We are going to perform and analyze several quantum-chemistry calculations for the
potential energy curve of HCl and electronic excitations in C_{2}. We will use
Molpro to perform a number of "expert" multi-reference calculations using
the complete-active-space self-consistent-field (CASSCF) approach, the second-order
multi-reference perturbation theory based on CASSCF, commonly referred to as
CASPT2, and the internally contracted multi-reference configuration interaction
singles and doubles method with the quasi-degenerate Davidson correction,
commonly abbreviated as MRCI(Q). We will use GAMESS to carry out a number
of "black-box" single-reference coupled-cluster (CC) and equation-of-motion coupled-cluster
(EOMCC) calculations, including the CC and EOMCC methods with singles and
doubles (CCSD and EOMCCSD, respectively), the conventional CC approach with
singles and doubles, and a quasi-perturbative non-iterative treatment of triples
(CCSD(T)), the completely renormalized, left-eigenstate extension of CCSD(T)
developed by the Piecuch MSU group, abbreviated as CR-CC(2,3), and one of the
analogs of CR-CC(2,3) that corrects the EOMCCSD results for the leading
effects due to triples, termed CR-EOMCCSD(T), also developed by Piecuch et al.

**IMPORTANT NOTES:**

**(1)** In addition to
the homework problem in which you will be asked to investigate the isomerization
pathways of bicyclobutane into butadiene using a few CC methods, your next
homework no. 3 will
have questions related to performance
of the CASSCF, CASPT2, MRCI(Q), CCSD, CCSD(T), CR-CC(2,3), EOMCCSD, and CR-EOMCCSD(T)
approaches in the calculations for HCl and C_{2} discussed during the lab.
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 return back to this web site
after the lab on February 17, 2010 to re-examine or even redo the calculations discussed during the lab.

**(2)** Unlike in the previous two labs, we will carry all of our computational work
on 'hydra'. We will use 'bignode' on 'hydra', which is set-up as a dedicated node for this lab and
homework no. 3.

In addition to performing a number of calculations for the
potential energy curve of HCl and electronic excitations in C_{2},
we will talk about finding basis sets for electronic structure
calculations with a variety of quantum-chemistry packages using the
wonderful Basis Set Exchange software and the EMSL Basis Set Library
available at https://bse.pnl.gov/bse/portal.
This will help you in the long-term
if you ever get involved in quantum-chemistry computing again.

All of the files relevant to this lab and to part of homework no. 3
that deals with the potential energy curve of HCl and electronic excitations in C_{2}
reside in the directory ~piecuch/cem888_SS10/students3/ on 'hydra'.
The subdirectories 'set1' and 'set2' correspond to two sets of
calculations we are interested in during the lab.
Use 'cp -r ~piecuch/cem888_SS10/students3/* ./'
to copy the files relevant to today's lab to the
appropriate working subdirectory in your home area on 'hydra'. All of the calculations
will be submitted to 'bignode' on 'hydra' through a queue option '-l bignode' (see below
for further details).

The GAMESS implementation of the aug-cc-pVnZ basis sets for the Al-Ar atoms (and this includes Cl) via the 'GBASIS=ACCn' option that one would normally conveniently use to produce the equivalent of the aug-cc-pVTZ basis set requested in our Molpro inputs includes, as a default, one additional tight d-function to produce the so-called aug-cc-pV(n+d)Z sets. In our case, we want to use the plain aug-cc-pVTZ basis set for both H and Cl. Thus, we cannot use the the standard 'GBASIS=ACCT' option in our GAMESS calculations for HCl and must input the plain aug-cc-pVTZ basis for H and Cl manually. The easiest way to do it is via the external basis set file 'basis'. The EMSL Basis Set Library available at https://bse.pnl.gov/bse/portal becomes very useful in this effort.

The appropriate input files are described below.
Use **gmssub -b basis -l bignode file**, where 'file.inp' is the input file, to run
GAMESS jobs. The 'basis' file is the external file containing the basis set information.
As already pointed out,
this file can be generated by the user with the help of the EMSL Basis Set Library
available at https://bse.pnl.gov/bse/portal.
As discussed in the previous two labs, GAMESS accesses the information in this file
via the 'EXTFIL=.TRUE.' and 'GBASIS=...' input options.
Use **m06sub -l bignode file.inp** to run Molpro jobs.
Before running the calculations,
please examine the input files. We will discuss the meaning of each
keyword in the input files during the lab.

You will find the following input files in the subdirectory 'set1':

hcl_molpro_scan-mrci.inp - the Molpro input file for the scan of the potential energy curve of HCl with the CASSCF, MRCI, and MRCI(Q) methods. Although one can use Molpro defaults in these calculations, the information about the active orbitals and orbitals optimized in CASSCF calculations, and the information about the active and core orbitals that are frozen in MRCI calculations is completely spelled out. hcl_molpro_scan-default-mrci.inp - the Molpro input file for the scan of the potential energy curve of HCl with the CASSCF, MRCI, and MRCI(Q) methods using Molpro defaults. hcl_molpro_scan-mrpt.inp - the Molpro input file for the scan of the potential energy curve of HCl with the CASSCF and CASPT2 methods. hcl_GAMESS_scan_ccsd-t.inp - the GAMESS input file for the scan of the potential energy curve of HCl with the CCSD and CCSD(T) approaches using the RHF reference. hcl_crcc23_M_NNre.inp - the GAMESS input files for the single-point CCSD and CR-CC(2,3) calculations at the nuclear geometries defined as M.NN times Re (Re is the experimental equilibrium bond length), where M.NN ranges from 0.75 to 5.0. The set of the M.NN values, which are 0.75, 0.90, 1.00, 1.10, 1.25, 1.50, 1.75, 2.00, 2.25, 2.50, 3.00, and 5.00, is exactly the same as that used to define the above potential energy surface scans. One can run the complete set of the GAMESS CR-CC(2,3) calculations using the script 'runall-gamess'.The corresponding output files, provided in the subdirectory 'OUTPUTS', have extensions '.log' for GAMESS and '.out' for Molpro. Note that in each each post-SCF (CASPT2, MRCI, MRCI(Q), CCSD, CCSD(T), abd CR-CC(2,3)) calculation, the lowest five orbitals that correlate with the 1s, 2s, and 2p shells of the chlorine atom are frozen (cf. the CORE and NCORE settings in the Molpro and GAMESS inputs, respectively).

**Things to do during the lab:**

1. Compare the results obtained with CASSCF, CASPT2, CCSD, CCSD(T), and CR-CC(2,3) with the MRCI(Q) and full CCSDT data. The MRCI(Q) results will be obtained with Molpro, using the input files provided during the lab (see the above input file description). The full CCSDT energies, taken from P. Piecuch et al., Chem. Phys. Lett.418, 467 (2006), can be found in the 'hcl-ccsdt.dat' file in subdirectory 'PLOTS'. 2. Plot various potential energy curves resulting from our calculations usinggnuplot(on 'hbar'). The complete set of gnuplot input files and the examples of the resulting '.eps' files can be found in the subdirectory 'PLOTS', but you may want to practice the use ofgrepto prepare the corresponding data files and the use ofgnuplotto generate the '.eps' files. The latter files that contain plots of the potential energy curves resulting from our calculations for HCl can be previewed on 'hbar' usinggv. 3. Examine the GAMESS and Molpro outputs to learn about various elements of the calculations, such as stages that the CC, CASSCF, CASPT2, and MRCI(Q) calculations must go through, weights of the dominant configuration state functions (multi-reference calculations), the largest cluster amplitudes (CC calculations), the natural orbital occupation numbers (CC calculations), and the dipole moment values (all calculations) as a function of the H-Cl distance.

1. Calculate the approximate dissociation energies from the data provided in subdirectory 'PLOTS' by forming the energy differences E(R=5.0*Re) - E(R=Re), where Re = 1.27455 Angstroem is the equilibrium value of the H-Cl distance R. Does it make sense to do this for every potential energy curve we calculated? Please elaborate. Compare the results with the accurate MRCI(Q) and CCSDT values of the dissociation energy, which are 4.54 and 4.58 eV, respectively (1 Hartree = 27.2114 eV). The experimental value of the pure electronic dissociation energy is about 4.62 eV. 2. Plot the differences between the energies obtained with CASSCF, CASPT2, CCSD, CCSD(T), and CR-CC(2,3) and the corresponding MRCI(Q) energies as a function of the H-Cl distance (error curves relative to MRCI(Q)). Discuss the error variation as a function of the H-Cl distance. 3. Determine the so-called non-parallelity error (NPE) values relative to MRCI(Q) for each of the follwing methods: CASSCF, CASPT2, CCSD, CCSD(T), and CR-CC(2,3). NPE is defined as the difference between the maximum and minimum signed errors along the bond breaking coordinate (in our case, the H-Cl internuclear separation) resulting from a given calculation. NPE = 0 implies that a given potential energy curve is parallel to the MRCI(Q) curve. The positive NPE values imply the departure from the parallel behavior. Comment on your findings.

Excited states of C_{2} that interest us
here are the lowest states of the ^{1}Π_{u},
^{1}Δ_{g},
^{1}Σ_{u}^{+},
and ^{1}Π_{g} symmetries. They can be obtained as the
^{1}B_{3u} (or ^{1}B_{2u}),
^{1}B_{1g} (or ^{1}A_{g}),
^{1}B_{1u},
and ^{1}B_{2g} (or ^{1}B_{3g})
states, respectively, if the Abelian D_{2h} subgroup
of the D_{∞h} group is used. We will use the
^{1}B_{3u}, ^{1}B_{1g},
^{1}B_{1u}, and ^{1}B_{2g} symmmetries
to obtain the lowest-energy ^{1}Π_{u},
^{1}Δ_{g},
^{1}Σ_{u}^{+},
and ^{1}Π_{g} states
using the CASSCF, CASPT2, and MRCI(Q) methods in Molpro and
the EOMCCSD and CR-EOMCCSD(T) methods in Gamess.
The appropriate input files are described below.
Use **gmssub -l bignode file**, where 'file.inp' is the input file, to run
GAMESS.
Use **m06sub -l bignode file.inp** to run Molpro jobs.
Before running the calculations,
please examine the input files. We will discuss the meaning of each
keyword in the input files during the lab.

You will find the following input files in the subdirectory 'set2':

c2_molpro.inp - the Molpro input file for the CASSCF, MRCI, and MRCI(Q) calculations. c2_molpro-caspt2.inp - the Molpro input file for the CASSCF and CASPT2 calculations. c2_GAMESS.inp - the GAMESS input file for the EOMCCSD and CR-EOMCCSD(T) calculations.The corresponding output files, provided in the subdirectory 'OUTPUTS', have extensions '.log' for GAMESS and '.out' for Molpro.

**Things to do during the lab:**

1. Discuss the performance of CASPT2, MRCI(Q), EOMCCSD, and CR-EOMCCSD(T) relative to the exact full CI calculations, which give the following excitation energies for the states that interest us here (taken from O. Christiansen et al.,Chem. Phys. Lett.256, 185 (1996)):^{1}Π_{u}1.385 eV^{1}Δ_{g}2.293 eV^{1}Σ_{u}^{+}5.602 eV^{1}Π_{g}4.494 eV. In analyzing the CR-EOMCCSD(T) data, you may focus on the CR-EOMCCSD(T),ID and CR-EOMCCSD(T),ID/IB approaches. 2. Examine the GAMESS and Molpro outputs to learn about various elements of the calculations, steps that the CC, CASSCF, CASPT2, and MRCI(Q) calculations require, the largest EOMCCSD excitation amplitudes, and the so-called REL (reduced excitation level) diagnostic.

1. Create the following table (all energies in eV): State Full CI CASSCF CASPT2 MRCI(Q) EOMCCSD CR-EOMCCSD(T),ID CR-EOMCCSD(T),ID/IB REL^{1}Π_{u}1.385^{1}Δ_{g}2.293^{1}Σ_{u}^{+}5.602^{1}Π_{g}4.494 where the CASSCF, CASPT2, MRCI(Q), EOMCCSD, CR-EOMCCSD(T),ID, and CR-EOMCCSD(T),ID/IB excitation energies are reported as signed errors relative to full CI (i.e., as E(Method) - E(Full CI)) and the EOMCCSD REL values are extracted from the GAMESS output. 2. Provide a brief analysis of the results in the above table, focusing on the accuracy vs. ease-of-use (e.g., ease of setting up the input, costs of the calculations, etc.).