Electronic Energy at Fixed Nuclear Geometry =========================================== The |molcas| suite of Quantum Chemical programs is modular in design, and a desired calculation is achieved by executing a list of |molcas| program modules in succession, occasionally manipulating the program information files. If the information files from a previous calculation are saved, then a subsequent calculation need not recompute them. This is dependent on the correct information being preserved in the information files for the subsequent calculations. Each module has keywords to specify the functions to be carried out, and many modules rely on the specification of keywords in previous modules. In the present examples the calculations will be designed by preparing a single file in which the input for the different programs is presented sequentially. The initial problem will be to compute an electronic energy at a fixed geometry of the nuclei, and this will be performed using different methods and thus requiring different |molcas| program modules. First, the proper |molcas| environment has to be set up which requires that following variables must be properly defined, for instance: :: export MOLCAS=/home/molcas/molcas export Project=CH4 export WorkDir=/home/user/tmp If not defined, |molcas| provides default values for the above environment variables: * The :variable:`MOLCAS` variable will be set to the latest implemented version of the code. This variable is set directly in the |molcas| home directory * :variable:`Project` and :variable:`WorkDir` have the default values None and $PWD, respectively. It is very important that the molcas driver, called by command :command:`molcas`, and built during the installation of the code, is included in the $PATH. The first run involves a calculation of the SCF energy of the methane (:math:`\ce{CH4}`) molecule. Three programs should be used: :program:`GATEWAY` to specify information about the system, :program:`SEWARD` to compute and store the one- and two-electron integrals, and :program:`SCF` to obtain the Hartree--Fock SCF wave function and energy. .. compound:: The three |molcas| programs to be used leads to three major entries in the input file: :program:`GATEWAY`, :program:`SEWARD`, and :program:`SCF`. The :program:`GATEWAY` program contains the nuclear geometry in cartesian coordinates and the label for the one-electron basis set. The keyword :kword:`coord` allows automatic insertion of :program:`GATEWAY` input from a standard file containing the cartesian coordinates in Angstrom which can be generated by programs like :program:`LUSCUS` or :program:`MOLDEN`). No symmetry is being considered so the keyword :kword:`group=C1` is used to force the program not to look for symmetry in the :math:`\ce{CH4}` molecule, and ,thus, input for :program:`SEWARD` is not required. In closed-shell cases, like :math:`\ce{CH4}`, input for :program:`SCF` is not required. All the input files discussed here can be found at :file:`$MOLCAS/doc/samples/problem_based_tutorials`, including the file :file:`SCF.energy.CH4` described below. .. extractfile:: problem_based_tutorials/SCF.energy.CH4.input *SCF energy for CH4 at a fixed nuclear geometry. *File: SCF.energy.CH4 * &GATEWAY Title = CH4 molecule coord = CH4.xyz basis = STO-3G group = C1 &SEWARD &SCF where the content of the :file:`CH4.xyz` file is: .. extractfile:: problem_based_tutorials/CH4.xyz 5 distorted CH4 coordinates in Angstroms C 0.000000 0.000000 0.000000 H 0.000000 0.000000 1.050000 H 1.037090 0.000000 -0.366667 H -0.542115 -0.938971 -0.383333 H -0.565685 0.979796 -0.400000 .. compound:: To run |molcas|, simply execute the command :: molcas SCF.energy.CH4.input > SCF.energy.CH4.log 2 > SCF.energy.CH4.err where the main output is stored in file :file:`SCF.energy.CH4.log` or :: molcas -f SCF.energy.CH4.input where the main output is stored in :file:`SCF.energy.CH4.log`, and the default error file in :file:`SCF.energy.CH4.err`. The most relevant information is contained in the output file, where the :program:`GATEWAY` program information describing the nuclear geometry, molecular symmetry, and the data regarding the one-electron basis sets and the calculation of one- and two-electron integrals, as described in :numref:`TUT:sec:seward`. Next, comes the output of program :program:`SCF` with information of the electronic energy, wave function, and the Hartree--Fock (HF) molecular orbitals (see :numref:`TUT:sec:scf`). Files containing intermediate information, integrals, orbitals, etc, will be kept in the $WorkDir directory for further use. For instance, files :file:`$Project.OneInt` and :file:`$Project.OrdInt` contain the one- and two-electron integrals stored in binary format. File :file:`$Project.ScfOrb` stores the HF molecular orbitals in ASCII format, and :file:`$Project.RunFile` is a communication file between programs. All these files can be used later for more advanced calculations avoiding a repeat of certain calculations. There are graphical utilities that can be used for the analysis of the results. By default, |molcas| generates files which can be read with the :program:`MOLDEN` program and are found in the :file:`$WorkDir` including the file :file:`CH4.scf.molden`. This file contains information about molecular geometry and molecular orbitals, and requires the use if *Density Mode* in :program:`MOLDEN`. However, |molcas| has its own graphical tool, program :program:`LUSCUS`, which is a viewer based on openGL and allows the visualization of molecular geometries, orbitals, densities, and density differences. For example, a graphical display of the :math:`\ce{CH4}` molecule can be obtained from a standard coordinate file by the following command: :: luscus CH4.xyz In order to obtain the information for displaying molecular orbitals and densities, it is necessary to run the |molcas| program called :program:`GRID_IT`: .. extractfile:: problem_based_tutorials/SCF.energy_grid.CH4.input *SCF energy for CH4 at a fixed nuclear geometry plus a grid for visualization. *File: SCF.energy_grid.CH4 * &GATEWAY Title = CH4 molecule coord = CH4.xyz basis = STO-3G Group = C1 &SEWARD; &SCF &GRID_IT All Now, execute the |molcas| program: :: molcas SCF.energy_grid.CH4.input -f .. compound:: In the :file:`$WorkDir` and :file:`$PWD` directories a new file is generated, :file:`CH4.lus` which contains the information required by the :program:`GRID_IT` input. The file can be visualized by :program:`LUSCUS` (Open source program, which can be downloaded and installed to your Linux, Windows, or MacOS workstation or laptop). By typing the command: :: luscus CH4.lus a window will be opened displaying the molecule and its charge density. By proper selection of options with the mouse buttons, the shape and size of several molecular orbitals can be visualized. :program:`GRID_IT` can also be run separately, if an orbital file is specified in the input, and the :file:`$WorkDir` directory is available. More information can be found in :numref:`UG:sec:gridit`. As an alternative to running a specific project, the short script provided below can be placed in the directory :file:`$MOLCAS/doc/samples/problem_based_tutorials` with the name :file:`project.sh`. Simply execute the shell script, :command:`project.sh $Project`, where :command:`$Project` is the |molcas| input, and output files, error files, and a :file:`$WorkDir` directory called :file:`$Project.work` will be obtained. .. extractfile:: problem_based_tutorials/project.sh #!/bin/bash export MOLCAS=$PWD export MOLCAS_DISK=2000 export MOLCAS_MEM=64 export MOLCAS_PRINT=3 export Project=$1 export HomeDir=$MOLCAS/doc/samples/problem_based_tutorials export WorkDir=$HomeDir/$Project.work mkdir $WorkDir 2>/dev/null molcas $HomeDir/$1 >$HomeDir/$Project.log 2>$HomeDir/$Project.err exit In order to run a Kohn--Sham density functional calculation, |molcas| uses the same :program:`SCF` module, and, therefore, the only change needed are the specification of the DFT option and required functional (e.g. B3LYP) in the :program:`SCF` input: .. extractfile:: problem_based_tutorials/DFT.energy.CH4.input *DFT energy for CH4 at a fixed nuclear geometry plus a grid for visualization. *File: DFT.energy.CH4 * &GATEWAY Title = CH4 molecule coord = CH4.xyz basis = STO-3G group = C1 &SEWARD &SCF KSDFT = B3LYP &GRID_IT All Similar graphical files can be found in :file:`$WorkDir` and :file:`$PWD`. The next step is to obtain the second-order Møller--Plesset perturbation (MP2) energy for methane at the same molecular geometry using the same one-electron basis set. Program :program:`MBPT2` is now used, and it is possible to take advantage of having previously computed the proper integrals with :program:`SEWARD` and the reference closed-shell HF wave function with the :program:`SCF` program. In such cases, it is possible to keep the same definitions as before and simply prepare a file containing the :program:`MBPT2` input and run it using the :command:`molcas` command. The proper intermediate file will be already in :file:`$WorkDir`. On the other hand, one has to start from scratch, all required inputs should be placed sequentially in the :file:`MP2.energy.CH4` file. If the decision is to start the project from the beginning, it is probably a good idea to remove the entire :file:`$WorkDir` directory, unless it is known for certain the exact nature of the files contained in this directory. .. extractfile:: problem_based_tutorials/MP2.energy.CH4.input *MP2 energy for CH4 at a fixed nuclear geometry. *File: MP2.energy.CH4 * &GATEWAY Title = CH4 molecule coord = CH4.xyz basis = STO-3G group = C1 &SEWARD &SCF &MBPT2 Frozen = 1 In addition to the calculation of a HF wave function, an MP2 calculation has been performed with a frozen deepest orbital, the carbon 1s, of :math:`\ce{CH4}`. Information about the output of the :program:`MBPT2` program can be found on :numref:`TUT:sec:mbpt2`. .. compound:: The :program:`SCF` program works by default with closed-shell systems with an even number of electrons at the Restricted Hartee--Fock (RHF) level. If, instead there is a need to use the Unrestricted Hartree--Fock (UHF) method, this can be schieved by invoking the keyword :kword:`UHF`. This is possible for both even and odd electron systems. For instance, in a system with an odd number of electrons such as the :math:`\ce{CH3}` radical, with the following Cartesian coordinates .. extractfile:: problem_based_tutorials/CH3.xyz 4 CH3 coordinates in Angstrom C 0.000000 0.000000 0.000000 H 0.000000 0.000000 1.050000 H 1.037090 0.000000 -0.366667 H -0.542115 -0.938971 -0.383333 the input to run an open-shell UHF calculation is easily obtained: .. extractfile:: problem_based_tutorials/SCF.energy_UHF.CH3.input *SCF/UHF energy for CH3 at a fixed nuclear geometry *File: SCF.energy_UHF.CH3 * &GATEWAY Title = CH3 molecule coord = CH3.xyz basis = STO-3G group = C1 &SEWARD &SCF UHF If the system is charged, this must be indicated in the :program:`SCF` input, for example, by computing the cation of the :math:`\ce{CH4}` molecule at the UHF level: .. extractfile:: problem_based_tutorials/SCF.energy_UHF.CH4plus.input *SCF/UHF energy for CH4+ at a fixed nuclear geometry *File: SCF.energy_UHF.CH4plus * &GATEWAY Title = CH4+ molecule coord = CH4.xyz basis = STO-3G group = c1 &SEWARD &SCF UHF Charge = +1 The Kohn--Sham DFT calculation can be also run using the UHF algorithm: .. extractfile:: problem_based_tutorials/DFT.energy.CH4plus.input *DFT/UHF energy for CH4+ at a fixed nuclear geometry *File: DFT.energy.CH4plus * &GATEWAY Title = CH4+ molecule coord = CH4.xyz basis = STO-3G group = C1 &SEWARD &SCF KSDFT = B3LYP UHF Charge = +1 For the UHF and UHF/DFT methods it is also possible to specify :math:`\alpha` and :math:`\beta` orbital occupations in two ways. #. First, the keyword :kword:`ZSPIn` can be invoked in the :program:`SCF` program, which represents the difference between the number of :math:`\alpha` and :math:`\beta` electrons. For example, setting the keyword to 2 forces the program to converge to a result with two more :math:`\alpha` than :math:`\beta` electrons. .. extractfile:: problem_based_tutorials/DFT.energy_zspin.CH4.input *DFT/UHF energy for different electronic occupation in CH4 at a fixed nuclear geometry *File: DFT.energy_zspin.CH4 * &GATEWAY Title = CH4 molecule coord = CH4.xyz basis = STO-3G group = c1 &SEWARD &SCF Title = CH4 molecule zspin 2 UHF; ZSPIN = 2 KSDFT = B3LYP The final occupations in the output will show six :math:`\alpha` and four :math:`\beta` orbitals. #. Alternatively, instead of :kword:`ZSPIn`, it is possible to specify occupation numbers with keyword :kword:`Occupation` at the beginning of the SCF calculation. This requires an additional input line containing the occupied :math:`\alpha` orbitals (e.g. 6 in this case), and a second line with the :math:`\beta` orbitals (e.g. 4 in this case). Sometimes, SCF convergence may be improved by using this option. Different sets of methods use other |molcas| modules. For example, to perform a Complete Active Space (CAS) SCF calculation, the :program:`RASSCF` program has to be used. This module requires starting trial orbitals, which can be obtained from a previous SCF calculation or, automatically, from the :program:`SEWARD` program which provides trial orbitals by using a model Fock operator. Recommended keywords are * :kword:`Nactel` defines the total number of active electrons, holes in Ras1, and particles in Ras3, respectively. The last two values are only for RASSCF-type calculations. * :kword:`Inactive` indicates the number of inactive orbitals where the occupation is always 2 in the CASSCF reference, and * :kword:`Ras2` defines the number of active orbitals. By default, the wave function for the lowest state corresponds to the symmetry with spin multiplicity of 1. Most of the input may not be necessary, if one has prepared and linked an INPORB file with the different orbital types defined by a program like :program:`LUSCUS`. .. extractfile:: problem_based_tutorials/CASSCF.energy.CH4.input *CASSCF energy for CH4 at a fixed nuclear geometry *File: CASSCF.energy.CH4 * &GATEWAY coord = CH4.xyz basis = STO-3G group = C1 &SEWARD &RASSCF Title = CH4 molecule Spin = 1; Nactel = 8 0 0; Inactive = 1; Ras2 = 8 &GRID_IT All In this case, the lowest singlet state (i.e. the ground dstate) is computed, since this is a closed-shell situation with an active space of eight electrons in eight orbitals and with an inactive C 1s orbital, the lowest orbital of the :math:`CH4` molecule. This is a CASSCF example in which all the valence orbitals and electrons (C 2s, C 2p and 4 |x| H 1s) are included in the active space and allows complete dissociation into atoms. If this is not the goal, then the three almost degenerate highest energy occupied orbitals and the corresponding antibonding unoccupied orbitalsmust be active, leading to a 6 in 6 active space. Using the CASSCF wave function as a reference, it is possible to perform a second-order perturbative, CASPT2, correction to the electronic energy by employing the :program:`CASPT2` program. If all previously calculated files are retained in the :file:`$WorkDir` directory, in particular, integral files (:file:`CH4.OneInt`, :file:`CH4.OrdInt`), the CASSCF wave function information file (:file:`CH4.JobIph`), and communication file :file:`CH4.RunFile`), it will not be necessary to re-run programs :program:`SEWARD`, and :program:`RASSCF`. In this case case, it is enough to prepare a file containing input only for the :program:`CASPT2` program followed be execution. Here, however, for the sake of completness, input to all |molcas| modules is provided: .. extractfile:: problem_based_tutorials/CASPT2.energy.CH4.input *CASPT2 energy for CH4 at a fixed nuclear geometry *File: CASPT2.energy.CH4 * &GATEWAY coord = CH4.xyz; basis = STO-3G; group = C1 &SEWARD &RASSCF LumOrb Spin = 1; Nactel = 8 0 0; Inactive = 1; Ras2 = 8 &CASPT2 Multistate = 1 1 In most of cases, the Hartree--Fock orbitals will be a better choice as starting orbitals. In that case, the :program:`RASSCF` input has to include keyword :kword:`LumOrb` to read from any external source of orbitals other than those generated by the :program:`SEWARD` program. By modifying input to the :program:`SCF` program, it is possible to generate alternative trial orbitals for the :program:`RASSCF` program. Since a new set of trial orbitals is used, the input to the :program:`RASSCF` program is also changed. Now, the number of active orbitals, as well as the number of active electrons, are 6. The two lowest orbitals (:kword:`Inactive` 2) are excluded from the active space and one other orbital is placed in the secondary space. If the previous (8,8) full valence space was used, the :program:`CASPT2` program would not be able to include more electronic correlation energy, considering that the calculation involves a minimal basis set. The input for the :program:`CASPT2` program includes a frozen C 1s orbital, the lowest orbital in the :math:`\ce{CH4}` molecule. The charge and multiplicity of our wave function can be changed by computing the :math:`\ce{CH4^+}` cation with the same methods. The :program:`RASSCF` program defines the character of the problem by specifying the number of electrons, the spin multiplicity, and the spatial symmetry. In the example below, there is one less electron giving rise to doublet multiplicity: .. extractfile:: problem_based_tutorials/CASSCF.energy.CH4plus.input *CASSCF energy for CH4+ at a fixed nuclear geometry *File: CASSCF.energy.CH4plus * &GATEWAY Title = CH4+ molecule coord = CH4.xyz; basis = STO-3G; Group = C1 &SEWARD &RASSCF Spin = 2; Nactel = 7 0 0; Inactive = 1; Ras2 = 8 No further modification is needed to the :program:`CASPT2` input: .. extractfile:: problem_based_tutorials/CASPT2.energy.CH4plus.input *CASPT2 energy for CH4+ at a fixed nuclear geometry *File: CASPT2.energy.CH4plus * &GATEWAY coord = CH4.xyz; basis = STO-3G; group = C1 &SEWARD &RASSCF Title = CH4+ molecule Spin = 2; Nactel = 1 0 0; Inactive = 4; Ras2 = 1 &CASPT2 A somewhat more sophisticated calculation can be performed at the Restricted Active Space (RAS) SCF level. In such a situation, the level of excitation in the CI expansion can be controlled by restricting the number of holes and particles present in certain orbitals. .. extractfile:: problem_based_tutorials/RASSCF.energy.CH4.input *RASSCF energy for CH4 at a fixed nuclear geometry *File: RASSCF.energy.CH4 * &GATEWAY coord = CH4.xyz; basis = STO-3G; group = C1 &SEWARD &RASSCF Title = CH4 molecule Spin = 1; Nactel = 8 1 1 Inactive = 1; Ras1 = 1; Ras2 = 6; Ras3 = 1 In particular, the previous calculation includes one orbital within the Ras1 space and one orbital within the Ras3 space. One hole (single excitation) at maximum is allowed from Ras1 to Ras2 or Ras3, while a maximum of one particle is allowed in Ras3, derived from either Ras1 or Ras2. Within Ras2, all types of orbital occupations are allowed. The RASSCF wave functions can be used as reference for multiconfigurational perturbation theory (RASPT2), but this approach has not been as extensively tested as CASPT2, and, so experience is still somewhat limited. |molcas| also has the possibility of computing electronic energies at different CI levels by using the :program:`MRCI` program. The input provided below involves a Singles and Doubles Configuration Interaction (SDCI) calculation on the :math:`\ce{CH4}` molecule. To set up the calculations, program :program:`MOTRA` which transforms the integrals to molecular basis, and program :program:`GUGA` which computes the coupling coefficients, must be run before the :program:`MRCI` program. In :program:`MOTRA` the reference orbitals are specifiedi, and those employed here are from an HF :program:`SCF` calculation including frozen orbitals. In :program:`GUGA` the reference for the CI calculation is described by the number of correlated electrons, the spatial and spin symmetry, the inactive orbitals always occupation 2 in the reference space, and the type of CI expansion. .. extractfile:: problem_based_tutorials/SDCI.energy.CH4.input *SDCI energy for CH4 at a fixed nuclear geometry *File: SDCI.energy.CH4 * &GATEWAY coord = CH4.xyz; basis = STO-3G; group = c1 &SEWARD &SCF &MOTRA Lumorb Frozen= 1 &GUGA Electrons = 8 Spin = 1 Inactive= 4 Active= 0 Ciall= 1 &MRCI SDCI To use reference orbitals from a previous CASSCF calculation, the :program:`RASSCF` program will have to be run before the :program:`MOTRA` module. Also, if the spatial or spin symmetry are changed for the CI calculation, the modifications will be introduced in the input to :program:`GUGA` program. Many alternatives are possible for performing an MRCI calculation as shown in the next example below, in which the reference space to perform the CI is multiconfigurational: .. extractfile:: problem_based_tutorials/MRCI.energy.CH4.input *MRCI energy for CH4 at a fixed nuclear geometry *File: MRCI.energy.CH4 * &GATEWAY Title = CH4 molecule coord = CH4.xyz; basis = STO-3G; group = c1 &SEWARD &SCF &RASSCF LumOrb Spin= 1; Nactel= 6 0 0; Inactive= 2; Ras2= 6 &MOTRA Lumorb Frozen= 1 &GUGA Electrons= 8 Spin= 1 Inactive= 2 Active= 3 Ciall= 1 &MRCI SDCI The :program:`MRCI` program also allows the calculation of electronic energies using the ACPF method. Another |molcas| program, :program:`CPF`, offers the possibility to use the CPF, MCPF, and ACPF methods with a single reference function. The required input is quite similar to that for the :program:`MRCI` program: .. extractfile:: problem_based_tutorials/CPF.energy.CH4.input *CPF energy for CH4 at a fixed nuclear geometry *File: CPF.energy.CH4 * &GATEWAY Title= CH4 molecule coord = CH4.xyz; basis = STO-3G; group = c1 &SEWARD &SCF &MOTRA Lumorb Frozen= 1 &GUGA Electrons= 8 Spin = 1 Inactive = 4 Active = 0 Ciall= 1 &CPF CPF End Of Input Finally, |molcas| can also perform closed- and open-shell coupled cluster calculations at the CCSD and CCSD(T) levels. These calculations are controlled by the :program:`CCSDT` program, whose main requirement is that the reference function has to be generated with the :program:`RASSCF` program. The following input is required to obtain a CCSD(T) energy for the :math:`\ce{CH4}` molecule: .. extractfile:: problem_based_tutorials/CCSDT.energy.CH4.input *CCSDT energy for CH4 at a fixed nuclear geometry *File: CCSDT.energy.CH4 * &GATEWAY Title= CH4 molecule coord = CH4.xyz; basis = STO-3G; group = c1 &SEWARD &RASSCF Spin= 1; Nactel= 0 0 0; Inactive= 5; Ras2= 0 OutOrbitals Canonical &MOTRA JobIph Frozen= 1 &CCSDT CCT Since this is a closed-shell calculation, the :program:`RASSCF` input computes a simple RHF wave function with zero active electrons and orbitals using keywords :kword:`OutOrbitals` and :kword:`Canonical`. The :program:`MOTRA` must include the keyword :kword:`JobIph` to extract the wave function information from file :file:`JOBIPH` which is automatically generated by :program:`RASSCF`. Finally, the keywork :kword:`CCT` in program :program:`CCSDT` leads to the calculation of the CCSD(T) energy using the default algorithms. The :program:`CCSDT` program in |molcas| is especially suited to compute open-shell cases. The input required to obtain the electronic energy of the :math:`\ce{CH4^+}` cation with the CCSD(T) method is: .. extractfile:: problem_based_tutorials/CCSDT.energy.CH4plus.input *CCSDT energy for CH4+ at a fixed nuclear geometry *File: CCSDT.energy.CH4plus * &GATEWAY Title= CH4+ molecule coord = CH4.xyz; basis = STO-3G; group = c1 &SEWARD &RASSCF Spin= 2; Nactel= 1 0 0; Inactive= 4; Ras2= 1 OutOrbitals Canonical &MOTRA JobIph Frozen= 1 &CCSDT CCT where the :program:`RASSCF` program generated the proper Restricted Open-Shell Hartree--Fock (ROHF) reference. Different levels of spin adaptation are also available. If solvent effects are desired, |molcas| includes two models: Kirkwood and PCM. Adding a solvent effect to a ground state at HF, DFT, or CASSCF levels, simply requires the inclusion of the keyword :kword:`RF-input` within the input for the :program:`SEWARD` which calculates a self-consistend reaction field. .. extractfile:: problem_based_tutorials/DFT.energy_solvent.CH4.input *DFT energy for CH4 in water at a fixed nuclear geometry *File: DFT.energy_solvent.CH4 * &GATEWAY Title= CH4 molecule coord = CH4.xyz; basis = STO-3G; group = c1 RF-input PCM-model; solvent= water End of RF-input &SEWARD &SCF KSDFT= B3LYP Other programs such as :program:`CASPT2`, :program:`RASSI`, and :program:`MOTRA` require that the reaction field is included as a perturbation with keyword :kword:`RFPErturbation`. In the next example the correction is added at both the CASSCF and CASPT2 levels. .. extractfile:: problem_based_tutorials/CASPT2.energy_solvent.CH4.input *CASPT2 energy for CH4 in acetone at a fixed nuclear geometry *File: CASPT2.energy_solvent.CH4 * &GATEWAY Title= CH4 molecule coord = CH4.xyz; basis = STO-3G; group = c1 RF-input PCM-model; solvent= acetone; AAre= 0.2 End of RF-input &SEWARD &RASSCF Spin= 1; Nactel= 6 0 0; Inactive= 2; Ras2= 6 &CASPT2 Frozen= 1 Multistate= 1 1 RFPert Notice that the tesserae of the average area in the PCM model (keyword has been changed to the value required for acetone by the keyword :kword:`Aare`, while the default is 0.4 Å:math:`^2` for water (see :numref:`UG:sec:rfield`). More detailed examples can be found in :numref:`TUT:sec:cavity`.