Vibrational frequencies of water ================================ Vibrational frequency calculations should always be carried out to verify that a geometry optimisation has found a true minimum, and not just a saddle point. They are also useful in their own right to find and visualise the normal modes of vibration. Create the GAMESS input file and run GAMESS ------------------------------------------- The vibrational frequencies are only valid at an optimised geometry so we need to use the geometry obtained in the previous calculation. To open a GAMESS output file in Avogadro, we need to first rename it from :file:`.out` to :file:`.gamout`. Once this is done, use File/Open in Avogadro to open the file. Next click Extensions/GAMESS/"Input Generator" and choose "Frequencies" under Calculate. Click on :guilabel:`Generate` and save the GAMESS input file. Run GAMESS using drag-and-drop as before. Analyse the frequencies ----------------------- It is worth opening the GAMESS output file in Wordpad and taking a look at the NORMAL COORDINATE ANALYSIS section (see below). (Hint: In Wordpad, it is useful to "Select All" and change the font size to 8 pt.) Q. Is this molecule at a true geometry minimum? Q. How many frequencies are expected for a 3-atom non-linear molecule? (Hint: 3N-6) Q. How many frequencies are present in the file? How can you account for the difference? :: -------------------------------------------------------- NORMAL COORDINATE ANALYSIS IN THE HARMONIC APPROXIMATION -------------------------------------------------------- ATOMIC WEIGHTS (AMU) 1 O 15.99491 2 H 1.00782 3 H 1.00782 MODES 1 TO 6 ARE TAKEN AS ROTATIONS AND TRANSLATIONS. ANALYZING SYMMETRY OF NORMAL MODES... FREQUENCIES IN CM**-1, IR INTENSITIES IN DEBYE**2/AMU-ANGSTROM**2, REDUCED MASSES IN AMU. 1 2 3 4 5 FREQUENCY: 1.33 0.16 0.00 0.33 6.17 SYMMETRY: A A A A A REDUCED MASS: 1.01401 6.22305 6.00353 12.81051 1.03666 IR INTENSITY: 8.39984 0.00224 0.00000 0.52570 3.14657 1 O X -0.00000000 -0.04742972 0.23101688 -0.00000000 0.03749320 Y -0.00000000 0.23166471 0.04641338 -0.00000000 -0.02121402 Z -0.02017373 0.00000000 0.00000000 0.24794115 -0.00000000 2 H X -0.00000000 -0.04712588 0.23101681 -0.00000000 0.02610283 Y 0.00000000 0.21251345 0.04641346 -0.00000000 0.69693540 Z 0.87470814 0.00000000 0.00000000 0.02267176 -0.00000000 3 H X -0.00000000 -0.02927595 0.23101629 -0.00000000 -0.64326004 Y -0.00000000 0.23777094 0.04641325 -0.00000000 -0.25019888 Z 0.46974713 0.00000000 0.00000000 0.12677581 -0.00000000 TRANS. SAYVETZ X -0.00000000 -0.83563375 4.16074267 -0.00000000 -0.02228604 Y -0.00000000 4.15926402 0.83593088 -0.00000000 0.11091595 Z 1.03229856 0.00000000 0.00000000 4.11641335 -0.00000000 TOTAL 1.03229856 4.24237681 4.24388501 4.11641335 0.11313273 ROT. SAYVETZ X 0.74353714 -0.00000000 -0.00000000 -0.18361186 -0.00000000 Y -1.26256812 0.00000000 0.00000000 0.31924861 0.00000000 Z 0.00000000 -0.06777613 0.00000119 0.00000000 2.54154460 TOTAL 1.46523914 0.06777613 0.00000119 0.36828385 2.54154460 6 7 8 9 FREQUENCY: 8.88 1799.28 3812.34 3945.80 SYMMETRY: A A A A REDUCED MASS: 1.01756 1.08983 1.03858 1.08500 IR INTENSITY: 0.86226 1.89217 0.00115 0.21702 1 O X 0.00000000 -0.04089486 -0.02564877 -0.05626299 Y -0.00000000 -0.05786491 -0.03630837 0.03975514 Z -0.02526058 0.00000000 -0.00000000 -0.00000000 2 H X 0.00000000 0.01882370 0.69075509 0.67710255 Y 0.00000000 0.67521698 -0.05628041 0.01073177 Z -0.47603300 0.00000000 -0.00000000 0.00000000 3 H X -0.00000000 0.63020849 -0.28369066 0.21583219 Y -0.00000000 0.24314193 0.63252054 -0.64167502 Z 0.86919577 -0.00000000 -0.00000000 0.00000000 TRANS. SAYVETZ X -0.00000000 0.00000129 -0.00000014 0.00000052 Y 0.00000000 0.00000111 0.00000004 -0.00000057 Z -0.00780139 0.00000000 -0.00000000 0.00000000 TOTAL 0.00780139 0.00000170 0.00000015 0.00000077 ROT. SAYVETZ X 1.50357589 -0.00000000 0.00000000 0.00000000 Y 1.38590886 -0.00000000 0.00000000 -0.00000000 Z 0.00000000 -0.00001496 -0.00000000 0.00000153 TOTAL 2.04486768 0.00001496 0.00000000 0.00000153 REFERENCE ON SAYVETZ CONDITIONS - A. SAYVETZ, J.CHEM.PHYS., 7, 383-389(1939). NOTE - THE MODES J,K ARE ORTHONORMALIZED ACCORDING TO SUM ON I M(I) * (X(I,J)*X(I,K) + Y(I,J)*Y(I,K) + Z(I,J)*Z(I,K)) = DELTA(J,K) ------------------------------- THERMOCHEMISTRY AT T= 298.15 K ------------------------------- USING IDEAL GAS, RIGID ROTOR, HARMONIC NORMAL MODE APPROXIMATIONS. P= 1.01325E+05 PASCAL. ALL FREQUENCIES ARE SCALED BY 1.00000 THE MOMENTS OF INERTIA ARE (IN AMU*BOHR**2) 2.07948 4.38456 6.46404 THE ROTATIONAL SYMMETRY NUMBER IS 1.0 THE ROTATIONAL CONSTANTS ARE (IN GHZ) 867.08597 411.23564 278.94127 THE HARMONIC ZERO POINT ENERGY IS (SCALED BY 1.000) 0.021773 HARTREE/MOLECULE 4778.712676 CM**-1/MOLECULE 13.663039 KCAL/MOL 57.166155 KJ/MOL Q LN Q ELEC. 1.00000E+00 0.000000 TRANS. 3.00431E+06 14.915558 ROT. 8.69029E+01 4.464791 VIB. 1.00017E+00 0.000170 TOT. 2.61127E+08 19.380518 E H G CV CP S KJ/MOL KJ/MOL KJ/MOL J/MOL-K J/MOL-K J/MOL-K ELEC. 0.000 0.000 0.000 0.000 0.000 0.000 TRANS. 3.718 6.197 -36.975 12.472 20.786 144.800 ROT. 3.718 3.718 -11.068 12.472 12.472 49.594 VIB. 57.170 57.170 57.166 0.106 0.106 0.014 TOTAL 64.607 67.086 9.123 25.050 33.364 194.407 VIB. THERMAL CORRECTION E(T)-E(0) = H(T)-H(0) = 3.649 J/MOL E H G CV CP S KCAL/MOL KCAL/MOL KCAL/MOL CAL/MOL-K CAL/MOL-K CAL/MOL-K ELEC. 0.000 0.000 0.000 0.000 0.000 0.000 TRANS. 0.889 1.481 -8.837 2.981 4.968 34.608 ROT. 0.889 0.889 -2.645 2.981 2.981 11.853 VIB. 13.664 13.664 13.663 0.025 0.025 0.003 TOTAL 15.441 16.034 2.180 5.987 7.974 46.464 VIB. THERMAL CORRECTION E(T)-E(0) = H(T)-H(0) = 0.872 CAL/MOL ......END OF NORMAL COORDINATE ANALYSIS...... Visualise the normal modes -------------------------- Open the output file in wxMacMolPlt. List the normal modes with Subwindow/Frequencies. If you click on any mode, the main window will update to show you the displacement vectors associated with it. You can animate the vibration with View/Animate Mode.