Assignment 2, due date February 17, 2010 (Dr. Piotr Piecuch)Geometry, harmonic vibrational frequencies, and excited states of formaldehyde. ------------------------------------------------------------------------------- You will use Gaussian and GAMESS to optimize the geometry and calculate the harmonic frequencies of formaldehyde, H2CO (Problem 2), and to obtain information about the excited states of formaldehyde (Problem 1). Please re-examine and understand the input files for H2O that you used in the lab before working on this homework.
Problem 1
1. Prepare input files for: 1.1 Gaussian geometry optimization at the RHF level using the 6-311++G(d,p) basis set. Please do not assume that the molecule is planar (although we know it is). Let Gaussian decide about it. The suggested form of the Z-matrix is: O C 1 rco H 2 rch 1 ang H 2 rch 1 ang 3 dih rco=1.208 rch=1.116 ang=121.8 dih=150.0 where the initial values of rco and rch are the experimental values in Angstroem and the initial value of ang is the experimental value in degree. The dihedral angle dih should be 180.0 degree, but we use some other value (150.0 degree here) to let Gaussian decide if the molecule is planar or not. 1.2 Gaussian geometry optimization at the RHF level using the 6-311++G(d,p) basis set, in which we assume that the molecule is planar. The suggested form of the Z-matrix is: O C 1 rco H 2 rch 1 ang H 2 rch 1 ang 3 180.0 rco=1.208 rch=1.116 ang=121.8 (distances in Angstroem, angles in degrees). 1.3 Gaussian CIS calculation for 14 singlet excited states of formaldehyde using the 6-311++G(d,p) basis set and the experimental geometry. Freeze the two lowest-energy orbitals by adding in a window a line '3,0'; do not forget about rw in '# cis=(...) ...'. Use the following form of the Z-matrix: O C 1 rco H 2 rch 1 ang H 2 rch 1 ang 3 dih rco=1.208 rch=1.116 ang=121.8 dih=180.0 (distances in Angstroem, angles in degrees). 1.4 Gaussian CIS calculation for 14 singlet excited states of formaldehyde using the 6-311++G(d,p) basis set and the RHF-optimized geometry. Use the same form of the Z-matrix as in 1.3 (of course, you must obtain the RHF values of rco, rch, ang). 1.5 Gaussian optimization of geometry of formaldehyde, as described by the 6-311++G(d,p) basis set, in the first-excited singlet state. Use the following input line: # cis=(rw,Nstate=1,Root=1)/6-311++G(d,p) UNITS=angs SCF=Direct Opt. Use the following form of the Z-matrix: O C 1 rco H 2 rch 1 ang H 2 rch 1 ang 3 dih rco=1.208 rch=1.116 ang=121.8 dih=150.0 Since excited states of formaldehyde do not have to be planar, we set the initial value of dih at 150.0 degrees. 1.6 GAMESS EOMCCSD calculation of the 3 excited singlet states of the A1 symmetry, 4 excited singlet states of the A2 symmetry, 4 excited singlet states of the B1 symmetry, and 2 excited singlet states of the B2 symmetry using the [5s3p2d/3s2p] basis set of Sadlej. Use the external basis set file 'basis' provided to you during the lab on February 10, 2010 (in subdirectory set1). You can always retrieve this file by 'cp -r ~piecuch/cem888_SS10/students2/set1/basis ./'). Remember that you must use the '-b' flag at 'gmssub' when submitting GAMESS jobs with external basis sets to an hbar queue and that your input file must contain the line '$basis gbasis=SADLEJ extfil=.true. $end'. Make sure that you freeze the two lowest-energy orbitals ('ncore=2', which is a default in GAMESS). Use the experimental geometry. The suggested form of the Z-matrix is the same as in point 1.3 above, i.e., O C 1 rco H 2 rch 1 ang H 2 rch 1 ang 3 dih rco=1.208 rch=1.116 ang=121.8 dih=180.0 Remember that due to different conventions used by Gaussian and GAMESS, the B1 states in Gaussian are listed as the B2 states in GAMESS and vice versa. 2. Perform calculations with inputs 1.1-1.6. 3. Things to do: 3.1 Prepare a table with the following results: ------------------------------------------------------------------------------- Excitation energies (eV) Excited State Experiment CIS(exp. geom.) CIS(RHF geom.) EOMCCSD (exp. geom.) ------------------------------------------------------------------------------- 1 1A2 4.07 ... ------------------------------------------------------------------------------- The experimental excitation energies can be found in S.R. Gwaltney and R.J. Bartlett, Chem. Phys. Lett. 241, 26-32 (1995) (page 31 in the lecture notes, right after the page with the CIS equations). Again, remember that the B1 states in Gaussian are listed as the B2 states in GAMESS and vice versa. Please provide information about the RHF-optimized geometry below the table. 3.2 Prepare a table with the following information: Title: The first-excited singlet state (1 1A2) of formaldehyde -------------------------------------------------------------------------- Parameter Experiment CIS -------------------------------------------------------------------------- rco/Angstroem 1.323 rch/Angstroem 1.093 ang/degree 119.0 dih/degree 149.0 -------------------------------------------------------------------------- 3.3 Prepare figures showing formaldehyde in the ground and the first-excited singlet states (using, for example, MOLDEN and reading the results of the RHF and CIS optimizations).Problem 2
1. The following Gaussian input can be used to calculate the geometries and harmonic frequencies of formaldehyde, as described by the 6-31++G(d,p) basis set, with the RHF method: $RunGauss %Chk=rhffreq # rhf/6-31++G(d,p) UNITS=angs SCF=Direct Opt formaldehyde 0 1 O C 1 rco H 2 rch 1 ang H 2 rch 1 ang 3 180.0 rco=1.208 rch=1.116 ang=121.8 --Link1-- %chk=rhffreq # rhf/6-31++G(d,p) Geom=Allcheckpoint Guess=Read UNITS=angs SCF=Direct Freq Using this file and the files used for the lab exercise for water as examples, prepare the analogous input files for MP2 and CISD methods. One of the things that you have to remember about when switching from RHF to MP2 or CISD is the fact that you are going to freeze the lowest two orbitals for the MP2 and CISD calculations using the 'rw' keyword and the '3,0' lines in appropriate places. 2. Prepare two GAMESS input files for (i) the geometry optimization at the MP2 level and (ii) the frequency calculations at the MP2 level. Remember that you must optimize the geometry first and then transfer the resulting Z-matrix data to the input for the subsequent frequency calculation. You may consult the examples in the subdirectory 'set2' of subdirectory 'lab2' used during the February 10, 2010 lab. To be consistent with the Gaussian calculation, please remove the 'ispher=1' option from the GAMESS input files, so that you use 6 Cartesian rather than 5 spherical d basis set functions.
3. Things to do: 3.1. Run all three calculations (RHF, MP2, CISD; MP2 with Gaussian and GAMESS) and report the results for the geometries and harmonic frequencies of formaldehyde by creating the following table: ---------------------------------------------------------------------------------- Method r(C-O) r(C-H) <(H-C-O) omega1 omega2 omega3 omega4 omega5 omega6 ---------------------------------------------------------------------------------- RHF MP2 (G98) MP2 (GAMESS) CISD Experiment ---------------------------------------------------------------------------------- where omega[1-6] are the harmonic frequencies. The experimental values can be found in the lecture notes (page 28). Discuss the observed patterns. 3.2. Prepare another input file for the CISD calculation for formaldehyde using the 6-31++G(d,p) basis set. This time use the experimental geometry given in the lecture notes and prepare an input for the single-point energy calculation only. Freeze the lowest two core orbitals. Run Gaussian calculation. Analyze the output. In particular, extract from it: - the RHF energy, - the MP2 energy, - the CISD energy. Calculate (or extract) the MP2 and CISD correlation energies. Assuming that the exact (full CI) total energy for the 6-31++G(d,p) basis set approximately equals -114.2164928724 hartree (which is the full CCSDT result; we will talk about it later), calculate the fraction of the exact correlation energy (in percent of the exact correlation energy) reproduced by the MP2 and CISD methods. Is any of these methods giving you 100 % of the exact correlation energy? What type of excited configurations would have to be included in the calculations to obtain an almost exact correlation energy?