# Mode tracking versus a full normal-mode calculation ## Introduction Mode tracking calculates one chosen normal mode without building the complete molecular Hessian. It starts from a physically motivated displacement and iteratively improves that vector until it is an eigenvector of the target-method Hessian. This report tests whether that focused calculation reproduces the PBE/DZ analytical normal mode for the non-ring C=O stretch of dydrogesterone, and measures the time saved against a full normal-mode calculation. Dydrogesterone was built from its stereochemical SMILES. Bond data identified atom 3 as the O double-bonded to non-ring atom 2 C. These two atoms form region `CO`. The geometry was preoptimized with GFN1-xTB and normal modes, then optimized with ADF/PBE/DZ, large frozen core, and NumericalQuality Normal. The DFT optimization used the GFN1-xTB Hessian as its initial Hessian. Every subsequent calculation used the final DFT geometry without further optimization. ## Tracked structure and displacement The translucent region marks the selected carbonyl atoms. The outer structures show equal negative and positive displacements along the converged tracked mode. ![Negative displacement, optimized geometry, and positive displacement](figures/mode_displacement_grid.png) ## Spectra ### Partial Hessian ![Partial-Hessian spectrum](figures/partial_hessian_spectrum.png) ### Mode tracking ![Mode-tracking spectrum](figures/mode_tracking_spectrum.png) ### Full normal modes ![Full normal-mode spectrum](figures/full_spectrum.png) ## Selected-mode accuracy | Calculation | Mode number | Frequency (cm^-1) | IR intensity (km/mol) | Overlap with tracked mode | |:----------------------|--------------:|--------------------:|------------------------:|----------------------------:| | Partial Hessian guess | 153 | 1556.5220 | 106.7533 | nan | | Mode tracking | 1 | 1580.7417 | 81.0010 | 1.0000 | | Full normal modes | 118 | 1578.4632 | 81.0663 | 0.9977 | The full-spectrum mode was matched by normal-mode overlap, not frequency proximity. Its absolute overlap with the tracked vector is 0.997713. Mode tracking differs from the full calculation by 2.2785 cm^-1 in frequency, or 0.144%, and 0.0653 km/mol in IR intensity, or 0.081%. ## Timings | Job | Elapsed time (s) | Elapsed time (min) | |:----------------------------------------|-------------------:|---------------------:| | DFTB preoptimization + modes | 29.610 | 0.494 | | DFT geometry optimization | 230.328 | 3.839 | | DFT partial Hessian | 123.386 | 2.056 | | DFTB Hessian guess | 26.915 | 0.449 | | DFT mode tracking | 154.543 | 2.576 | | DFT full normal modes | 1952.166 | 32.536 | | DFT partial Hessian + DFT mode tracking | 277.929 | 4.632 | | Full DFT normal modes | 1952.166 | 32.536 | The two DFT steps specific to the focused route, partial Hessian plus mode tracking, took 277.929 s. The full analytical normal-mode job took 1952.166 s, so the DFT-only focused route was 7.02x faster. Including the 26.915 s GFN1-xTB Hessian-guess job gives a focused-route time of 304.843 s and a 6.40x speedup. Geometry optimization timings are excluded from both comparisons because both vibrational routes use the same optimized geometry. ## Conclusion For this carbonyl mode, mode tracking reproduced the full-Hessian reference with a frequency error of 2.2785 cm^-1, an intensity error of 0.0653 km/mol, and a mode-vector overlap of 0.997713. The full calculation had no imaginary frequencies. The DFT partial-Hessian plus mode-tracking steps were 7.02x faster than the full analytical Hessian, or 6.40x faster after including the DFTB Hessian guess. ## Calculation provenance and inputs Jobs were loaded directly from `01-run_workdir`. ### DFTB preoptimization + modes GFN1-xTB preoptimization and initial Hessian for the DFT optimization. ```ams Properties NormalModes yes End Task GeometryOptimization System Atoms C -4.5753007624 2.4335757077 -0.3051238140 C -4.1654044269 1.4231319749 0.7300567028 region=CO O -4.4674968841 1.6330354323 1.8950202972 region=CO C -3.4249194595 0.1349544347 0.3858899036 C -3.3192691179 -0.1859566386 -1.1125546573 C -2.0693702052 -1.0486415561 -1.2804430380 C -1.3924473893 -1.1266345242 0.0973200504 C -1.9726158255 0.0491246723 0.9254402220 C -1.1997086852 1.3730512519 0.6537656577 C 0.3222386059 1.2194765553 0.7371377451 C 0.8338420837 0.1739848117 -0.2850518607 C 0.1597751178 -1.1965994917 0.0065967194 C 0.7603192912 -1.8095625610 1.2512107198 C 2.0788335458 -1.8018448697 1.4263619842 C 2.9391408645 -1.1699416326 0.4132904296 C 4.1328084585 -1.7217137353 0.1453610078 C 4.9015536137 -1.3363797622 -1.0501572441 O 6.0660755057 -1.7889615227 -1.2081132259 C 4.3173352277 -0.4223716682 -2.0919404215 C 2.8083777155 -0.1913471249 -1.8811425169 C 2.4223452480 0.0318179121 -0.3877414796 C 3.1524503365 1.2995573959 0.1344050991 C -1.9750236367 -0.2703983542 2.4407161276 H -5.2374058363 1.9570953870 -1.0578338512 H -3.6770724868 2.8518506737 -0.8043078900 H -5.1308577997 3.2722925799 0.1664734311 H -4.0167277510 -0.6968517270 0.8346116809 H -3.1923349535 0.7292849107 -1.7274037391 H -4.2265497822 -0.7238688541 -1.4649990443 H -1.4024495612 -0.5921318180 -2.0431039754 H -2.3440017427 -2.0668804766 -1.6343452623 H -1.7508120077 -2.0825689555 0.5474413253 H -1.4447604627 1.7617058398 -0.3585794330 H -1.5182697896 2.1543818490 1.3782845605 H 0.7454608423 2.2195687215 0.5081281572 H 0.6300684955 0.9484578987 1.7688376311 H 0.4645801947 0.5269992359 -1.2733759104 H 0.4129277678 -1.8847911774 -0.8310984850 H 0.1367904154 -2.3082919568 1.9827164786 H 2.5127169465 -2.3283090113 2.2680463583 H 4.4996337377 -2.5454953282 0.7474026720 H 4.8575609769 0.5477101379 -2.0691281882 H 4.4765118113 -0.8661087541 -3.0983229054 H 2.4950166965 0.6819829426 -2.4946876398 H 2.2624511353 -1.0792067427 -2.2710233174 H 2.8637673384 2.1918824411 -0.4610878495 H 4.2554742135 1.1973245897 0.0771896657 H 2.9244125570 1.4787509336 1.2061068447 H -2.4612486216 0.5441744889 3.0152424596 H -2.5221771041 -1.2147790409 2.6483217466 H -0.9462444517 -0.3755354951 2.8356480095 End BondOrders 1 2 1.0 1 24 1.0 1 25 1.0 1 26 1.0 2 3 2.0 2 4 1.0 4 5 1.0 4 8 1.0 4 27 1.0 5 6 1.0 5 28 1.0 5 29 1.0 6 7 1.0 6 30 1.0 6 31 1.0 7 8 1.0 7 12 1.0 7 32 1.0 8 9 1.0 8 23 1.0 9 10 1.0 9 33 1.0 9 34 1.0 10 11 1.0 10 35 1.0 10 36 1.0 11 12 1.0 11 21 1.0 11 37 1.0 12 13 1.0 12 38 1.0 13 14 2.0 13 39 1.0 14 15 1.0 14 40 1.0 15 16 2.0 15 21 1.0 16 17 1.0 16 41 1.0 17 18 2.0 17 19 1.0 19 20 1.0 19 42 1.0 19 43 1.0 20 21 1.0 20 44 1.0 20 45 1.0 21 22 1.0 22 46 1.0 22 47 1.0 22 48 1.0 23 49 1.0 23 50 1.0 23 51 1.0 End End Engine dftb Model GFN1-xTB EndEngine ``` ### DFT geometry optimization Reference PBE/DZ geometry and ADF engine restart data. ```ams GeometryOptimization InitialHessian File /home/ubuntu/work/01-run_workdir/01_dftb_preopt/dftb.rkf Type FromFile End End Task GeometryOptimization System Atoms C -5.2635718170 1.9648547176 -0.0681789075 C -4.0439754295 1.5941151849 0.7474148234 region=CO O -3.7044014479 2.2519419727 1.6951402611 region=CO C -3.3276550073 0.3268153713 0.3204009087 C -3.2176707540 0.1191069084 -1.2012182637 C -1.9649380483 -0.7484007906 -1.4133915693 C -1.3598772476 -0.9954286465 -0.0172481657 C -1.8866946860 0.1564450444 0.8672525818 C -1.0606973256 1.4334805767 0.6456681895 C 0.4465457228 1.1928215636 0.7570255757 C 0.9052227532 0.1789583428 -0.3004423277 C 0.1679177058 -1.1546192613 -0.0546444997 C 0.7021027328 -1.7909186635 1.1988314342 C 2.0142638254 -1.7789107480 1.4448037025 C 2.9169483370 -1.2137119227 0.4580502991 C 4.1305496660 -1.7541732250 0.2300712944 C 4.9833084353 -1.3830305690 -0.9017572107 O 6.1403142415 -1.7251931433 -0.9880124294 C 4.3292882735 -0.5808838122 -2.0194096644 C 2.8275189545 -0.3509264722 -1.8434925795 C 2.4453239409 -0.0420232349 -0.3788278604 C 3.2179964604 1.2035303736 0.1011402690 C -1.9220890561 -0.2072323192 2.3545440406 H -5.8581849037 1.0862479633 -0.3094805194 H -4.9344443950 2.4261273143 -0.9992373211 H -5.8631904390 2.6843691301 0.4859616321 H -3.9408764161 -0.4878020034 0.7332742136 H -3.1023895554 1.0777140206 -1.7136207065 H -4.1117242860 -0.3683362491 -1.5958332577 H -1.2554719948 -0.2278168589 -2.0614413153 H -2.2172586142 -1.6972116988 -1.8925465542 H -1.7795047433 -1.9353201608 0.3681083193 H -1.2766125702 1.8434479135 -0.3467549410 H -1.3513786133 2.1849994779 1.3833973030 H 0.9390965468 2.1545269181 0.5976402313 H 0.7058392720 0.8413421469 1.7598561916 H 0.5899399635 0.5702556699 -1.2776102501 H 0.3973551446 -1.8310234528 -0.8926644337 H 0.0090433685 -2.2978772616 1.8598192177 H 2.4405847751 -2.2859335923 2.3033455736 H 4.5067019605 -2.5584127053 0.8535476837 H 4.8637191615 0.3707478453 -2.0882483703 H 4.5202697299 -1.1140452915 -2.9546068861 H 2.5116450830 0.4749029771 -2.4879265899 H 2.2851229702 -1.2477954572 -2.1614197145 H 2.9388664294 2.0772295293 -0.4876150056 H 4.2899469568 1.0437238179 -0.0023811800 H 3.0160027766 1.3992689572 1.1530539068 H -2.4244954455 0.5810312223 2.9143080284 H -2.4606059928 -1.1430678946 2.5091058616 H -0.9137263987 -0.3179095254 2.7517069196 End BondOrders 1 2 1.0 1 24 1.0 1 25 1.0 1 26 1.0 2 3 2.0 2 4 1.0 4 5 1.0 4 8 1.0 4 27 1.0 5 6 1.0 5 28 1.0 5 29 1.0 6 7 1.0 6 30 1.0 6 31 1.0 7 8 1.0 7 12 1.0 7 32 1.0 8 9 1.0 8 23 1.0 9 10 1.0 9 33 1.0 9 34 1.0 10 11 1.0 10 35 1.0 10 36 1.0 11 12 1.0 11 21 1.0 11 37 1.0 12 13 1.0 12 38 1.0 13 14 2.0 13 39 1.0 14 15 1.0 14 40 1.0 15 16 2.0 15 21 1.0 16 17 1.0 16 41 1.0 17 18 2.0 17 19 1.0 19 20 1.0 19 42 1.0 19 43 1.0 20 21 1.0 20 44 1.0 20 45 1.0 21 22 1.0 22 46 1.0 22 47 1.0 22 48 1.0 23 49 1.0 23 50 1.0 23 51 1.0 End End Engine adf Basis Core Large Type DZ End NumericalQuality Normal XC GGA PBE End EndEngine ``` ### DFT partial Hessian Two-atom CO partial Hessian used to construct the tracked-mode guess. ```ams EngineRestart /home/ubuntu/work/01-run_workdir/02_dft_opt/adf.rkf LoadEngine /home/ubuntu/work/01-run_workdir/02_dft_opt/adf.rkf Properties NormalModes yes SelectedRegionForHessian CO End Task SinglePoint System Atoms C -5.5272702836 1.7383362856 0.0582569671 C -4.1685168218 1.5794986849 0.7215959954 region=CO O -3.7738054138 2.4062279095 1.5807198590 region=CO C -3.3492755853 0.3693323239 0.3005236493 C -3.2200033078 0.2069590175 -1.2485626587 C -1.9658951634 -0.7030021370 -1.4454143318 C -1.3643012691 -0.9399535601 -0.0226345679 C -1.8953008505 0.2432122596 0.8513331893 C -1.0523937563 1.5151903380 0.5643006145 C 0.4672044135 1.2663845151 0.6986431056 C 0.9475399655 0.1968378578 -0.3093237635 C 0.1718837451 -1.1308785250 -0.0381903285 C 0.7046271611 -1.7674667959 1.2305357331 C 2.0390934856 -1.8180847112 1.4510129547 C 2.9443661126 -1.2863928887 0.4345990398 C 4.1332273770 -1.9056016869 0.1644207305 C 4.9773230598 -1.5652844813 -0.9797350199 O 6.1148350071 -2.1049902516 -1.1434458560 C 4.4356054071 -0.5733864669 -2.0045972197 C 2.9271150329 -0.2885453311 -1.8516186580 C 2.5106858508 -0.0488066215 -0.3693139467 C 3.3041110912 1.1604381115 0.2075515121 C -1.9135464039 -0.0711638036 2.3623275318 H -6.0747496156 0.7819576090 0.0347114338 H -5.4000524410 2.0793314586 -0.9840203771 H -6.1078420136 2.4919895674 0.6093185440 H -3.9100052907 -0.5149291198 0.6768433131 H -3.0659919108 1.1925320325 -1.7196342644 H -4.1280195239 -0.2358669101 -1.6887264871 H -1.2332484026 -0.2079855012 -2.1035001561 H -2.2327948171 -1.6640683575 -1.9163765522 H -1.8105076210 -1.8717559662 0.3805686025 H -1.2548909320 1.8737526759 -0.4629964858 H -1.3677999012 2.3157905998 1.2524073535 H 0.9844983116 2.2224307518 0.5154260491 H 0.7139489870 0.9547493811 1.7286849039 H 0.6604843338 0.5588961238 -1.3151404423 H 0.3977490997 -1.8372831200 -0.8675966541 H 0.0074180033 -2.2541508917 1.9191317095 H 2.4589042416 -2.3590713012 2.3047569954 H 4.4770029396 -2.7487577793 0.7708457423 H 5.0245330270 0.3576057816 -1.9136610432 H 4.6627744958 -0.9848378819 -3.0032885010 H 2.6492616781 0.5940998054 -2.4552691215 H 2.3566244969 -1.1552545388 -2.2345909144 H 3.0850569827 2.0782462989 -0.3645264663 H 4.3866832153 0.9663480951 0.1619594535 H 3.0473793396 1.3281479486 1.2651725786 H -2.4246752406 0.7430327650 2.9022373158 H -2.4531817527 -1.0160759641 2.5574704220 H -0.8958685428 -0.1677336054 2.7722664559 End BondOrders 1 2 1.0 1 24 1.0 1 25 1.0 1 26 1.0 2 3 2.0 2 4 1.0 4 5 1.0 4 8 1.0 4 27 1.0 5 6 1.0 5 28 1.0 5 29 1.0 6 7 1.0 6 30 1.0 6 31 1.0 7 8 1.0 7 12 1.0 7 32 1.0 8 9 1.0 8 23 1.0 9 10 1.0 9 33 1.0 9 34 1.0 10 11 1.0 10 35 1.0 10 36 1.0 11 12 1.0 11 21 1.0 11 37 1.0 12 13 1.0 12 38 1.0 13 14 2.0 13 39 1.0 14 15 1.0 14 40 1.0 15 16 2.0 15 21 1.0 16 17 1.0 16 41 1.0 17 18 2.0 17 19 1.0 19 20 1.0 19 42 1.0 19 43 1.0 20 21 1.0 20 44 1.0 20 45 1.0 21 22 1.0 22 46 1.0 22 47 1.0 22 48 1.0 23 49 1.0 23 50 1.0 23 51 1.0 End End ``` ### DFTB Hessian guess GFN1-xTB full Hessian at the DFT geometry, used as the mode-tracking preconditioner. ```ams Properties NormalModes yes End Task SinglePoint System Atoms C -5.5272702836 1.7383362856 0.0582569671 C -4.1685168218 1.5794986849 0.7215959954 region=CO O -3.7738054138 2.4062279095 1.5807198590 region=CO C -3.3492755853 0.3693323239 0.3005236493 C -3.2200033078 0.2069590175 -1.2485626587 C -1.9658951634 -0.7030021370 -1.4454143318 C -1.3643012691 -0.9399535601 -0.0226345679 C -1.8953008505 0.2432122596 0.8513331893 C -1.0523937563 1.5151903380 0.5643006145 C 0.4672044135 1.2663845151 0.6986431056 C 0.9475399655 0.1968378578 -0.3093237635 C 0.1718837451 -1.1308785250 -0.0381903285 C 0.7046271611 -1.7674667959 1.2305357331 C 2.0390934856 -1.8180847112 1.4510129547 C 2.9443661126 -1.2863928887 0.4345990398 C 4.1332273770 -1.9056016869 0.1644207305 C 4.9773230598 -1.5652844813 -0.9797350199 O 6.1148350071 -2.1049902516 -1.1434458560 C 4.4356054071 -0.5733864669 -2.0045972197 C 2.9271150329 -0.2885453311 -1.8516186580 C 2.5106858508 -0.0488066215 -0.3693139467 C 3.3041110912 1.1604381115 0.2075515121 C -1.9135464039 -0.0711638036 2.3623275318 H -6.0747496156 0.7819576090 0.0347114338 H -5.4000524410 2.0793314586 -0.9840203771 H -6.1078420136 2.4919895674 0.6093185440 H -3.9100052907 -0.5149291198 0.6768433131 H -3.0659919108 1.1925320325 -1.7196342644 H -4.1280195239 -0.2358669101 -1.6887264871 H -1.2332484026 -0.2079855012 -2.1035001561 H -2.2327948171 -1.6640683575 -1.9163765522 H -1.8105076210 -1.8717559662 0.3805686025 H -1.2548909320 1.8737526759 -0.4629964858 H -1.3677999012 2.3157905998 1.2524073535 H 0.9844983116 2.2224307518 0.5154260491 H 0.7139489870 0.9547493811 1.7286849039 H 0.6604843338 0.5588961238 -1.3151404423 H 0.3977490997 -1.8372831200 -0.8675966541 H 0.0074180033 -2.2541508917 1.9191317095 H 2.4589042416 -2.3590713012 2.3047569954 H 4.4770029396 -2.7487577793 0.7708457423 H 5.0245330270 0.3576057816 -1.9136610432 H 4.6627744958 -0.9848378819 -3.0032885010 H 2.6492616781 0.5940998054 -2.4552691215 H 2.3566244969 -1.1552545388 -2.2345909144 H 3.0850569827 2.0782462989 -0.3645264663 H 4.3866832153 0.9663480951 0.1619594535 H 3.0473793396 1.3281479486 1.2651725786 H -2.4246752406 0.7430327650 2.9022373158 H -2.4531817527 -1.0160759641 2.5574704220 H -0.8958685428 -0.1677336054 2.7722664559 End BondOrders 1 2 1.0 1 24 1.0 1 25 1.0 1 26 1.0 2 3 2.0 2 4 1.0 4 5 1.0 4 8 1.0 4 27 1.0 5 6 1.0 5 28 1.0 5 29 1.0 6 7 1.0 6 30 1.0 6 31 1.0 7 8 1.0 7 12 1.0 7 32 1.0 8 9 1.0 8 23 1.0 9 10 1.0 9 33 1.0 9 34 1.0 10 11 1.0 10 35 1.0 10 36 1.0 11 12 1.0 11 21 1.0 11 37 1.0 12 13 1.0 12 38 1.0 13 14 2.0 13 39 1.0 14 15 1.0 14 40 1.0 15 16 2.0 15 21 1.0 16 17 1.0 16 41 1.0 17 18 2.0 17 19 1.0 19 20 1.0 19 42 1.0 19 43 1.0 20 21 1.0 20 44 1.0 20 45 1.0 21 22 1.0 22 46 1.0 22 47 1.0 22 48 1.0 23 49 1.0 23 50 1.0 23 51 1.0 End End Engine dftb Model GFN1-xTB EndEngine ``` ### DFT mode tracking PBE/DZ mode-tracking result for the selected CO-stretch guess. ```ams EngineRestart /home/ubuntu/work/01-run_workdir/02_dft_opt/adf.rkf LoadEngine /home/ubuntu/work/01-run_workdir/02_dft_opt/adf.rkf Task VibrationalAnalysis VibrationalAnalysis ModeTracking HessianGuess File HessianPath /home/ubuntu/work/01-run_workdir/04_dftb_hessian_guess/dftb.rkf End NormalModes ModeFile /home/ubuntu/work/01-run_workdir/03_dft_partial_hessian/adf.rkf ModeInputFormat File ModeSelect ModeNumber 153 End End Type ModeTracking End System Atoms C -5.5272702836 1.7383362856 0.0582569671 C -4.1685168218 1.5794986849 0.7215959954 region=CO O -3.7738054138 2.4062279095 1.5807198590 region=CO C -3.3492755853 0.3693323239 0.3005236493 C -3.2200033078 0.2069590175 -1.2485626587 C -1.9658951634 -0.7030021370 -1.4454143318 C -1.3643012691 -0.9399535601 -0.0226345679 C -1.8953008505 0.2432122596 0.8513331893 C -1.0523937563 1.5151903380 0.5643006145 C 0.4672044135 1.2663845151 0.6986431056 C 0.9475399655 0.1968378578 -0.3093237635 C 0.1718837451 -1.1308785250 -0.0381903285 C 0.7046271611 -1.7674667959 1.2305357331 C 2.0390934856 -1.8180847112 1.4510129547 C 2.9443661126 -1.2863928887 0.4345990398 C 4.1332273770 -1.9056016869 0.1644207305 C 4.9773230598 -1.5652844813 -0.9797350199 O 6.1148350071 -2.1049902516 -1.1434458560 C 4.4356054071 -0.5733864669 -2.0045972197 C 2.9271150329 -0.2885453311 -1.8516186580 C 2.5106858508 -0.0488066215 -0.3693139467 C 3.3041110912 1.1604381115 0.2075515121 C -1.9135464039 -0.0711638036 2.3623275318 H -6.0747496156 0.7819576090 0.0347114338 H -5.4000524410 2.0793314586 -0.9840203771 H -6.1078420136 2.4919895674 0.6093185440 H -3.9100052907 -0.5149291198 0.6768433131 H -3.0659919108 1.1925320325 -1.7196342644 H -4.1280195239 -0.2358669101 -1.6887264871 H -1.2332484026 -0.2079855012 -2.1035001561 H -2.2327948171 -1.6640683575 -1.9163765522 H -1.8105076210 -1.8717559662 0.3805686025 H -1.2548909320 1.8737526759 -0.4629964858 H -1.3677999012 2.3157905998 1.2524073535 H 0.9844983116 2.2224307518 0.5154260491 H 0.7139489870 0.9547493811 1.7286849039 H 0.6604843338 0.5588961238 -1.3151404423 H 0.3977490997 -1.8372831200 -0.8675966541 H 0.0074180033 -2.2541508917 1.9191317095 H 2.4589042416 -2.3590713012 2.3047569954 H 4.4770029396 -2.7487577793 0.7708457423 H 5.0245330270 0.3576057816 -1.9136610432 H 4.6627744958 -0.9848378819 -3.0032885010 H 2.6492616781 0.5940998054 -2.4552691215 H 2.3566244969 -1.1552545388 -2.2345909144 H 3.0850569827 2.0782462989 -0.3645264663 H 4.3866832153 0.9663480951 0.1619594535 H 3.0473793396 1.3281479486 1.2651725786 H -2.4246752406 0.7430327650 2.9022373158 H -2.4531817527 -1.0160759641 2.5574704220 H -0.8958685428 -0.1677336054 2.7722664559 End BondOrders 1 2 1.0 1 24 1.0 1 25 1.0 1 26 1.0 2 3 2.0 2 4 1.0 4 5 1.0 4 8 1.0 4 27 1.0 5 6 1.0 5 28 1.0 5 29 1.0 6 7 1.0 6 30 1.0 6 31 1.0 7 8 1.0 7 12 1.0 7 32 1.0 8 9 1.0 8 23 1.0 9 10 1.0 9 33 1.0 9 34 1.0 10 11 1.0 10 35 1.0 10 36 1.0 11 12 1.0 11 21 1.0 11 37 1.0 12 13 1.0 12 38 1.0 13 14 2.0 13 39 1.0 14 15 1.0 14 40 1.0 15 16 2.0 15 21 1.0 16 17 1.0 16 41 1.0 17 18 2.0 17 19 1.0 19 20 1.0 19 42 1.0 19 43 1.0 20 21 1.0 20 44 1.0 20 45 1.0 21 22 1.0 22 46 1.0 22 47 1.0 22 48 1.0 23 49 1.0 23 50 1.0 23 51 1.0 End End ``` ### DFT full normal modes PBE/DZ analytical full-Hessian reference calculation. ```ams EngineRestart /home/ubuntu/work/01-run_workdir/02_dft_opt/adf.rkf LoadEngine /home/ubuntu/work/01-run_workdir/02_dft_opt/adf.rkf Properties NormalModes yes End Task SinglePoint System Atoms C -5.5272702836 1.7383362856 0.0582569671 C -4.1685168218 1.5794986849 0.7215959954 region=CO O -3.7738054138 2.4062279095 1.5807198590 region=CO C -3.3492755853 0.3693323239 0.3005236493 C -3.2200033078 0.2069590175 -1.2485626587 C -1.9658951634 -0.7030021370 -1.4454143318 C -1.3643012691 -0.9399535601 -0.0226345679 C -1.8953008505 0.2432122596 0.8513331893 C -1.0523937563 1.5151903380 0.5643006145 C 0.4672044135 1.2663845151 0.6986431056 C 0.9475399655 0.1968378578 -0.3093237635 C 0.1718837451 -1.1308785250 -0.0381903285 C 0.7046271611 -1.7674667959 1.2305357331 C 2.0390934856 -1.8180847112 1.4510129547 C 2.9443661126 -1.2863928887 0.4345990398 C 4.1332273770 -1.9056016869 0.1644207305 C 4.9773230598 -1.5652844813 -0.9797350199 O 6.1148350071 -2.1049902516 -1.1434458560 C 4.4356054071 -0.5733864669 -2.0045972197 C 2.9271150329 -0.2885453311 -1.8516186580 C 2.5106858508 -0.0488066215 -0.3693139467 C 3.3041110912 1.1604381115 0.2075515121 C -1.9135464039 -0.0711638036 2.3623275318 H -6.0747496156 0.7819576090 0.0347114338 H -5.4000524410 2.0793314586 -0.9840203771 H -6.1078420136 2.4919895674 0.6093185440 H -3.9100052907 -0.5149291198 0.6768433131 H -3.0659919108 1.1925320325 -1.7196342644 H -4.1280195239 -0.2358669101 -1.6887264871 H -1.2332484026 -0.2079855012 -2.1035001561 H -2.2327948171 -1.6640683575 -1.9163765522 H -1.8105076210 -1.8717559662 0.3805686025 H -1.2548909320 1.8737526759 -0.4629964858 H -1.3677999012 2.3157905998 1.2524073535 H 0.9844983116 2.2224307518 0.5154260491 H 0.7139489870 0.9547493811 1.7286849039 H 0.6604843338 0.5588961238 -1.3151404423 H 0.3977490997 -1.8372831200 -0.8675966541 H 0.0074180033 -2.2541508917 1.9191317095 H 2.4589042416 -2.3590713012 2.3047569954 H 4.4770029396 -2.7487577793 0.7708457423 H 5.0245330270 0.3576057816 -1.9136610432 H 4.6627744958 -0.9848378819 -3.0032885010 H 2.6492616781 0.5940998054 -2.4552691215 H 2.3566244969 -1.1552545388 -2.2345909144 H 3.0850569827 2.0782462989 -0.3645264663 H 4.3866832153 0.9663480951 0.1619594535 H 3.0473793396 1.3281479486 1.2651725786 H -2.4246752406 0.7430327650 2.9022373158 H -2.4531817527 -1.0160759641 2.5574704220 H -0.8958685428 -0.1677336054 2.7722664559 End BondOrders 1 2 1.0 1 24 1.0 1 25 1.0 1 26 1.0 2 3 2.0 2 4 1.0 4 5 1.0 4 8 1.0 4 27 1.0 5 6 1.0 5 28 1.0 5 29 1.0 6 7 1.0 6 30 1.0 6 31 1.0 7 8 1.0 7 12 1.0 7 32 1.0 8 9 1.0 8 23 1.0 9 10 1.0 9 33 1.0 9 34 1.0 10 11 1.0 10 35 1.0 10 36 1.0 11 12 1.0 11 21 1.0 11 37 1.0 12 13 1.0 12 38 1.0 13 14 2.0 13 39 1.0 14 15 1.0 14 40 1.0 15 16 2.0 15 21 1.0 16 17 1.0 16 41 1.0 17 18 2.0 17 19 1.0 19 20 1.0 19 42 1.0 19 43 1.0 20 21 1.0 20 44 1.0 20 45 1.0 21 22 1.0 22 46 1.0 22 47 1.0 22 48 1.0 23 49 1.0 23 50 1.0 23 51 1.0 End End ``` ## References - Amsterdam Modeling Suite 2026 documentation, `Doc/text/Tutorials/VibrationalSpectroscopy/ModeTracking.txt`, and the AMS Vibrational Spectroscopy manual. - S. Luber, J. Neugebauer, and M. Reiher, "Intensity tracking for theoretical infrared spectroscopy of large molecules," *Journal of Chemical Physics* **130**, 064105 (2009). - G. L. G. Sleijpen and H. A. van der Vorst, "A Jacobi-Davidson iteration method for linear eigenvalue problems," *SIAM Journal on Matrix Analysis and Applications* **17**, 401 (1996).