Transition Moments and Spin-Orbit Coupling A review of various ways of computing spin-orbit coupling: D.G.Fedorov, S.Koseki, M.W.Schmidt, M.S.Gordon, Int.Rev.Phys.Chem. 22, 551-592(2003) GAMESS can compute transition moments and oscillator strengths for the radiative transitions between states written in terms of CI wavefunctions (GUGA only). The transition moments are computed using both the "length form" and the "velocity form". In a.u., where h-bar=m=1, we start from [A,q] = -i dA/dp For A=H, dH/dp=p, and p= -i d/dq, [H,q] = -i p = -d/dq. For non-degenerate states, = (Ea-Eb) = - This relates the dipole to the velocity form, = -1/(Ea-Eb) but the CI states will give different numbers for each side, since the states aren't exact eigenfunctions. Transition moment computation is OPERAT=DM in $TRANST. For transition moments, the CI is necessarily performed on states of the same multiplicity. All other operators are various spin-orbit coupling options. There are two kinds of calculations possible, which we will call SO-CI and SO-MCQDPT. Note that there is a hyphen in "spin-orbit CI" to avoid confusion with "second order CI" in the sense of the SOCI keyword in $DRT input. For SO-CI, the initial states may be any CI wave- function that the GUGA package can generate. For SO-MCQDPT the initial states for spin-orbit coupling are of CAS type, and the operator mixing them corresponds to MCQDPT generalised for spin-dependent operators (with certain approximations). GAMESS can compute the "microscopic Breit-Pauli spin-orbit operator", which includes both a one and two electron operator. Additional information is given in a subsection below states For transition moments, the states are generated by CI calculations using the GUGA package. These states are the final states, and the results are just the transition moments between these states. The states are defined by $DRTx input groups. For SO-CI, the energy of the CI states forms the diagonal of a spin-orbit Hamiltonian, as in the state basis the spin-free Hamiltonian is of course diagonal. Addition of the Pauli-Breit operator does not change the diagonal, but does add off-diagonal H-so elements. For SO-MCQDPT, the spin-free MCQDPT matrix elements are expanded into matrices corresponding to all Ms values for a pair of multiplicities. These matrices are block-diagonal before the addition of spin-orbit coupling terms, coupling Ms values. The diagonalization of this spin-orbit Hamiltonian gives new energy levels, and spin-mixed final states. Optionally, the transition dipoles between the final states can be computed. The input requirements are $DRTx or $MCQDx groups which define the original pure spin states. We will call the initial states CAS-CI, since most of the time they will be MCSCF states. There may be cases such as the Na example below where SCF orbitals are used, or other cases where a FOCI or SOCI wavefunction might be used for the initial states. Please keep in mind that the term does not imply the states must be MCSCF states, just that they commonly are. In the above, x may vary from 1 to 64. The reason for allowing such a large range is to permit the use of Abelian point group symmetry during the generation of the initial states. The best explanation will be an example, but the number of these input groups depends on both the number of orbital sets input, and how much symmetry is present. The next two subsections discuss these points. orbitals The orbitals for transition moments or for SO-CI can be one common set of orbitals used by all CI states. If one set of orbitals is used, the transition moment or spin- orbit coupling can be found for any type of GUGA CI wave- function. Alternatively, two sets of orbitals (obtained by separate MCSCF orbital optimizations) can be used. Two or more separate CIs will be carried out. The two MO sets must share a common set of frozen core orbitals, and the CI must be of the complete active space type. These restrictions are needed to leave the CI wavefunctions invariant under the necessary rotation to corresponding orbitals. The non-orthogonal procedure implemented is a GUGA driven equivalent to the method of Lengsfield, et al. Note that the FOCI and SOCI methods described by these workers are not available in GAMESS. If you would like to use separate orbitals during the CI, they may be generated with the FCORE option in $MCSCF. Typically you would optimize the ground state completely, then use these MCSCF orbitals in an optimization of the excited state, under the constraint of FCORE=.TRUE. For SO-MCQDPT calculations, only one set of orbitals may be input to describe all CAS-CI states. Typically that orbital set will be obtained by state-averaged MCSCF, see WSTATE in $DET/$DRT, and also in the $MCQDx input. Note that although the RUNTYP=TRANSITN driver is tied to the GUGA CI package, there is no reason the orbitals cannot be obtained using the determinant CI package. In fact, for the case of spin-orbit coupling, you might want to utilize the ability to state average over several spins, see PURES in $DET. If there is no molecular symmetry present, transition moment calculations will provide $DRT1 if there is one set of orbitals, otherwise $DRT1 defines the CI based on $VEC1 and $DRT2 the CI based on $VEC2. Also for the case of no symmetry, a spin-orbit job should enter one $DRTx or $MCQDx for every spin multiplicity, and all states of the same multiplicity have to be generated from $VEC1 or $VEC2, according to IVEX input. symmetry The CAS-CI states are most efficiently generated using symmetry, since states of different symmetry have zero Hamiltonian matrix elements. It is probably more efficient to do four CI calculations in the group C2v on A1, A2, B1, and B2 symmetry, than one CI with a combined Hamiltonian in C1 symmetry (unless the active space is very small), and similar remarks apply to the SO-MCQDPT case. In order to avoid repeatedly saying $DRTx or $MCQDx, the following few paragraphs say $DRTx only. Again supposing the group is C2v, and you are interested in singlet-triplet coupling. After some preliminary CI calculations, you might know that the lowest 8 states are two 1-a1, 1-b1, two 1-b2, one 3-a1, and two 3- b2 states. In this case your input would consist of five $DRTx, of which you can give the three singlets in any order but these must preceed the two triplet input groups to follow the rule of increasing multiplicity. Clearly it is not possible to write a formula for how many $DRTx there will be, this depends not only on the point group, but also the chemistry of the situation. If you are using two sets of orbitals, the generation of the corresponding orbitals for the two sets will permute the active orbitals in an unpredictable way. Use STSYM to define the desired state symmetry, rather than relying on the orbital order. It is easy and safer to be explicit about the spatial orbital symmetry. The users are encouraged to specify full symmetry in their $DATA input even though they may choose to set the symmetry in $DRTx to C1. The CI states will be labelled in the group given in $DATA. The use of non-Abelian symmetry is limited by the absence of non-Abelian CI or MCQDPT. In this case the users can choose between setting full non- Abelian symmetry in $DATA and C1 in $DRT or else an Abelian subgroup in both $DATA and $DRT. The latter choice appears to be most efficient at present. An example of SO-MCQDPT illustrating how the carbon atom of Kh symmetry (full rotation-reflection group) can be entered in D2h, Kh's highest Abelian group. The run time is considerably longer in C1 symmetry. As another example, consider an organic molecule with a singly excited state, where that state might be coupled to low or high spin, and where these two states might be close enough to have a strong spin-orbit coupling. If it happens that the S1 and S0 states possess different symmetry, a very reaasonable calculation would be to treat the S1 and T1 state with the same $VEC2 orbitals, leaving the ground state described by $VEC1. After doing an MCSCF on the S0 ground state for $VEC1, you could do a state-averaged MCSCF for $VEC2 optimized for T1 and S1 simultaneously, using PURES. The spin orbit job would obtain its initial states from three GUGA CI computations, S0 from $VEC1 and $DRT1, S1 from $VEC2 and $DRT2, and T1 from $VEC2 and $DRT3. Your $TRANST would be NUMCI=3, IROOTS(1)=1,1,1, IVEX(1)=1,2,2. Note that the second IROOTS value is 1 because S1 was presumed to have a different symmetry than S0, so STSYM in $DRT1 and $DRT2 will differ. The calculation just outlined cannot be done if S0 and S1 have the same spatial symmetry, as IROOTS(1)=1,2,1 to obtain S1 during the second CI will bring in an additional S0 state (one expressed in terms of the $VEC2, at slightly higher energy). This problem is the origin of the statement several paragraphs above that a system with no symmetry will have one $DRTx for every spin multiplicity included. For transition moments, which do not diagonalize a matrix containing these duplicated states, it is OK to proceed, provided you ignore all transition moments between the same states obtained in the two different CIs. spin orbit coupling Spin-orbit coupling calculations are always performed in a quasi-degenerate perturbative manner. Typically the states close in energy are included into the spin-orbit coupling matrix. "Close" has a easily understandable meaning, since in the limit of small coupling the quasi- degenerate treatment is reduced to a second order perturbative treatment, that is, the affect of a state upon the state of primary interest is given by the square of the spin-orbit coupling matrix element divided by the difference of the adiabatic energies. This is useful to keep in mind when deciding how many CI states to include in the matrix. The states that are included are treated in a fashion that is equivalent to infinite order perturbation theory (exact) whereas the states that are not included make no contribution. Spin-orbit runs can be done for even or odd numbers of electrons (any spin), for more than two different spin multiplicities at once, for general active spaces. At times, when the spatial wavefunction is degenerate, a spin- orbit run might involve only one spin multiplicity, e.g. a triplet-pi state in a linear molecule. The most common case is two different spins, with non-zero spin orbit coupling possible only for delta-S=1: singlets spin-orbit couple with triplets, but not with quintets. Use of three spins, such as S=0,1,2, will generate couplings between singlets and triplets, and between triplets and quintets, which together engender an indirect singlet/quintet mixing. As noted above, the treatment of spin-orbit involves first obtaining a handful of spin-pure states, whose energies form the diagonal of a model Hamiltonian. The spin-orbit operator introduces off-diagonal couplings, and the resulting small Hamiltonian is diagonalized. This generates spin-mixed states in the model space. Since the model states are not fully relaxed (internally contracted), this is essentially a perturbative treatment: certainly the spin-orbit effects have no influence on orbital optimizations or potential energy surfaces when treated in this manner, at the very last stage. The Breit-Pauli spin-orbit operator contains a one electron term arising from Pauli's reduction of the Dirac hydrogenic equation to a single-component form, and a two electron term due to Breit. Computation of the full Breit- Pauli operator is OPERAT=HSO2 (or HSOFF). A close approximation to the latter is HSO2P (P=partial), which neglects all active-active two electron terms, which usually do not contribute very much to the total coupling, while saving substantial computer time. HSO1 completely omits the two electron terms, so is much faster than any of the two electron operators, but represents a potentially much greater loss of accuracy. HSO1's error can be remedied to some extent by regarding the nuclear charge in the one electron term as an adjustable parameter. In addition, these effective charges are often used to compensate for missing nodes in valence orbitals of ECP runs, in which case the ZEFF are typically very far from the two nuclear charges. ZEFTYP selects some built in values obtained by S.Koseki et al, but if you have some favorite parameters, they can be read in as the ZEFF input array. Effective charges may be used for any OPERAT, but are most often used with HSO1. Theoretical considerations indicate that the Breit- Pauli operator is not variationally stable, if it were to be used during the SCF iterations determining orbitals. However, a first order Douglas-Kroll type correction to the one electron part of the operator reduces its size by means of certain kinematic factors, removing this problem. This can produce substantially better results, even if the operator is being treated pertubatively. This correction (at first order) is automatically applied to the one electron part of the Breit-Pauli operator by any run that selects RELWFN=DK (at any order) in the scalar relativity treatment during the variational steps prior to the spin- orbit perturbation. See paper 32 below. Because the diagonalization of the model spin-orbit Hamiltonian leads to spin-mixed eigenvectors, approximate wavefunctions including spin-orbit coupling are generated. It is now possible to generate the density matrix for the spin-mixed states, so that property values for spin-mixed states can be found: see keyword ISTNO. The natural orbitals of these spin-orbit density matrices turn out to be good approximations to the two spinors of the large components of full Dirac four component runs. The total density of these spinors can be obtained for interpretation purposes. Recognition that the spin-orbit coupling is a rotational operator (L dot S, where L = R cross P) when it acts on an orbital can lead to chemical interpretability of the spin orbit results. See papers 40 and 41 below. It is also possible to obtain the dipole transition moments between the final spin-mixed wavefunctions, which of course do not any longer have a rigourous S quantum no. When the run is SO-MCQDPT, the transition moment are first computed only between CAS states, and then combined with the spin-mixed SO-MCQDPT coefficients. technical matters: The only practical limitation on the computation of the Breit term is that HSO2FF is limited to 10 active orbitals on 32 bit machines, and to about 26 active orbitals on 64 bit machines. The spin-orbit matrix elements vanish for |delta-S| > 1, but it is possible to include three or more spins in the computation. Since singlets interact with triplets, and triplets interact with pentuplets, inclusion of S=0,1,2 simultaneously lets you pick up the indirect interaction between singlets and pentuplets that the intermediate triplets afford. The choice between HSO2 and HSO2FF is very often in favor of the former. HSO2 computes the matrix elements in CSF basis and then contracts them with CI coefficients, whereas HSO2FF uses a generalized density in AO basis computed for each pair of states, thus HSO2 is much more efficient in case of multiple states given in IROOTS. HSO2FF takes less memory for integral storage, thus it can be superior in case of small active spaces and large basis sets, in part because it does not store 2e SOC integrals on disk and secondly, it does not redundantly treat the same pair of determinants if they appear in different CSFs. The numerical results with HSO2 and HSO2FF should be identical within machine and algorithmic accuracy. Various symmetries are used to avoid computing zero spin-orbit matrix elements. NOSYM in $TRANST allows some control over this: NOSYM=1 gives up point group symmetry completely, while 2 turns off additional symmetries such as spin selection rules. HSO1,2,2P compute all matrix elements in a group (i.e. between two $DRTx groups with fixed Ms(ket)-Ms(bra)) if at least one of them does not vanish by symmetry, and HSO2P actually avoids computation for each pair of states if forbidden by symmetry. Setting NOSYM=2 will cause HSO2FF to consider the elements between two singlets, which are always calculated for HSO1,2,2P when transition dipoles are requested as well. SYMTOL has a dramatic effect on the run speed. This cutoff is applied to CSF coefficcients, their products, and these products times CSF orbital overlaps. The value permits a tradeoff of accuracy for run time, and since the error in the spin-orbit properties approaches SYMTOL mainly for SOCI functions, it may be useful to increase SYMTOL to save time for CAS or FOCI functions. Some experimenting will tell you what you can get away with. SYMTOL is also used during CI state symmetry assignment, for NOIRR=-1 in $DRT. In case if you do not provide enough storage for the form factors sorting then some extra disk space will be used; the extra disk space can be eliminated if you set SAVDSK=.TRUE. (the amount of savings depends on the active space and memory provided, it some cases it can decrease the disk space up to one order of magnitude). The form factors are in binary format, and so can be transfered between computers only if they have compatible binary files. There is a built-in check for consistency of a restart file DAFL30 with the current run parameters. input nitty-gritty The transition moment and spin-orbit coupling driver is a rather restricted path through the GUGA CI part of GAMESS. Note that $GUESS is not read, instead the MOs will be MOREAD in a $VEC1 and perhaps a $VEC2 group. It is not possible to reorder MOs. For SO-CI, 1) Give SCFTYP=NONE CITYP=GUGA MPLEVL=0. 2) $CIINP is not read. The CI is hardwired to consist of CI DRT generation, integral transformation/sorting, Hamiltonian generation, and diagonalization. This means $DRT1 (and maybe $DRT2,...), $TRANS, $CISORT, $GUGEM, and $GUGDIA input is read, and acted upon. 3) The density matrices are not generated, and so no properties (other than the transition moment or the spin-orbit coupling) are computed. 4) There is no restart capability provided, except for saving some form-factor information. 5) $DRT1, $DRT2, $DRT3, ... must go from lowest to highest multiplicity. 6) IROOTS will determine the number of CI states in each CI for which the properties are calculated. Use NSTATE to specify the number of CI states for the CI Hamiltonian diagonalization. Sometimes the CI convergence is assisted by requesting more roots to be found in the diagonalization than you want to include in the property calculation. For SO-MCQDPT, the steps are 1) Give SCFTYP=NONE CITYP=NONE MPLEVL=2. 2) the number of roots in each MCQDPT is controlled by $TRANST's IROOTS, and each such calculation is defined by $MCQD1, $MCQD2, ... input. These must go from lowest multiplicity to highest. references The review already mentioned: "Spin-orbit coupling in molecules: chemistry beyond the adiabatic approximation". D.G.Fedorov, S.Koseki, M.W.Schmidt, M.S.Gordon, Int.Rev.Phys.Chem. 22, 551-592(2003) Reference for separate active orbital optimization: 1. B.H.Lengsfield, III, J.A.Jafri, D.H.Phillips, C.W.Bauschlicher, Jr. J.Chem.Phys. 74,6849-6856(1981) References for transition moments: 2a. H.C.Longuet-Higgins Proc.Roy.Soc.(London) A235, 537-543(1956) 2b. F.Weinhold, J.Chem.Phys. 54,1874-1881(1970) 3. C.W.Bauschlicher, S.R.Langhoff Theoret.Chim.Acta 79:93-103(1991) 4. "Intermediate Quantum Mechanics, 3rd Ed." Hans A. Bethe, Roman Jackiw Benjamin/Cummings Publishing, Menlo Park, CA (1986), chapters 10 and 11. 5. S.Koseki, M.S.Gordon J.Mol.Spectrosc. 123, 392-404(1987) References for HSO1 spin-orbit coupling, and Zeff values: 6. S.Koseki, M.W.Schmidt, M.S.Gordon J.Phys.Chem. 96, 10768-10772 (1992) 7. S.Koseki, M.S.Gordon, M.W.Schmidt, N.Matsunaga J.Phys.Chem. 99, 12764-12772 (1995) 8. N.Matsunaga, S.Koseki, M.S.Gordon J.Chem.Phys. 104, 7988-7996 (1996) 9. S.Koseki, M.W.Schmidt, M.S.Gordon J.Phys.Chem.A 102, 10430-10435 (1998) 10. S.Koseki, D.G.Fedorov, M.W.Schmidt, M.S.Gordon J.Phys.Chem.A 105, 8262-8268 (2001) 11. S.Koseki, T.Matsushita, M.S.Gordon J.Phys.Chem.A 110, 2560-2570(2006) References for full Breit-Pauli spin-orbit coupling: 20. T.R.Furlani, H.F.King J.Chem.Phys. 82, 5577-5583 (1985) 21. H.F.King, T.R.Furlani J.Comput.Chem. 9, 771-778 (1988) 22. D.G.Fedorov, M.S.Gordon J.Chem.Phys. 112, 5611-5623 (2000) Paper 22 contains information on the HSO2P partial two electron operator method. Symmetry in spin-orbit coupling: 23. D.G.Fedorov, M.S.Gordon ACS Symposium Series 828, pp 1-22(2002) Reference for SO-MCQDPT: 25. D.G.Fedorov, J.P.Finley Phys.Rev.A 64, 042502 (2001) Reference for Spin-Orbit with Model Core Potentials: 30. D.G.Fedorov, M.Klobukowski Chem.Phys.Lett. 360, 223-228(2002) 31. T.Zeng, D.G.Fedorov, M.Klobukowski J.Chem.Phys. 131, 124109/1-17(2009) 32. T.Zeng, D.G.Fedorov, M.Klobukowski J.Chem.Phys. 132, 074102/1-15(2010) The last two of these also discuss the 1st order Douglas- Kroll transformation of the 1e- part of the spin orbit operator. Reference for properties, interpretations, and Spin-Orbit Natural Spinors: 40. T. Zeng, D. G. Fedorov, M. W. Schmidt, M. Klobukowski J. Chem. Phys. 134, 214107/1-9(2011) 41. T. Zeng, D. G. Fedorov, M. W. Schmidt, M. Klobukowski J. Chem. Theor. Comput. 7, 2864-2875(2011) with an application being 42. T.Zeng, D.G.Federov, M.W.Schmidt, M.Klobukowski J.Chem.Theo.Comput. 8, 3061-3071(2012). Recent applications (see also 32,40,41): 50. S.P.Webb, M.S.Gordon J.Chem.Phys. 109, 919-927(1998) 51. D.G.Fedorov, M.Evans, Y.Song, M.S.Gordon, C.Y.Ng J.Chem.Phys. 111, 6413-6421 (1999) 52. D.G.Fedorov, M.S.Gordon, Y.Song, C.Y.Ng J.Chem.Phys. 115, 7393-7400 (2001) 53. B.J.Duke J.Comput.Chem. 22, 1552-1556 (2001) 54. C.M.Aikens, M.S.Gordon J.Phys.Chem.A 107, 104-114(2003) 55. D.G.Fedorov, S.Koseki, M.W.Schmidt, M.S.Gordon K.Hirao and Y.Ishikawa (eds.) Recent Advances in Relativistic Molecular Theory, Vol. 5, (World Scientific, Singapore), 2004, pp 107-136. * * * Special thanks to Bob Cave and Dave Feller for their assistance in performing check spin-orbit coupling runs with the MELDF programs. Special thanks to Tom Furlani for contributing his 2e- spin-orbit code and answering many questions about its interface. Special thanks to Haruyuki Nakano for explaining the spin functions used in the MCQDPT package. examples We end with 2 examples. Note that you must know what you are doing with term symbols, J quantum numbers, point group symmetry, and so on in order to make skillful use of this part of the program. Seeing your final degeneracies turn out like a text book says it should is beautiful! ! Compute the splitting of the famous sodium D line. ! Joseph von Fraunhofer (Denkschriften der Koeniglichen ! Akademie der Wissenschf. zu Muenchen, 5, 193(1814-1815)) ! observed the sun through good prisms, finding 700 lines, ! and named the brightest ones A, B, C... just in order. ! He was able to resolve the D line into two lines, which ! occur at 5895.940 and 5889.973 Angstroms. It would take ! a century to understand the D line is Na's 3s <-> 3p ! transition, and that spin-orbit coupling is what splits ! the D line into two. Charlotte Moore's Atomic Energy ! Levels, volume 1, gives the experimental 2-P interval ! as 17.1963, since the three relevent levels are at ! 2-S-1/2= 0.0, 2-P-1/2= 16,956.183, 2-P-3/2= 16,973.379. 1. generate ground state 2-S orbitals by conventional ROHF. the energy of the ground state is -161.8413919816 --- $contrl scftyp=rohf mult=2 $end --- $system kdiag=3 memory=300000 $end --- $guess guess=huckel $end 2. generate excited state 2-P orbitals, using a state- averaged SCF wavefunction to ensure radial degeneracy of the 3p shell is preserved. The open shell SCF energy is -161.7682895801. The computation is both spin and space restricted open shell SCF on the 2-P Russell-Saunders term. Starting orbitals are reordered orbitals from step 1. --- $contrl scftyp=gvb mult=2 $end --- $system kdiag=3 memory=300000 $end --- $guess guess=moread norb=13 --- norder=1 iorder(6)=7,8,9,6 $end --- $scf nco=5 nseto=1 no(1)=3 rstrct=.t. couple=.true. --- f(1)= 1.0 0.16666666666667 --- alpha(1)= 2.0 0.33333333333333 0.0 --- beta(1)= -1.0 -0.16666666666667 0.0 $end 3. compute spin-orbit coupling in the 2-P term. The use of C1 symmetry in $DRT1 ensures that all three spatial CSFs are kept in the CI function. In the preliminary CI, the spin function is just the alpha spin doublet, and all three roots should be degenerate, and furthermore equal to the GVB energy at step 2. The spin-orbit coupling code uses both doublet spin functions with each of the three spatial wavefunctions, so the spin-orbit Hamiltonian is a 6x6 matrix. The two lowest roots of the full 6x6 spin-orbit Hamiltonian are the doubly degenerate 2-P-1/2 level, while the other four roots are the degenerate 2-P-3/2 level. $contrl scftyp=none cityp=guga runtyp=transitn mult=2 $end $system memory=2000000 $end $basis gbasis=n31 ngauss=6 $end $gugdia nstate=3 $end $transt operat=hso1 numvec=1 numci=1 nfzc=5 nocc=8 iroots=3 zeff=10.04 $end $drt1 group=c1 fors=.true. nfzc=5 nalp=1 nval=2 $end $data Na atom...2-P excited state...6-31G basis Dnh 2 Na 11.0 $end --- GVB ORBITALS --- GENERATED AT 7:46:08 CST 30-MAY-1996 Na atom...2-P excited state E(GVB)= -161.7682895801, E(NUC)= .0000000000, 5 ITERS $VEC1 1 1 9.97912679E-01 8.83038094E-03 0.00000000E+00... ... orbitals from step 2 go here ... 13 3-1.10674398E+00 0.00000000E+00 0.00000000E+00 $END As an example of both SO-MCQDPT, and the use of as much symmetry as possible, consider carbon. The CAS-CI uses an active space of 2s,2p,3s,3p orbitals, and the spin-orbit job includes all terms from the lowest configuration, 2s2,2p2. These terms are 3-P, 1-D, and 1-S. If you look at table 58 in Herzberg's book on electronic spectra, you will be able to see how the Kh spatial irreps P, D, S are partitioned into the D2h irreps input below. ! C SO-MRMP on all levels in the s**2,p**2 configuration. ! ! levels CAS and MCQDPT ! 1 .0000 .0000 cm-1 3-P-0 ! 2-4 12.6879-12.8469 13.2721-13.2722 3-P-1 ! 5-9 37.8469-37.8470 39.5638-39.5639 3-P-2 ! 10-14 12169.1275 10251.7910 1-D-2 ! 15 19264.4221 21111.5130 1-S-0 ! ! The active space consists of (2s,2p,3s,3p) with 4 e-. ! D2h symmetry speeds up the calculation considerably, ! on the same computer D2h = 78 and C1 = 424 seconds. $contrl scftyp=none cityp=none mplevl=2 runtyp=transitn $end $system memory=5000000 $end ! ! below is input to run in C1 subgroup ! --- $transt operat=hso2 numvec=-2 numci=2 nfzc=1 nocc=9 --- iroots(1)=6,3 parmp=3 --- ivex(1)=1,1 $end --- $mrmp mrpt=mcqdpt rdvecs=.t. $end --- $MCQD1 nosym=1 nstate=6 mult=1 iforb=3 --- nmofzc=1 nmodoc=0 nmoact=8 --- wstate(1)=1,1,1,1,1,1 thrcon=1e-8 thrgen=1e-10 $END --- $MCQD2 nosym=1 nstate=3 mult=3 iforb=3 --- nmofzc=1 nmodoc=0 nmoact=8 --- wstate(1)=1,1,1 thrcon=1e-8 thrgen=1e-10 $END ! ! below is input to run in D2h subgroup ! $transt operat=hso2 numvec=-7 numci=7 nfzc=1 nocc=9 iroots(1)=3,1,1,1, 1,1,1 parmp=3 ivex(1)=1,1,1,1,1,1,1 $end $mrmp mrpt=mcqdpt rdvecs=.t. $end $MCQD1 nosym=-1 mult=1 iforb=3 nmofzc=1 nmodoc=0 nmoact=8 stsym=Ag wstate(1)=1,1,1 thrcon=1e-8 thrgen=1e-10 $END $MCQD2 nosym=-1 mult=1 iforb=3 nmofzc=1 nmodoc=0 nmoact=8 stsym=B1g wstate(1)=1 thrcon=1e-8 thrgen=1e-10 $END $MCQD3 nosym=-1 mult=1 iforb=3 nmofzc=1 nmodoc=0 nmoact=8 stsym=B2g wstate(1)=1 thrcon=1e-8 thrgen=1e-10 $END $MCQD4 nosym=-1 mult=1 iforb=3 nmofzc=1 nmodoc=0 nmoact=8 stsym=B3g wstate(1)=1 thrcon=1e-8 thrgen=1e-10 $END $MCQD5 nosym=-1 mult=3 iforb=3 nmofzc=1 nmodoc=0 nmoact=8 stsym=B1g wstate(1)=1 thrcon=1e-8 thrgen=1e-10 $END $MCQD6 nosym=-1 mult=3 iforb=3 nmofzc=1 nmodoc=0 nmoact=8 stsym=B2g wstate(1)=1 thrcon=1e-8 thrgen=1e-10 $END $MCQD7 nosym=-1 mult=3 iforb=3 nmofzc=1 nmodoc=0 nmoact=8 stsym=B3g wstate(1)=1 thrcon=1e-8 thrgen=1e-10 $END ! ! input to prepare the 3-P ground state orbitals ! great care is taken to create symmetry equivalent p's ! --- $contrl scftyp=mcscf cityp=none mplevl=0 --- runtyp=energy mult=3 $end --- $guess guess=moread norb=55 purify=.t. $end --- $mcscf cistep=guga fullnr=.t. $end --- $drt group=c1 fors=.true. --- nmcc=1 ndoc=1 nalp=2 nval=5 $end --- $gugdia nstate=9 maxdia=1000 $end --- $gugdm2 wstate(1)=1,1,1 $end ! $data C...aug-cc-pvtz (10s,5p,2d,1f) -> [4s,3p,2d,1f] (1s,1p,1d,1f) Dnh 2 C 6.0 S 8 1 8236.000000 0.5310000000E-03 2 1235.000000 0.4108000000E-02 3 280.8000000 0.2108700000E-01 4 79.27000000 0.8185300000E-01 5 25.59000000 0.2348170000 6 8.997000000 0.4344010000 7 3.319000000 0.3461290000 8 0.3643000000 -0.8983000000E-02 S 8 1 8236.000000 -0.1130000000E-03 2 1235.000000 -0.8780000000E-03 3 280.8000000 -0.4540000000E-02 4 79.27000000 -0.1813300000E-01 5 25.59000000 -0.5576000000E-01 6 8.997000000 -0.1268950000 7 3.319000000 -0.1703520000 8 0.3643000000 0.5986840000 S 1 1 0.9059000000 1.000000000 S 1 1 0.1285000000 1.000000000 P 3 1 18.71000000 0.1403100000E-01 2 4.133000000 0.8686600000E-01 3 1.200000000 0.2902160000 P 1 1 0.3827000000 1.000000000 P 1 1 0.1209000000 1.000000000 D 1 1 1.097000000 1.000000000 D 1 1 0.3180000000 1.000000000 F 1 1 0.7610000000 1.000000000 S 1 1 0.440200000E-01 1.00000000 P 1 1 0.356900000E-01 1.00000000 D 1 1 0.100000000 1.00000000 F 1 1 0.268000000 1.00000000 $end --- OPTIMIZED MCSCF MO-S --- GENERATED 22-AUG-2000 E(MCSCF)= -37.7282408589, 11 ITERS $VEC1 1 1 9.75511467E-01 ...snipped... $END