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Most methods require a basis set be specified; if no basis set keyword is included in the route section, then the STO-3G basis will be used. Note that there is only one CEP basis set defined beyond the second row, and all three keywords are equivalent for these atoms. These basis sets may be augmented with diffuse functions by adding the AUG- prefix to the basis set keyword (rather than using the + and ++ notation—see below).

Basis sets from of Ahlrichs and coworkers: the SV, SVP, TZV, TZVP keywords refer to the initial formations of the split valence and triple zeta basis sets from this group [Schaefer92, Schaefer94]. EPR-II and EPR-III: The basis sets of Barone [Barone96a] which are optimized for the computation of hyperfine coupling constants by DFT methods (particularly B3LYP). Diffuse functions may be added as usual with + or ++; the first of these may be specified as 2+ to add two diffuse functions for heavy atoms. MTSmall of Martin and de Oliveira, defined as part of their W1 method (see the W1U keyword) [Martin99]. CBSB7: Selects the 6-311G(2d,d,p) basis set used by CBS-QB3 high accuracy energy method [Montgomery99]. Single first polarization functions can also be requested using the usual * or ** notation. Nevertheless, by default, at least s and p diffuse functions are always included in these basis sets. When a frozen core calculation is done using the D95 basis, both the occupied core orbitals and the corresponding virtual orbitals are frozen.

STO-3G and 3-21G accept a * suffix, but this does not actually add any polarization functions.

Within a job, all d functions must be 5D or 6D, and all f and higher functions must be pure or Cartesian. Gaussian 09 provides the density fitting approximation for pure DFT calculations [Dunlap83, Dunlap00]. Note that slashes must be used as separator characters between the method, basis set, and fitting set when a density fitting basis set is specified. Density fitting sets can be generated automatically from the AO primitives within the basis set. Density fitting can be made the default for jobs using pure DFT functionals by adding the DenFit keyword to the route section (-#-) line in the Default.Route file. This is a typical transition metal system in which antiferromagnetic coupling is of interest: Mn2O2(NH3)8.

In doing computations on this set of molecules, it is easiest to start with the system having half-filled d shells (in this case, the neutral). This molecule can have D2h symmetry, so it is best to start the optimization from this high symmetry configuration.

We next replace two hydrogens with oxygens and then add the other Mn atom as a separate fragment. We go on to delete the two unneeded hydrogens on the second Mn atom, and then create the bonds between this atom and each oxygen atom, setting the bond length to the 1.83 Angstrom length we recorded. If D2h is not a selection listed in the popup menu when you build this molecule, symmetrize the molecule to the highest listed point group and them examine it in Inquire mode. Note that you must be sure to set the action for Atom 1 to Fixed to constrain movement in the molecule to rotation of the methyl group. The final step is to replace the carbon atoms with nitrogens, and then impose D2h symmetry one final time to produce the final input structure. Job 1: Here we optimize the structure for the high spin state from the input generated with GaussView. Note: When we actually ran this job, we also included additional directives in the route section specifying memory and the desired number of processors. Note: We copied the checkpoint file from the first job to the one named afc2 prior to running this job. As we suspected would be the case, a lower energy high spin state was found by the Stable=Opt job. Job 4: Check the stability of the high-spin wavefunction at the final geometry of the second optimization. Job 5: If the molecule did not have high symmetry, we would now be ready to use the high-spin wavefunction as input for the antiferromagnetic singlet. The resulting checkpoint file will be used to examine and select MOs for the antiferromagnetic single initial guess.

Initially, GaussView is a bit confused by having 11 open shells, so it starts out showing singlet as the Spin in the dialog. The 5 highest occupied orbitals from the high spin calculation are now the lowest 5 virtuals for the singlet. We need to move electrons around in both spin cases, so that each d orbital was occupied in exactly one spin case. The default contour level in GaussView is appropriate for valence, orbitals but is too small a value to pick up the d orbitals well. Once the orbital selection was complete, we used the dialog to drag electrons to the proper orbitals in both the alpha and beta lists. Job 6: Next, we generated the Gaussian input file for a single-point SCF calculation, adding Guess=Alpha to the Additional Keywords field. Note that this job is to be performed for the singlet, so we do not alter the spin multiplicity in the input file. The job produced a wavefunction which had a reasonable energy and which had spin densities of about +4 on one Mn and -4 on the other.

Note that Raghavachari and Trucks recommend both scaling and including diffuse functions when using the Wachters-Hay basis set for first transition row elements; the 6-311+G form must be specified to include the diffuse functions. These basis sets have had redundant functions removed and have been rotated [Davidson96] in order to increase computational efficiency. The second item is a code letter indicating which function should be augmented polarization functions: P adds them to all functions, V adds them to all valence functions, and O requests the scheme used in Gaussian 03 (see below).

The notation specifies two additional d polarization functions on second rows atoms, one d function on first row atoms and a p function on hydrogens (note that this three-field polarization function syntax is not supported by Gaussian 09). For example, the AUG-cc-pVTZ basis places one s, one d, and one p diffuse functions on hydrogen atoms, and one d, one p, one d, and one f diffuse functions on B through Ne and Al through Ar. This serves to avoid some inherent inconsistencies, but it differs from Truhlar and coworkersa€™ original definitions. 6-311G(d)) will result in one d function for first and second row atoms and one f function for first transition row atoms, since d functions are already present for the valence electrons in the latter. Thus while a D95** calculation on water has 26 basis functions, and a 6-31G** calculation on the same system has 25 functions, there will be 24 orbitals used in a frozen core post-SCF calculation involving either basis set. The ChkBasis keyword indicates that the basis set is to read from the checkpoint file (defined via the %Chk command).

This approach expands the density in a set of atom-centered functions when computing the Coulomb interaction instead of computing all of the two-electron integrals. Fitting is faster than doing the Coulomb term exactly for systems up to several hundred atoms (depending on basis set), but is slower than exact Coulomb using linear scaling techniques (which are turned on automatically with exact Coulomb) for very large systems.

In the netural molecule, in which the Mn atoms are nominally MnII, there are 5 d electrons on each Mn, and the antiferromagnetic singlet (5 alpha d electrons on one Mn and 5 beta d electrons on the other) may be the ground state. The rationale behind this approach is that because the charged systems with partially filled d shells give rise to additional issues of symmetry breaking in both the wavefunction and in the geometry. We then move it into its approximate position by holding down the Alt key while dragging it. We open the dialog (via the Edit=>Point Group menu path), and check Enable Point Group Symmetry. You may need to adjust some bond or dihedral angles manually in order for D2h symmetry to be recognized. First, we replace the four hydrogens which are above and below the plane of the heavy atoms.

In this case, you will almost certainly need to adjust dihedral atoms to achieve D2h symmetry. We leave the Spin set to Singlet since GaussView is currently limited to 9 as its highest spin multiplicity (this will be fixed in a future release). However, in this case, the two Mn atoms are equivalent in D2h symmetry, and so the d orbitals produced by the high-spin SCF are sums and differences of the d functions on each Mn. The next step is to generate an initial guess for the antiferromagnetic singlet, using the 5 unpaired orbitals from the high spin calculation which are primarily on one Mn atom as the highest five alpha orbitals in the guess, and the other 5 unpaired orbitals from the high spin as the highest five beta spin orbitals in the guess.

We open the afc5 checkpoint file in GaussView, and then open the Edit MOs dialog using the Edit=>MOs menu path.

However, you must select a different spin-state and then change the setting back to Singlet in order for GaussView to function properly (this will be fixed in a future release).

Most of the d orbitals were clear from inspection, but a couple are mixed with other occupied orbitals and so some care is required in inspecting the orbitals.

The closed-shell singlet was unstable, as expected, and a subsequent Stable=Opt found a wavefunction with Sz=0 which was lower in energy than the closed shell but not as low as the antiferromagnetic one, consistent with the antiferromagnetic state being the ground state.

EPR-III is a triple-zeta basis set including diffuse functions, double d-polarizations and a single set of f-polarization functions. For example, the UGBS1P keyword requests this basis set with one additional polarization function to all orbitals, and UGBS2V adds two additional polarization function to all valence orbitals. The + and ++ diffuse functions [Clark83] are available with some basis sets, as are multiple polarization functions [Frisch84]. Similarly, adding a diffuse function to the 6-311G basis set will produce one s, one p, and one d diffuse functions for third-row atoms. It provides significant performance gains for pure DFT calculations on medium sized systems too small to take advantage of the linear scaling algorithms without a significant degradation in the accuracy of predicted structures, relative energies and molecular properties. The options to the DensityFit keyword can be used to control some aspects of the fitting set used within calculations. The cations Mn2O2(NH3)8n+ (n=1-4) are also of interest and may also have antiferromagnetic ground states. So it is best to do the filled case first, and then use its orbitals as the initial guess for the other cases.

We change the tolerance to Very loose, and select D2h from the popup menu in the Approximate higher-order point groups section. After doing so, we again use the Point Group Symmetry dialog to return the molecule to D2h symmetry. After doing this, specify Unrestricted (alpha) as the Wavefunction, which says that the alpha orbitals will be used for both the alpha and beta guess orbitals. Orbitals exhibiting d character on both Mn atoms were assigned to one or other by determining which had the larger values.

The keyword syntax is best illustrated by example: 6-31+G(3df,2p) designates the 6-31G basis set supplemented by diffuse functions, 3 sets of d functions and one set of f functions on heavy atoms, and supplemented by 2 sets of p functions on hydrogens.

Note that basis functions are generally converted to the other type automatically when necessary, for example, when a wavefunction is read from the checkpoint file for use in a calculation using a basis consisting of the other type [Schlegel95a]. Likewise, if you want to add basis functions for Xe from the 3-21G basis set to the 6-311 basis set via the ExtraBasis keyword, the Xe basis functions will be pure functions. Gaussian 09 can generate an appropriate fitting basis automatically from the AO basis, or you may select one of the built-in fitting sets. You can request that all generated functions be used with Auto=All, or request those up to a certain level with Auto=N, where N is the maximum angular momentum retained in the fitting functions.

Finally, the PAuto form generates all products of AO functions on one center instead of just squares of the AO primitives, but this is typically more functions than are needed.

Basis sets from of Ahlrichs and coworkers: the SV, SVP, TZV, TZVP keywords refer to the initial formations of the split valence and triple zeta basis sets from this group [Schaefer92, Schaefer94]. EPR-II and EPR-III: The basis sets of Barone [Barone96a] which are optimized for the computation of hyperfine coupling constants by DFT methods (particularly B3LYP). Diffuse functions may be added as usual with + or ++; the first of these may be specified as 2+ to add two diffuse functions for heavy atoms. MTSmall of Martin and de Oliveira, defined as part of their W1 method (see the W1U keyword) [Martin99]. CBSB7: Selects the 6-311G(2d,d,p) basis set used by CBS-QB3 high accuracy energy method [Montgomery99]. Single first polarization functions can also be requested using the usual * or ** notation. Nevertheless, by default, at least s and p diffuse functions are always included in these basis sets. When a frozen core calculation is done using the D95 basis, both the occupied core orbitals and the corresponding virtual orbitals are frozen.

STO-3G and 3-21G accept a * suffix, but this does not actually add any polarization functions.

Within a job, all d functions must be 5D or 6D, and all f and higher functions must be pure or Cartesian. Gaussian 09 provides the density fitting approximation for pure DFT calculations [Dunlap83, Dunlap00]. Note that slashes must be used as separator characters between the method, basis set, and fitting set when a density fitting basis set is specified. Density fitting sets can be generated automatically from the AO primitives within the basis set. Density fitting can be made the default for jobs using pure DFT functionals by adding the DenFit keyword to the route section (-#-) line in the Default.Route file. This is a typical transition metal system in which antiferromagnetic coupling is of interest: Mn2O2(NH3)8.

In doing computations on this set of molecules, it is easiest to start with the system having half-filled d shells (in this case, the neutral). This molecule can have D2h symmetry, so it is best to start the optimization from this high symmetry configuration.

We next replace two hydrogens with oxygens and then add the other Mn atom as a separate fragment. We go on to delete the two unneeded hydrogens on the second Mn atom, and then create the bonds between this atom and each oxygen atom, setting the bond length to the 1.83 Angstrom length we recorded. If D2h is not a selection listed in the popup menu when you build this molecule, symmetrize the molecule to the highest listed point group and them examine it in Inquire mode. Note that you must be sure to set the action for Atom 1 to Fixed to constrain movement in the molecule to rotation of the methyl group. The final step is to replace the carbon atoms with nitrogens, and then impose D2h symmetry one final time to produce the final input structure. Job 1: Here we optimize the structure for the high spin state from the input generated with GaussView. Note: When we actually ran this job, we also included additional directives in the route section specifying memory and the desired number of processors. Note: We copied the checkpoint file from the first job to the one named afc2 prior to running this job. As we suspected would be the case, a lower energy high spin state was found by the Stable=Opt job. Job 4: Check the stability of the high-spin wavefunction at the final geometry of the second optimization. Job 5: If the molecule did not have high symmetry, we would now be ready to use the high-spin wavefunction as input for the antiferromagnetic singlet. The resulting checkpoint file will be used to examine and select MOs for the antiferromagnetic single initial guess.

Initially, GaussView is a bit confused by having 11 open shells, so it starts out showing singlet as the Spin in the dialog. The 5 highest occupied orbitals from the high spin calculation are now the lowest 5 virtuals for the singlet. We need to move electrons around in both spin cases, so that each d orbital was occupied in exactly one spin case. The default contour level in GaussView is appropriate for valence, orbitals but is too small a value to pick up the d orbitals well. Once the orbital selection was complete, we used the dialog to drag electrons to the proper orbitals in both the alpha and beta lists. Job 6: Next, we generated the Gaussian input file for a single-point SCF calculation, adding Guess=Alpha to the Additional Keywords field. Note that this job is to be performed for the singlet, so we do not alter the spin multiplicity in the input file. The job produced a wavefunction which had a reasonable energy and which had spin densities of about +4 on one Mn and -4 on the other.

Note that Raghavachari and Trucks recommend both scaling and including diffuse functions when using the Wachters-Hay basis set for first transition row elements; the 6-311+G form must be specified to include the diffuse functions. These basis sets have had redundant functions removed and have been rotated [Davidson96] in order to increase computational efficiency. The second item is a code letter indicating which function should be augmented polarization functions: P adds them to all functions, V adds them to all valence functions, and O requests the scheme used in Gaussian 03 (see below).

The notation specifies two additional d polarization functions on second rows atoms, one d function on first row atoms and a p function on hydrogens (note that this three-field polarization function syntax is not supported by Gaussian 09). For example, the AUG-cc-pVTZ basis places one s, one d, and one p diffuse functions on hydrogen atoms, and one d, one p, one d, and one f diffuse functions on B through Ne and Al through Ar. This serves to avoid some inherent inconsistencies, but it differs from Truhlar and coworkersa€™ original definitions. 6-311G(d)) will result in one d function for first and second row atoms and one f function for first transition row atoms, since d functions are already present for the valence electrons in the latter. Thus while a D95** calculation on water has 26 basis functions, and a 6-31G** calculation on the same system has 25 functions, there will be 24 orbitals used in a frozen core post-SCF calculation involving either basis set. The ChkBasis keyword indicates that the basis set is to read from the checkpoint file (defined via the %Chk command).

This approach expands the density in a set of atom-centered functions when computing the Coulomb interaction instead of computing all of the two-electron integrals. Fitting is faster than doing the Coulomb term exactly for systems up to several hundred atoms (depending on basis set), but is slower than exact Coulomb using linear scaling techniques (which are turned on automatically with exact Coulomb) for very large systems.

In the netural molecule, in which the Mn atoms are nominally MnII, there are 5 d electrons on each Mn, and the antiferromagnetic singlet (5 alpha d electrons on one Mn and 5 beta d electrons on the other) may be the ground state. The rationale behind this approach is that because the charged systems with partially filled d shells give rise to additional issues of symmetry breaking in both the wavefunction and in the geometry. We then move it into its approximate position by holding down the Alt key while dragging it. We open the dialog (via the Edit=>Point Group menu path), and check Enable Point Group Symmetry. You may need to adjust some bond or dihedral angles manually in order for D2h symmetry to be recognized. First, we replace the four hydrogens which are above and below the plane of the heavy atoms.

In this case, you will almost certainly need to adjust dihedral atoms to achieve D2h symmetry. We leave the Spin set to Singlet since GaussView is currently limited to 9 as its highest spin multiplicity (this will be fixed in a future release). However, in this case, the two Mn atoms are equivalent in D2h symmetry, and so the d orbitals produced by the high-spin SCF are sums and differences of the d functions on each Mn. The next step is to generate an initial guess for the antiferromagnetic singlet, using the 5 unpaired orbitals from the high spin calculation which are primarily on one Mn atom as the highest five alpha orbitals in the guess, and the other 5 unpaired orbitals from the high spin as the highest five beta spin orbitals in the guess.

We open the afc5 checkpoint file in GaussView, and then open the Edit MOs dialog using the Edit=>MOs menu path.

However, you must select a different spin-state and then change the setting back to Singlet in order for GaussView to function properly (this will be fixed in a future release).

Most of the d orbitals were clear from inspection, but a couple are mixed with other occupied orbitals and so some care is required in inspecting the orbitals.

The closed-shell singlet was unstable, as expected, and a subsequent Stable=Opt found a wavefunction with Sz=0 which was lower in energy than the closed shell but not as low as the antiferromagnetic one, consistent with the antiferromagnetic state being the ground state.

EPR-III is a triple-zeta basis set including diffuse functions, double d-polarizations and a single set of f-polarization functions. For example, the UGBS1P keyword requests this basis set with one additional polarization function to all orbitals, and UGBS2V adds two additional polarization function to all valence orbitals. The + and ++ diffuse functions [Clark83] are available with some basis sets, as are multiple polarization functions [Frisch84]. Similarly, adding a diffuse function to the 6-311G basis set will produce one s, one p, and one d diffuse functions for third-row atoms. It provides significant performance gains for pure DFT calculations on medium sized systems too small to take advantage of the linear scaling algorithms without a significant degradation in the accuracy of predicted structures, relative energies and molecular properties. The options to the DensityFit keyword can be used to control some aspects of the fitting set used within calculations. The cations Mn2O2(NH3)8n+ (n=1-4) are also of interest and may also have antiferromagnetic ground states. So it is best to do the filled case first, and then use its orbitals as the initial guess for the other cases.

We change the tolerance to Very loose, and select D2h from the popup menu in the Approximate higher-order point groups section. After doing so, we again use the Point Group Symmetry dialog to return the molecule to D2h symmetry. After doing this, specify Unrestricted (alpha) as the Wavefunction, which says that the alpha orbitals will be used for both the alpha and beta guess orbitals. Orbitals exhibiting d character on both Mn atoms were assigned to one or other by determining which had the larger values.

The keyword syntax is best illustrated by example: 6-31+G(3df,2p) designates the 6-31G basis set supplemented by diffuse functions, 3 sets of d functions and one set of f functions on heavy atoms, and supplemented by 2 sets of p functions on hydrogens.

Note that basis functions are generally converted to the other type automatically when necessary, for example, when a wavefunction is read from the checkpoint file for use in a calculation using a basis consisting of the other type [Schlegel95a]. Likewise, if you want to add basis functions for Xe from the 3-21G basis set to the 6-311 basis set via the ExtraBasis keyword, the Xe basis functions will be pure functions. Gaussian 09 can generate an appropriate fitting basis automatically from the AO basis, or you may select one of the built-in fitting sets. You can request that all generated functions be used with Auto=All, or request those up to a certain level with Auto=N, where N is the maximum angular momentum retained in the fitting functions.

Finally, the PAuto form generates all products of AO functions on one center instead of just squares of the AO primitives, but this is typically more functions than are needed.

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