FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 1Vertiefungsfach Theoretische ChemiePraktikum im Sommersemester 2011Versuch 7T:2011-05-24Calculating Vertical Spectra with TD-DFT: successes and failuresTime-dependent density functional theory has become a very important tool for the modelingof properties in the excited electronic states of medium and large size molecules. In most ofthe cases TD-DFT is able to provide accurate electronic spectra with low computational cost.However, TD-DFT has been pointed out to provide substantial errors in the calculation of theexcited states of extended π-systems, weakly interacting molecular complexes or for speciespresenting Rydberg excited states and charge transfer excited states. In today’s exercise wewill calculate the vertical excited spectrum of three systems, namely formaldehyde, a dipeptidemodel and the uracil molecule by means of TD-DFT as implemented in TURBOMOLEsoftware.Goals:• Calculating the vertical excitation energies for uracil, formaldehyde and a dipeptidemodel by means of TD-DFT.• Comparison of TD-DFT excitation energies with CASPT2 and experimental results.• Investigation of critical cases where TD-DFT fails to predict vertical excited spectra.Procedure:For the calculation of the vertical excited spectra of the above molecules we will use theground state structures provided at the end of the exercise. Before running your calculationsdevote some minutes to think which kind of excitations might be, in your opinion, present inthe low energy region of their vertical excited spectra.For the preparation of the inputs you will use the interactive input generator DEFINE ofTURBOMOLE. Proceed as follows (extracted from the TURBOMOLE manual):Before starting your calculations setup the correct environment by exporting the followingvariables:export TURBODIR=/usr/local/TURBOMOLE/export PATH=$TURBODIR/bin/x86_64-unknown-linux-gnu:$TURBODIR/scripts:$PATHSince response calculations require a set of converged SCF MOs, we will first perform a singlepoint calculation for the ground state. Follow the instructions below for uracil.
FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 2Single point calculation of the ground state1. Prepare a file called xyz with the initial xyz coordinates. (Use the geometry providedat the end of the exercise.)2. Use the TURBOMOLE script x2t to convert your xyz file to a coord file understandableby TURBOMOLE.x2t xyz > coord3. Call the define module. Follow interactively the instructions from the program. Introducethe title, and add the coordinates by typing a coord . By default TURBOMOLEconsiders C 1 symmetry for the system. By typing desy, TURBOMOLE automaticallydetermines the molecular symmetry. Leave the menu with *.What is the symmetry found by the program for our molecules?4. The next menu concerns the election of the basis set and the charge of the system. Wewill use the standard SV(P) basis set for uracil.5. In the next step we need to provide initial guess orbitals. For this, we will perform anextended Hückel calculation typing eht. Then, enter the molecular charge.6. Next, we will set up the functional details. In the next menu type dft . Activate dftby typing on. We will employ the hybrid b3-lyp functional and the grid m4 (thedefault is m3).7. Once the control file is ready, edit the following lines which tighten the scf anddensity matrix convergence criteria, respectively:$scfconv 7$denconv 1d-78. In order to run the dft calculation for the ground state, specify the keywords:dscf > dscf.out &In the case of the dipeptide, we will use the pure functional B-P86 with the SV(P) basisset to calculate its vertical excited spectrum. For non-hybrid functionals, it is possible tospeed up the calculation by a factor of 10, (at least), using the resolution of the identityapproximation:After Step 6 switch the resolution of the identity on, within the ri submenu. Augmentthe memory for storing 3-center integrals up to 1000MB. The more memory you allow, thefaster the calculation will be. Define the auxiliary basis set by typing jbas. Then typeb all SV(P), to provide the auxiliary basis set SV(P) to all the atoms. After that, proceedwith Step 7 and run the dft calculation for the ground state typing:
FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 3ridft > ridft.out &In the particular case of formaldehyde, we will use the B-P86 functional together with abasis set which includes diffuse functions. For this particular basis set, an auxiliary basis setis not available. Thus, we will work outside the resolution of the identity approximation.Follow Step 1 and 2 described above. Before calling the define module, copy the basisset provided below in a file called basis and prepare a file called control containing thefollowing information:$title$operating system unix$symmetry c2v$coord file=coord$user-defined bonds$atomsc 1 \basis =c Sadlej pVTZh 2,3 \basis =h Sadlej pVTZo4 \basis =o Sadlej pVTZ$basisfile=basis$endfile=coordTo complete the ground state dft calculation complete the Steps 5 and 6 provided above.In Step 6, choose the B-P86 functional. As already mentioned, there is no auxiliary basis setimplemented for the augmented Sadlej pVTZ basis set. Therefore, proceed with Step 7 and8.Calculation of the vertical excited spectra using TD-DFTNow proceed with the calculation of the TD vertical excited spectra for uracil, the dipeptideand formaldehyde. We will calculate 7 excited states for uracil, 3 excited states ofeach symmetry for formaldehyde and 11 A’ states and 3 A” states for the dipeptide. Forthis, edit the control file adding at the end the following lines which specify that weare just interested in closed-shell singlet excitations, the number of excitations per irreduciblerepresentation we want to calculate, the extra memory we are going to use and that wewant a summary of the excitation energies and oscillator strengths for the allowed transitions:$scfinstab rpasClosed shell singlet excitations
FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 4$soesSymmetry_1 ??Symmetry_2 ??..$rpacor 1000$spectrum nmNumber of excitations per irreduciblerepresentationExtra memory that will be usedSummary of the resultsSubstitute Symmetry_1 for every single irreducible representation within the symmetry pointgroup of each molecule, for instance a’ and a’’ for Cs (dipeptide). In the case of formaldehyde,we will additionally calculate the lowest lying triplet excited states since the experimentalband positions are available in the literature. Calculate 3 states of each symmetry.For the calculation of the triplets repeat the above procedure changing the first line for$scfinstab rpat .Discussions of the results• Once all the calculations are finished, report in a table for each molecule the calculatedexcitation energies in increasing energy ordering (in nm and eV), the oscillator strengthsfor allowed transitions, and the orbitals involved in each excitation.• Compare these results with the experiment, when possible, or with the CASPT2 excitationspectra (average errors below 0.3 eV). You can find a summary of this informationbelow. In the case of formaldehyde and the dipeptide, it might result very useful notonly to compare the position of the DFT and experimental/CASPT2 bands but also tocompare the band assignments.• Does TD-DFT predict the same excited state ordering that the experiment (CASPT2results)?• Are TD-DFT values in all the cases in good agreement with experimental or CASPT2values? If not, argue which might be the reasons.• Which are the errors associated to the main transitions? Now look at the oscillatorstrengths. Is there any dark transition? What does this imply? How were in the case ofuracil the position of the dark transition estimated?
FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 5Experimental/CASPT2 resultsUracilExc. Energy (eV)4.68 15.086.046.6DipeptideCASPT2States ∆E f1 A ′′ n 1 → π1 ∗ 5.61 0.00061 A ′′ n 2 → π2 ∗ 5.82 0.00061 A ′′ n 1 → π2 ∗ 7.91 0.00001 A ′ π 1 → π1 ∗ 6.32 0.27371 A ′ π 2 → π2 ∗ 6.29 0.32051 A ′ π 1 → π2 ∗ 6.92 0.11681 A ′ n 1 → σ ∗ 6.92 0.00851 A ′ n 1 → σ ∗ – –1 A ′ n 1 → σ ∗ – –1 A ′ n 2 → σ ∗ 7.19 0.01891 Value taken from the 1,3-dimethyluracil
FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 6FormaldehydeState Transition Expt.1 A 2 n → 3db 1 9.221 A 2 n → 3pb 1 8.381 B 1 σ → π∗ 8.681 B 2 n → 3pa 1 8.123 B 2 n → 3pa 1 7.961 A 1 n → 3pb 2 7.973 A 1 n → 3pb 2 7.791 B 2 n → 3sa 1 7.093 B 2 n → 3sa 1 6.833 A 1 π → π∗ 5.531 A 2 π → π∗ 3.943 A 2 π → π∗ 3.50
FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 7XYZ coordinates in Angstroms:UracilC -0.023276 0.003138 -0.008074C 0.001877 -0.001452 1.447218C 1.182979 -0.004781 2.095848N 2.376754 -0.003372 1.426544C 2.483132 0.000238 0.042557N 1.257288 0.004526 -0.586544O 3.550378 -0.000239 -0.533504O -1.015030 0.007088 -0.710354H -0.941536 -0.002432 1.975716H 3.256612 -0.006938 1.920553H 1.287515 0.007228 -1.598645H 1.257639 -0.008647 3.178302DipeptideC -2.360512 -0.001593 0.000000C -3.313486 -1.198391 0.000000H -3.159242 -1.832369 0.891912H -4.346766 -0.823020 0.000000H -3.159242 -1.832369 -0.891912N -1.029031 -0.327799 0.000000H -0.677990 -1.290708 0.000000O -2.743282 1.175947 0.000000C 0.000000 0.685985 0.000000H -0.092657 1.346344 0.886582H -0.092657 1.346344 -0.886582C 1.364341 -0.026011 0.000000N 2.452583 0.796781 0.000000O 1.462168 -1.262417 0.000000H 2.315280 1.806186 0.000000C 3.810530 0.260083 0.000000H 3.984335 -0.365202 -0.893055H 4.523404 1.098442 0.000000H 3.984335 -0.365202 0.893055FormaldehydeC 0.00000000 0.00000000 -0.52866907H -0.00000000 -0.93567261 -1.11085541H -0.00000000 0.93547650 -1.11117048O -0.00000000 0.00020256 0.67433029
FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 8Augmented Sadlej basis set for H, C and O (for formaldehyde molecule):$basis*h Sadlej pVTZ*4s33.8650140 0.00606805.0947880 0.04531601.1587860 0.20284600.3258400 0.50370901s0.1027410 1.00000001s0.0324000 1.00000002p1.1588000 0.18844000.3258000 0.88242002p0.1027000 0.11780000.0324000 0.0042000*c Sadlej pVTZ*5s5240.6353000 0.0009370782.2048000 0.0072280178.3508300 0.036344050.8159420 0.130600016.8235620 0.31893102s6.1757760 0.43874202.4180490 0.21497401s0.5119000 1.00000001s0.1565900 1.00000001s0.0479000 1.00000004p18.8418000 0.01388704.1592400 0.08627901.2067100 0.28874400.3855400 0.49941101p
FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 9*o*1p2d2d1s1s1p1d0.1219400 1.00000000.0385680 1.00000001.2067000 0.26285000.3855000 0.80430000.1219000 0.65350000.0386000 0.8636000Sadlej pVTZ0.01470 1.00000000.00448 1.00000000.012 1.00000000.012 1.00000005s10662.2850000 0.00079901599.7097000 0.0061530364.7252600 0.0311570103.6517900 0.115596033.9058050 0.30155202s12.2874690 0.44487004.7568050 0.24317201s1.0042710 1.00000001s0.3006860 1.00000001s0.0900300 1.00000004p34.8564630 0.01564807.8431310 0.09819702.3062490 0.30776800.7231640 0.49247001p1p2d0.2148820 1.00000000.0638500 1.0000000
FSU Jena, Institut für Physikalische Chemie, VF 7, St. Kupfer, M. Richter SS2011 102d*$end2.3062000 0.20270000.7232000 0.57910000.2149000 0.78545000.0639000 0.5338700