:orphan: ========================================== Getting excited states of :math:`Ir^{16+}` ========================================== In the following we are interested in getting the ground (:math:`^{2}S_{1/2}`) and two closest excited states (:math:`^{2}P_{1/2}`, :math:`^{2}P_{3/2}`) of the :math:`Ir^{16+}` cation and their correlation energies. The electronic configurations of these states are :: (^2S) : [Xe] 4f(14) 5s(1) 5p1/2(0) 5p3/2(0) (^2P_1/2) : [Xe] 4f(14) 5s(0) 5p1/2(1) 5p3/2(0) (^2P_3/2) : [Xe] 4f(14) 5s(0) 5p1/2(0) 5p3/2(1) For simplicity, we will work with the wo-component Hamiltonian (:ref:`HAMILTONIAN_.X2C`) and employ the smallest *v2z* decontracted basis set by K.Dyall. Due to the convergence problem of the standalone AMFI atomic SCF code we keep the +2 charge (:ref:`AMFI_.AMFICH`) for mean-field orbitals. There are two ways to obtain excited states - (i) from the converged SCF state, and, (ii) only at the correlated level from the 2P_aver SCF state. For subsequent Coupled Cluster (CC) correlated calculations please soften the DHOLU variable in the subroutine DENOM (file *src/relccsd/cceqns.F*) to the value of 5.0D-4 and recompile DIRAC. Note that this is not recommended approach as the *p32* states are in general not well described at the CC level. Nevertheless, with this little trick we can compare desired excited states calculated with both CC and Fock-space CC methods. The :math:`^{2}S_{1/2}` ground state ------------------------------------ Thanks to the linear symmetry, having two irreps, one can place the unpaired electron the 1st irrep to get the :math:`^{2}S_{1/2}` ground state. SCF calculations are followed by two CC calculations, where in the second one uses orbital energies for denominators. :: pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2S12.scf_cc33e.2fs.inp pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2S12.scf_cc33e_oe.2fs.inp Input files to download are :download:`Ir.dyall_v2z.lsym.mol <../../../../test/tutorial_Ir_16plus/Ir.dyall_v2z.lsym.mol>`, :download:`Z61.x2c.2S12.scf_cc33e.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2S12.scf_cc33e.2fs.inp>`, :download:`Z61.x2c.2S12.scf_cc33e_oe.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2S12.scf_cc33e_oe.2fs.inp>`. Corresponding output files are :download:`Z61.x2c.2S12.scf_cc33e.2fs_Ir.dyall_v2z.lsym.out <../../../../test/tutorial_Ir_16plus/result/Z61.x2c.2S12.scf_cc33e.2fs_Ir.dyall_v2z.lsym.out>`, :download:`Z61.x2c.2S12.scf_cc33e_oe.2fs_Ir.dyall_v2z.lsym.out <../../../../test/tutorial_Ir_16plus/result/Z61.x2c.2S12.scf_cc33e_oe.2fs_Ir.dyall_v2z.lsym.out>`. The SCF :math:`^{2}P_{1/2}`, :math:`^{2}P_{3/2}` excited states ---------------------------------------------------------------- By placing the unpaired electron into 2nd irrep one gets the :math:`^{2}P_{1/2}` first excited state: :: pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2P12.scf_cc33e.2fs.inp --get "DFCOEF=DFCOEF.v2z.2P12" pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2P12.scf_cc33e_oe.2fs.inp Input files to download :download:`Z61.x2c.2P12.scf_cc33e.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2P12.scf_cc33e.2fs.inp>`, :download:`Z61.x2c.2P12.scf_cc33e_oe.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2P12.scf_cc33e_oe.2fs.inp>`. Corresponding output files are :download:`Z61.x2c.2P12.scf_cc33e.2fs_Ir.dyall_v2z.lsym.out <../../../../test/tutorial_Ir_16plus/result/Z61.x2c.2P12.scf_cc33e.2fs_Ir.dyall_v2z.lsym.out>`, :download:`Z61.x2c.2P12.scf_cc33e_oe.2fs_Ir.dyall_v2z.lsym.out <../../../../test/tutorial_Ir_16plus/result/Z61.x2c.2P12.scf_cc33e_oe.2fs_Ir.dyall_v2z.lsym.out>`. How to obtain the :math:`^{2}P_{3/2}` second excited state at the SCF level, and, consequently, at the CC level ? For that, we utilize the :ref:`WAVE_FUNCTION_.REORDER MO` keyword with reading of the *DFCOEF.v2z.2P12* file from the previous run. Likewise one uses overlap selection in the SCF step: :: pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2P32.scf_cc33e.2fs.inp --put "DFCOEF.v2z.2P12=DFCOEF" pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2P32.scf_cc33e_oe.2fs.inp --put "DFCOEF.v2z.2P12=DFCOEF" Corresponding input files to download are :download:`Z61.x2c.2P32.scf_cc33e.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2P32.scf_cc33e.2fs.inp>`, :download:`Z61.x2c.2P32.scf_cc33e_oe.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2P32.scf_cc33e_oe.2fs.inp>`. Output files are :download:`Z61.x2c.2P12.scf_cc33e.2fs_Ir.dyall_v2z.lsym.out <../../../../test/tutorial_Ir_16plus/result/Z61.x2c.2P12.scf_cc33e.2fs_Ir.dyall_v2z.lsym.out>`, :download:`Z61.x2c.2P12.scf_cc33e_oe.2fs_Ir.dyall_v2z.lsym.out <../../../../test/tutorial_Ir_16plus/result/Z61.x2c.2P12.scf_cc33e_oe.2fs_Ir.dyall_v2z.lsym.out>`. The CCSD(T) :math:`^{2}P_{1/2}`, :math:`^{2}P_{3/2}` excited states ------------------------------------------------------------------- The other option is to start from the :math:`^{2}P_{aver}` averaged single determinant state and distinguish between individual :math:`^{2}P_{1/2}` and :math:`^{2}P_{3/2}` states at the Coupled Cluster correlated level thanks to the linear symmetry. First we test the averaged, :math:`^{2}P_{aver}`, state: :: pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2Paver.scf_cc33e.2fs.inp pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2Paver.scf_cc33e_oe.2fs.inp Files to download are :download:`Z61.x2c.2Paver.scf_cc33e.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2Paver.scf_cc33e.2fs.inp>`, :download:`Z61.x2c.2Paver.scf_cc33e_oe.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2Paver.scf_cc33e_oe.2fs.inp>`. Afterwards we can proceed to the individual spin-orbit distinguished states, based on :math:`M_{J}` splitted occupation of each fermion irrep at the Coupled Cluster level. First the first excited state, :math:`^{2}P_{1/2}`: :: pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2Paver.scf_cc33e_2P12.2fs.inp pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2Paver.scf_cc33e_oe_2P12.2fs.inp Input files to download are :download:`Z61.x2c.2Paver.scf_cc33e_2P12.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2Paver.scf_cc33e_2P12.2fs.inp>`, :download:`Z61.x2c.2Paver.scf_cc33e_oe_2P12.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2Paver.scf_cc33e_oe_2P12.2fs.inp>`. Corresponding output files are :download:`Z61.x2c.2Paver.scf_cc33e_2P12.2fs_Ir.dyall_v2z.lsym.out <../../../../test/tutorial_Ir_16plus/result/Z61.x2c.2Paver.scf_cc33e_2P12.2fs_Ir.dyall_v2z.lsym.out>`, :download:`Z61.x2c.2Paver.scf_cc33e_oe_2P12.2fs_Ir.dyall_v2z.lsym.out <../../../../test/tutorial_Ir_16plus/result/Z61.x2c.2Paver.scf_cc33e_oe_2P12.2fs_Ir.dyall_v2z.lsym.out>`. Then we proceed to the second excited state, :math:`^{2}P_{3/2}`: :: pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2Paver.scf_cc33e_2P32.2fs.inp pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.2Paver.scf_cc33e_oe_2P32.2fs.inp Files to download are :download:`Z61.x2c.2Paver.scf_cc33e_2P32.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2Paver.scf_cc33e_2P32.2fs.inp>`, :download:`Z61.x2c.2Paver.scf_cc33e_oe_2P32.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.2Paver.scf_cc33e_oe_2P32.2fs.inp>`. Corresponding output files are :download:`Z61.x2c.2Paver.scf_cc33e_2P32.2fs_Ir.dyall_v2z.lsym.out <../../../../test/tutorial_Ir_16plus/result/Z61.x2c.2Paver.scf_cc33e_2P32.2fs_Ir.dyall_v2z.lsym.out>`, :download:`Z61.x2c.2Paver.scf_cc33e_oe_2P32.2fs_Ir.dyall_v2z.lsym.out <../../../../test/tutorial_Ir_16plus/result/Z61.x2c.2Paver.scf_cc33e_oe_2P32.2fs_Ir.dyall_v2z.lsym.out>`. The :math:`^{2}S_{1/2}`, :math:`^{2}P_{1/2}` and :math:`^{2}P_{3/2}` FSCCSD states ---------------------------------------------------------------------------------- Simple and very stable approach to obtain ground and multiple excited states in one step is through the Fock-space Coupled Cluster method. Starting from the closed-shell system, :math:`Ir^{17+}`, one gets - by solving (01) sector all three correlated states of interest, :math:`^{2}S_{1/2}`, :math:`^{2}P_{1/2}` and :math:`^{2}P_{3/2}` : :: pam --noarch --mw=120 --mol=Ir.dyall_v2z.lsym.mol --inp=Z61.x2c.scf_fscc01_33ce_5s5p.2fs.inp The input file to download is :download:`Z61.x2c.scf_fscc01_33ce_5s5p.2fs.inp <../../../../test/tutorial_Ir_16plus/Z61.x2c.scf_fscc01_33ce_5s5p.2fs.inp>`. Corresponding output file is :download:`Z61.x2c.scf_fscc01_33ce_5s5p.2fs_Ir.dyall_v2z.lsym.out <../../../../test/tutorial_Ir_16plus/result/Z61.x2c.scf_fscc01_33ce_5s5p.2fs_Ir.dyall_v2z.lsym.out>`. Overview of excitation energies =============================== In the following table we summarize excitation energies. All values are in a.u. Energies in the Table are not rounded, the are cut to 8 decimal places ("oe" means orbital energies used in CC denominators, otherwise recalculated diagonal Fock matrix elements). ============ =============== =============== =============== =========== =========== Method ^2S_{1/2} ^2P_{1/2} ^P_{3/2} 2S12-2P12 2S12-2P32 ============ =============== =============== =============== =========== =========== (SCF ref) SCF -17751.10181462 -17749.67796221 -17748.96107014 1.42385 2.14074 CCSD -17751.90589433 -17750.48885480 -17749.77167089 1.41704 2.13422 CCSDoe -17751.90589433 -17750.48885479 -17749.77167088 1.41704 2.13422 CCSD(T) -17751.90998637 -17750.49777405 -17749.78015403 1.41221 2.12983 CCSD(T)oe -17751.90999205 -17750.49779342 -17749.78020119 1.41220 2.12979 (CC ref) CCSD -17751.90589433 -17750.48895732 -17749.77154045 1.41694 2.13435 CCSDoe -17751.90589433 -17750.48895728 -17749.77154043 1.41694 2.13435 CCSD(T) -17751.90998637 -17750.49779338 -17749.78012458 1.41219 2.12986 CCSD(T)oe -17751.90999205 -17750.49784867 -17749.78024342 1.41214 2.12974 FSCCSD -17751.90324662 -17750.48431436 -17749.76770431 1.41893 2.13554 ============ =============== =============== =============== =========== =========== It seems that quality of computed excitation energies increases in the line SCF-FSCCSD-CCSD-CCSD(T). Triple excitations (CCSD(T) results) are significant.