We are going to perform and analyze several quantum-chemistry calculations for the potential energy curve of HCl and electronic excitations in C2. 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 C2 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 C2, 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 C2 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 using gnuplot (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 of grep to prepare the corresponding data files and the use of gnuplot to 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' using gv. 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.Things to do after the lab as part of your homework assignment:
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 C2 that interest us here are the lowest states of the 1Πu, 1Δg, 1Σu+, and 1Πg symmetries. They can be obtained as the 1B3u (or 1B2u), 1B1g (or 1Ag), 1B1u, and 1B2g (or 1B3g) states, respectively, if the Abelian D2h subgroup of the D∞h group is used. We will use the 1B3u, 1B1g, 1B1u, and 1B2g symmmetries to obtain the lowest-energy 1Πu, 1Δg, 1Σu+, and 1Πg 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)): 1Πu 1.385 eV 1Δg 2.293 eV 1Σu+ 5.602 eV 1Πg 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.Things to do after the lab as part of your homework assignment:
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 1Πu 1.385 1Δg 2.293 1Σu+ 5.602 1Πg 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.).