2000 1000 Wavenumber (cm-1) Chemistry WebBook (http://webbook.nist.gov/chemistry) Martin Novák (NCBR) Frequency calculations 21. října 2014 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 • Rl and MARIJ approximations of Coulombic terms in DFT insanely fast code (not for hybrids) Martin Novák (NCBR) 4D^ 4|f^ 4J» J ^)C\CV Frequency calculations 21. října 2014 19 / 24 Workflow • Build a molecule and save it in xyz format • x2t molecule.xyz > coord • define • Interactive program • Prepares the confro/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) 4D^ 4|f^ 4J» J ^)C\CV Frequency calculations 21. října 2014 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 Huckel Theory • Accept all defaults Martin Novák (NCBR) 4D^ 4|f^ 4J» J ^)C\CV Frequency calculations 21. října 2014 21 /24 define - cont. • Method • dft Enter the DFT submenu • on Use DFT • tunc b-lyp Select the functional • grid m5 Increase the gridsize to m5 • * Exit the submenu • ri Enter the Rl submenu • m Assign memory for Rl • 2000 As much as possible • on Use Rl • * Exit the submenu • dsp Use dispersion correction • on Use Grimme D3 correction • * Exit the submenu • marij Multipole-Accelerated Rl-J • * End the define session Martin Novák (NCBR) 4D^ 4|f^ 4J» J ^)C\CV Frequency calculations 21. října 2014 22/24 Turbomole job • For running TM in parallel mode use the parallel build • module add turbomole:6.05:x86_64:para • Infinity selects it by default if ncpu > 1 mnovak@wolf #!/bin/bash module add turbomole:6.05 jobex -ri -c 1024 > dft.out aoforce > freq.out Martin Novák (NCBR) 4D^ 4J» J ^)C\CV Frequency calculations 21. října 2014 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 21. října 2014 24/24