We are going to learn how to use Gaussian to optimize geometries and calculate harmonic vibrational frequencies in a single two-step calculation at the restricted Hartree-Fock (RHF), second-order many-body perturbation theory [MBPT(2) or MP2], and configuration interaction singles and doubles (CISD) levels. We will also learn how to optimize geometries and how to calculate harmonic vibrational frequencies with GAMESS using MP2 and the completely renormalized coupled-cluster approach with singles, doubles, and a non-iterative treatment of triples termed CR-CC(2,3). We will use the configuration interaction with singles (CIS) approach in Gaussian and the equation-of-motion coupled-cluster singles and doubles (EOMCCSD) method in GAMESS to obtain information about excitation energies. We will also use the CIS approach in Gaussian to optimize the geometry of a molecule in the excited state.
You will have an opportunity to compare the results of geometry and frequency calculations with different methods, including RHF, MP2=MBPT(2), CISD, and CR-CC(2,3). You will also see how accurate the CIS method is relative to the more sophisticated, yet very practical, EOMCCSD approach in predicting vertical excitation energies, and how the computed excitation energies may depend on the basis set. The knowledge and experience acquired by performing the above calculations will be very useful for your homework, so please pay attention to details. You can always come back to this web site after the lab to re-examine the calculations we will perform during the lab.
All of the relevant files reside in the directory ~piecuch/cem888_SS10/students2/. The subdirectories 'set1' and 'set2' correspond to two sets of calculations we are interested in. Use 'cp -r ~piecuch/cem888_SS10/students2/* ./' to copy the files relevant to today's lab to the appropriate working subdirectory in your home area.
You will find the following input files in the subdirectory 'set1':
h2o_rhf_opt.com - the Gaussian input file for the geometry optimization
at the RHF level (the initial values of
the variables roh and ang are set at the
experimental values of the O-H bond length
and the H-O-H angle, respectively). As you know,
the CIS ground state is represented by
the Hartree-Fock (in this case, RHF) wave
function.
h2o_cis_exp.com - the Gaussian input file for the CIS calculations
of the 5 lowest singlet and 5 lowest triplet
excited states. The value of Nstate equals
the number of excited states you would like
to calculate. Since water is a closed-shell
molecule, the CIS calculation generates only
singlet states as default. If you would like to
learn about triplet states, you must add
the 50-50 option, as shown in the input file.
The experimental geometry of water in the
ground electronic state is used. The CIS
approach can only give singlet and triplet
excited states for closed-shell
molecules. Do you know why?
h2o_cis_rhfgeom.com - same as above for the RHF-optimized
geometry of water.
h2o_cis_2opt.com - the Gaussian input file for the optimization of the
geometry of water in the first-excited SINGLET
state (triplet states are not even considered
in this calculation, since we do not use the
50-50 option). The value of Root equals to
the excited-state number whose geometry is
being optimized (in our case, Root=1, which
means that we optimize geometry of water
in the first-excited singlet state).
h2o_eomccsd_exp.inp - the GAMESS input file for the EOMCCSD calculations
of the 5 lowest SINGLET excited states using
the 6-311++G(d,p) basis set (36 functions). As indicated
by the 'nstate(1)=2,1,0,2' option in the $eominp input
group (and 'CNV 2' in $data), GAMESS uses point symmetry
to help the calculations. The five low-lying excited
states that we are interested in determining are two
A1 singlets, one A2 singlet, and two B2 singlets;
note 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.
h2o_eomccsd_exp_acct.inp - same as above for the aug-cc-pVTZ basis set
(92 functions), which is considerably larger than the
6-311++G(d,p) basis. In order to save time
during the lab, the output is provided
for your convenience. Compare the results with the
earlier EOMCCSD calculation.
h2o_eomccsd_exp_diff.inp - same as above for the modifed variant of the
cc-pVTZ basis set, in which we added the suitably
optimized diffuse functions to obtain a better description
of some excited states. The basis set used in this
EOMCCSD calculation (68 functions) is smaller than aug-cc-pVTZ,
but it yields considerable improvements in the results for
the second singlet B1 and second singlet A1 excited states.
In each Gaussian CIS calculation, the lowest orbital (more or less, the 1s
orbital of the oxygen atom) is frozen (cf., '2,0' in the window and the rw
option). The same is true in the GAMESS EOMCCSD calculations ('ncore=1').
The lowest-energy molecular orbital of water is almost identical to the 1s orbital in the
oxygen atom and can be frozen.
Things to do:
1. Compare the RHF-optimized geometry with the experimental geometry of water (the initial values of roh and ang). 2. Look at the vertical excitation energies in h2o_cis_exp.log, h2o_cis_rhfgeom.log, h2o_eomccsd_exp.log, h2o_eomccsd_exp_acct.log, and h2o_eomccsd_exp_diff.log, and compare them to the experimental values of these energies, which are: 3B1: 7.0 or 7.2 eV, 1B1: 7.42 eV, 3A2: 8.9 eV, 1A2: 9.1 eV, 3A1: 9.3 eV, 1A1: 9.67 eV, 3A1: 9.81 eV, 3B1: 9.98 eV, 1B1: 10.01 eV, 1A1: 10.17 eV. Any comments? Remember that the B1 states in Gaussian and above are listed as the B2 states in GAMESS and vice versa. 3. Compare the geometries of water in the ground and excited states.
Gaussian input files
h2o_rhf_freq.com ---------------- This is an input file for the geometry optimization and frequency calculation at the RHF level. The geometry optimization is performed first using analytic gradients: # rhf/6-31++G(d,p) UNITS=angs SCF=Direct Opt The most essential information, including the optimum geometry obtained in the first calculation, is stored in the checkpoint file rhffreq (Chk=rhffreq). The geometry stored in file rhffreq is read into the second calculation, in which frequencies are calculated at the RHF level. The following line describes the frequency calculation, which is also done analytically: # rhf/6-31++G(d,p) Geom=Allcheckpoint Guess=Read UNITS=angs SCF=Direct Freq The --Link1-- line is essential for linking the two calculations together. h2o_mp2_freq.com ---------------- This is an input file for the geometry optimization and frequency calculation at the MBPT(2)=MP2 correlated level. The structure of this input file is essentially the same as in the RHF case. The only difference is the method employed (MP2) and information about the orbital frozen in the calculation (the 2,0 window). Analytic energy derivatives of MP2 are employed. h2o_cisd_freq.com ----------------- This is an input file for the geometry optimization and frequency calculation at the CISD level. The structure of this input file is essentially the same as in the MP2 case. The only difference is the method employed (CISD). Analytic energy gradients are followed by numerical differentiation of analytically computed first derivatives.Please note that we use different names for the checkpoint files produced and used by different calculations (rhffreq.chk, mp2freq.chk, cisdfreq.chk) to avoid confusion and accidental overwrite.
GAMESS input files
h2o_mp2_opt_GAMESS.inp ----------------------- This is a GAMESS input file for the geometry optimization at the MP2 level. Analytic gradients of MP2 are exploited. h2o_mp2_freq_GAMESS.inp ----------------------- This is a GAMESS input file for the frequency calculations at the MP2 level. Analytic energy gradients are followed by a numerical differentiation of analytically computed first derivatives. h2o_crcc23_opt_GAMESS.inp ------------------------- This is a GAMESS input file for the geometry optimization at the CR-CC(2,3) level. Numerical energy derivatives are exploited. If the time allocated to the lab becomes a constraint, we will examine the output provided by the instructor. h2o_crcc23_freq_GAMESS.inp ------------------------- This is a GAMESS input file for the frequency calculations at the CR-CC(2,3) level. Numerical energy derivatives are exploited. If the time allocated to the lab becomes a constraint, we will examine the output provided by the instructor.Things to do:
Compare the geometries and harmonic frequencies obtained in your calculations with the experimental values which are as follows: roh=0.957 Angs, ang=104.5 Degrees, omega1 = 1649 cm-1, omega2 = 3832 cm-1, omega3 = 3943 cm-1. Any thoughts? There is a useful program for visualization of molecules and for animating the normal-mode vibrations. It is called viewmol. A nice feature of this program is that it shows the theoretical harmonic spectrum (peaks with intensities corresponding to calculated values). You can try this program by typing 'viewmol h2o_rhf_freq.log', where h2o_rhf_freq.log is the output of your RHF frequency calculation. There are other tools in this category.