columbus in rio.doc - univie.ac.at · marcio soares pereira [email protected] ufrj marina...

COLUMBUS in RIO

A Quantum Chemistry Course on Multireference Methods, Energy Surfaces, Excited States, and Dynamics

Nov. 27 - Dec. 02, 2005

Instituto Militar de Engenharia Rio de Janeiro - Brazil

http://www.univie.ac.at/columbus/rio

Sponsors:

Columbus in Rio – IME, 2005 1

Program Mon Tue Wed Thu Fri 8:00-8:30 Regist. 8:30-9:30 Regist. MC-I HL-III PS-II PS-III 9:30-10:30 OP & HL-I PS-I MB-I MB-II HL-IV 10:30-11:00 Coff. break Coff. break Coff. break Coff. break Coff. break 11:00-12:30 HL-II IB-I MC-II IB-II MC-III 12:30-14:00 Lunch Lunch S. Lunch Lunch Lunch 14:00-16:30 Comp I Comp III Comp IV Comp VI T 16:30-17:00 Coff. break Coff. break Coff. break Coff. break T 17:00-18:00 Comp II Posters Comp V Comp VII - OP - Opening; Comp – computational work; S. Lunch - special lunch; T – Tour

Lectures General introduction to CI and MRCI methods; Potential energy surfaces; Optimization of geometries and other stationary points in the ground and excited states Hans Lischka (HL-I, II, III and IV) Wavefunctions simultaneously satisfying the full-symmetry of the hamiltonian and the Pauli principle: the GVB wavefunction and its application to the choice of active spaces Marco A. Chaer Nascimento (MC I, II and III) Size-consistency corrected MR-CI methods and their relation to Coupled Cluster theory; calculation of excited states and molecular properties. Peter Szalay (PS I, II and III) Conical intersections, nonadiabatic couplings, and their applications in chemical physics Itamar Borges (IB I and II) Adiabatic and nonadiabatic molecular dynamics with multireference ab initio methods Mario Barbatti (MB I and II)

Topics of the practical works Comp Topics

I Single point II Geometry optimization III Size extensivity IV Nonadiabatic couplings and MXS V Reference space restrictions VI Dynamics VII Size extensivity


Participants Name e-mail Institution Alejandro Lopez Castillo [email protected] UNIFIEO Alex Brown [email protected] U. of Alberta Aline Moreno Chagas Assumpção [email protected] USP André Gustavo [email protected] UFF Andre K. Okamoto [email protected] UNICAMP Antonio Carlos Borin [email protected] USP Antonio Eduardo da Hora Machado [email protected] UFU Antônio Maia de Jesus Chaves Neto [email protected] UFPA Caroline Arantes da Silva [email protected] UFF Cristina Ap. Setúbal [email protected] UFPR Eudes Eterno Fileti [email protected] USP Fabio Luiz Paranhos Costa [email protected] UFRJ Felipe Fleming [email protected] UFF Fernando Colmenares [email protected] UNAM-Mexico Fortunato S. de Menezes [email protected] UFLA Gerd Bruno da Rocha [email protected] UFPE Gunar Vingre da Silva Mota [email protected] UFRJ Hélcio José Batista [email protected] UFPE Humberto Luz Oliveira [email protected] UFSC Ian Hovell [email protected] CETEM Ivan Milas [email protected] UFRJ João Otávio M. A. Lins [email protected] UFRJ Juan de Dios Garrido [email protected] ISCTN-Cuba Leonardo Baptista [email protected] UFRJ Marcelo de Freitas Lima [email protected] UFSC Marcio Soares Pereira [email protected] UFRJ Marina Pelegrini [email protected] ITA Mauro Barbosa de Amorim [email protected] UFRJ Melissa Fabíola Siqueira Pinto [email protected] USP Nilo Makiuchi [email protected] UNB Peter Todorov [email protected] Utrecht University Rafael C. Bernardi [email protected] CBPF Rodrigo Ribeiro da Silva [email protected] IME Tadeu Leonardo [email protected] UFRJ Teodorico de Castro Ramalho [email protected] UFLA Thiago Messias Cardozo [email protected] UFRJ Tiago Giannerini da Costa [email protected] UFF Vladir W. Ribas [email protected] ITA Werner Gyorffy [email protected] Tyndall Nat. Institute Organizers and Lecturers Itamar Borges Jr. [email protected] IME Marco A. Chaer do Nascimento [email protected] UFRJ Hans Lischka [email protected] U. of Vienna Adelia Aquino [email protected] U. of Vienna Mario Barbatti [email protected] U. of Vienna Peter Szalay [email protected] Lorand Eotvos University

Columbus: http://www.univie.ac.at/columbus/


Practical work 1

Job 1A Subject: Single point calculation; vertical excitation; valence states. System: Ethylene at MRCI/SA-3-CAS(2,2)/6-31G* level.

• Fill out Table SM1 for the ethylene molecule for a CAS(2,2) and use the same space as reference space for MR-CISD. Use symmetry D2h (the character table is given in SM12). The active space consists of the π and π* orbitals. The molecule is on the zy plane. The main axis is z.

• Make the input with colinp. Use the geometry given in SM2. For the CASSCF calculation, average 3 states. Get the ground and two excited states (ππ* and (π*)2).

• Run COLUMBUS (runc). • Fill out Table SM3 with the computed energies and character of each state. • Use MOLEKEL to visualize the MCSCF orbitals.

Job 1B Subject: Single point calculation; vertical excitation; valence and Rydberg states. System: Ethylene at MRCI/SA-7-[CAS(2,2)+AUX(4)]/d-aug-cc-pVDZ level.

• Fill out Table SM4 for the ethylene molecule for a CAS(2,2)+AUX(4) space and use the same space as reference space for the MR-CISD calculation. Use symmetry D2h. The CAS contains the π and π* orbitals, the auxiliary space (AUX) is built from the 3s, 3px, 3py and 3pz Rydberg orbitals.

• Prepare the input with colinp. Use the geometry given in SM2. For the CASSCF calculation, average 7 states (3 valence and 4 Rydberg states). Compute the ground state and six excited states. Compute the oscillator strength between the ground and each one of the excited states.

• Run COLUMBUS. • Fill out Table SM5 with the energies and character of each state. • Use MOLEKEL to visualize the molecular orbitals.


Practical work 2

Job 2A Subject: geometry optimization in the ground state. System: CH2NH2

+ at MRCI/SA-3-CAS(4,3)/6-31G* level.

• Fill out Table SM6 for the CH2NH2+ for a CAS(4,3) and use this same space as the

reference space for the MR-CISD. Use symmetry C2 (the character table is given in SM12). Put into the active space the highest σ (2b), the π (3b) and the π* (4b) orbitals.

• Make the input with colinp. Optimize the ground state geometry. • Run COLUMBUS. • Fill out Table SM7 with geometry parameters. • Use MOLDEN to visualize the geometry and optimization steps.

Job 2B Subject: geometry optimization in the σπ* excited state. System: planar CH2NH2


• Copy the input files of JOB 2A and modify them with colinp to optimize the geometry of the σπ* (A) state restricted to the planar conformation. Hints: (1) set IFOLLOW = 2; (2) Freeze internal coordinate 12.

• Run COLUMBUS. • Fill out Table SM7 with geometric parameters.


Practical work 3

Job 3A Subject: Size-consistency test System: water + He, various methods, 6-31G* basis

• Create separate directory for water, He and the dimer • Create the He input for SCF and SRCI calculations. Hints: (1) MCSCF calculation is

not necessary, the CI will be based on the SCF (Hartree-Fock) orbitals; (2) due to program limitation, two active orbitals must be defined, but the proper orbital occupation can be used to define the single reference wave function.

• Create the water input for SCF, MCSCF/CAS(4,4), MR-CI/CAS(4,4) calculations. Consult SM13 for geometry and use the table to obtain the symmetry of the active orbitals.

• Create the dimmer input for SCF, MCSCF/CAS(4,4), MR-CI/CAS(4,4) calculations. Hints: (1) the geometry of the water subsystem must be the same as in the water calculation, the He atom should be at least 100 a.u. away. Place it on the z axis in order to preserve symmetry; (2) the active space will be the same, only the number of double occupied orbitals must be increased by one.

• Run all three calculations. Fill out the second table in SM13: get the Hartree-Fock, MCSCF, MR-CI, and various MR-CI+Q energies. Hints: (1) the various Davidson-corrections are given as the last lines of the file LISTINGS/ciudgsm.sp. dv1, dv2, dv3 represent the original Davidson-correction, the renormalized Davidson-correction and the Davidson-Silver-correction, respectively, while pople is the Pople-correction.

• In all three directories run colinp/CI input, but skip the DRT definition. Select AQCC to perform MR-AQCC calculations. Put the MR-AQCC energies into the table. Hint: (1) you can skip running colinp, and simply change NTYPE and GSET to 3 and 3, respectively in the input file ciudgin. (2) before the calculation, rename the LISTINGS directory in order to save the MR-CI results.

• In all three directories edit the ciudgin file, change NTYPE and GSET values to 3 and 2, respectively. This way, MR-ACPF calculations can be performed. Put the MR-ACPF energies into the table. Hint: before the calculation, rename the LISTINGS directory in order to save the MR-AQCC results.

• In all three directories edit the ciudgin file, change NTYPE and GSET values to 3 and 1, respectively. This way MR-CEPA(0) calculations can be performed. Put the MR-CEPA(0) energies into the table. Hint: before the calculation, rename the LISTINGS directory in order to save the MR-ACPF results.

• Extra exercise: repeat the calculations with two He atoms! Hint: the He atoms must be far enough from the water as well as from each other to avoid interaction.


Practical work 4

Job 4A Subject: Nonadiabatic coupling (see SM15). System: CH2NH2

+ at MRCI/SA-3-CAS(4,3)/6-31G*.

• Prepare the input for the CH2NH2+ without any symmetry restrictions (C1). Get the

nonadiabatic coupling (single point) for S0/S1, S1/S2 and S0/S2. Use the optimized geometry in job 2A. Hint: Run a simple mcscf calculation and copy the MOCOEF/mocoef_mc.sp to mocoef.start.

• Use colinp to create input files for the torsional coordinate from 0° to 90° in steps of 15°. Hints: (1) the definition of the internal coordinates is in the intcfl file; (2) To avoid problems with the transformation between internal and cartesian coordinates, make the curve from 0° to 89.94°, with 7 displacements.

• Run COLUMBUS ($COLUMBUS/disp.pl). • Use curve.pl to collect the energy data.($COLUMBUS/curve.pl < curvein >

curve.out). Hint: The file curvein should contai only the text “ci 3” in the first line. • Plot the energy of the three states against the angle. • Plot the couplings against the angle. Hint: To collect h21, type

grep "h(drt1.state1,drt1.state2)" nohup.out

Job 4B Subject: Minimum of the crossing seam (see SM15). System: CH2NH2


• Starting from the 90° geometry, get the minimum of the crossing seam (MXS). • Use MOLEKEL to visualize the MXS geometry and the g and h vectors. • Fill out Table SM8 with the topographic parameters (a.u.).

Job 4C Subject: Minimum of the crossing seam (see SM15). System: Ethylene at MRCI/SA-2-CAS(2,2)/6-31G* level.

• Get the MXS for ethylene (S0/S1). Hint: Start the optimization close to the 90° structure, with some pyramidalization in one CH2 group.

• Fill out Table SM8 and compare the shape of the MXSs for the two systems. • Compare the results of Job 4B and 4C. What MXS should be more efficient in terms of

nonadiabatic transition?


Practical work 5

Job 5A Subject: advanced manipulation of the configuration space. System: Ethylene

• Using the geometry provided in SM9, make an input for ethylene without symmetry (C1) for the following spaces (MCSCF):

Space* Description CAS(12,12): [2]4(12)12 PPMC: [2]4(2)2(2)2(2)2(2)2(2)2(2)2 RDP: [2]45×(2,S=0)2(ππ*)2 RCI: [2]46×(2,S=0)2 CAS(2,2): [7]14(2)2

* R. Shepard, Adv. Chem. Phys. 69, 63 (1987). Notation: [double occupieds]electrons(actives)electrons(actives, spin restriction)electrons

Hint: The PPMC, RDP and RCI are subspaces of the CAS(12,12). You should modify by hand the file mcdrtin.1 of the CAS(12,12) to include the restrictions necessary in each case. For instance, the RDP space is obtained by: 1 1 1 2 / doubly occupied orbitals 1 3 1 10 1 4 1 11 1 5 1 12 1 6 1 13 1 7 1 14 1 8 1 9 / active orbitals 0 2 2 4 4 6 6 8 8 10 10 12 / occmin 2 2 4 4 6 6 8 8 10 10 12 12 / occmax 0 0 0 0 0 0 0 0 0 0 / bmin 0 0 0 0 0 0 0 0 0 0 /bmax In this scheme, for example, orbitals 4 and 11 make a subspace in which the minimum cumulative occupation is 2 electrons and the maximum 4 electrons. The null values of bmin and bmax make the spin restriction for the first 5 subspaces. • Use the mcdrt.x program to fill out Table SM10 ($COLUMBUS/mcdrt.x <mcdrtin.1

> cas.out). • Make a MCSCF calculation with the RDP space (SA-3-RDP/6-31G*) and visualize

the orbitals. Hint: Change the FCIORB variable in mcscfin file to: FCIORB= 1,3,4,1,10,4, 1,4,40,1,11,40, 1,5,400,1,12,400, 1,6,4000,1,13,4000, 1,8,40000,1,14,40000, 1,8,400000,1,9,400000


Practical work 6

Job 6A Subject: Semiclassical dynamics with surface hopping System: CH2NH2

+ at MRCI/SA-3-CAS(4,3)/6-31G*; dynamics starting in the S1 surface.

• Create a directory named JOB_NAD containing an input for nonadiabatic coupling (single point) calculation for CH2NH2

+ at SA-3-CAS(4,3)/6-31G* (Use maximum excitation level equal 0).

• Create a directory named JOB_AD containing an input for geometry optimization (Use MRCI gradient and maximum excitation level equal 0).

• Use nxinp to make the input for a trajectory of 2 states, 25 fs, with time step of 0.5 fs. Use the initial geometry and nuclear velocities given in SM11.

• Run NEWTON-X program ($NEXTON_X/moldyn-02.pl > moldyn.log &). • Use MOLDEN to visualize the time evolution of the geometry (RESULTS/dyn.mld). • Use $NEWTON_X/plot to plot the potential energies against time.

Job 6B Subject: Semiclassical dynamics with surface hopping. Lifetime of the excited state. System: CH2NH2

+ at MRCI/SA-3-CAS(4,3)/6-31G*; dynamics starting in the S2 surface.

• Directory /home/cir1/PW6B contains a complete simulation of 50 MRCI trajectories, which run for 100 fs in time steps of 0.5 fs. Copy it to your own directory (traj.tgz). From the directory TRAJECTORIES, call nxinp to make the input for the statistical analysis (set proptype = 2).

• Run analysis.pl ($NEXTON_X/analysis.pl > analysis.log &) to get the fraction of trajectories in each state for each time step. Plot these fractions against time and estimate the lifetime of each one of the excited states. Hint: The results are in ANALYSIS/mean_value.2.


Practical work 7

Job 7A Subject: Excited by MR-AQCC; calculation of transition moments (oscillator strength) System: C3 molecule, MR-AQCC-LRT/SA-6-CAS(8,6)/6-31G* basis

• Fill out the first table in SM14 for a CAS(8,6) and use this same space as reference for the MR-CISD (MR-AQCC) calculations. Use symmetry D2h (character table and the correspondence of the irreps of D2h and D∞h points groups can be found in SM12). Put into the active space the highest σg and σu orbitals, as well as one pair of πu and πg orbitals. Hint: the electronic structure of C3 is described in SM14.

• Make the integral input with colinp, the bond length is 1.2936 Å. • Make the SCF and MCSCF input with colinp. Determine the number of DRT’s

and number of states used in the SA procedure by filling out the second table in SM14. Hint: the Π states have two components, both should be included in the averaging. Calculate also the transition moments between the ground state and the excited states.

• Make the CI input with colinp for the ground state. Use the same space as in the MCSCF calculation (see first table of SM14). As method select MR-AQCC.

• Run runc. Edit the out file LISINGS/ciudgls.sp and look for the line lrtshift. Save this number for the next step.

• Use colinp again to prepare the input for the excited state calculation. Now you have to make input for a calculation with several DRT’s. Use the second table in SM14 to determine the number of DRT’s and the number of states. Hint: now it is not necessary to calculate both components of the Π states. As method select AQCC-LRT, and also specify the LRTSHIFT value saved in the previous step. Prepare input also for the calculation of the transition moments between the ground state and the excited states.

• Run runc and collect the results into the third table in SM14. • Repeat the calculation at the MR-CISD level. Hint: skip the DRT input.


Supplementary Material

SM1 – Orbital occupation of ethylene CAS(2,2), D2h System: C2H4 Point Group: D2h

N. Electrons: 16 Multiplicity: 1

Level: MR-CISD/SA-3-CAS(2,2)

IRREP

ag b3u b2u b1g b1u b2g b3g au

SCF DOCC 3 1 1 0 2 0 1 0

MCSCF DOCC 3 0 1 0 2 0 1 0

RAS 0 0 0 0 0 0 0 0

CAS 0 1 0 0 0 1 0 0

AUX 0 0 0 0 0 0 0 0

MRCI FC 1 0 0 0 1 0 0 0

FV 0 0 0 0 0 0 0 0

DOCC 2 0 1 0 1 0 1 0

ACT 0 1 0 0 0 1 0 0

AUX 0 0 0 0 0 0 0 0

INT 2 1 1 0 1 1 1 0

State Multiplicity N. electrons Symmetry

0 1 16 1 (Ag) (π)2

1 1 16 5 (B1u) (π)1(π∗)1

2 1 16 1 (Ag) (π∗)2

Number of distinct row tables (DRTs): 2 Obs: Use Multiple DRTs; allowed reference symmetry =1 (DRT1); = 5 (DRT2).

SM2 – Ethylene geometry (planar, D2h) Unique atoms (a.u.): C 0.00000000 0.00000000 1.27572383 H 0.00000000 1.75798067 2.34867651 See file /home/cir1/SM2/geom.unique .


SM3 – Energy and character of the valence excitations of ethylene (valence) State Symmetry Character Energy (hartree)

c2 * CSF CAS MRCI MRCI+Q

S0 Ag 0.89 π2 -78.047447 -78.295067 -78.316239

S1 B1u 0.90 ππ* -77.674455 -77.956392 -77.985770

S2 Ag 0.85 (π*)2 -77.493282 -77.781526 -77.815860

* c2 for the main CFS at MRCI level.

SM4 – Orbital occupation of ethylene for CAS(2,2)+AUX(4), D2h System: C2H4 Point Group: D2h


Level: MR-CISD/SA-7-[CAS(2,2)+aux(4)]

IRREP

ag b3u b2u b1g b1u b2g b3g au

SCF DOCC 3 1 1 0 2 0 1 0

MCSCF DOCC 3 0 1 0 2 0 1 0

RAS 0 0 0 0 0 0 0 0

CAS 0 1 0 0 0 1 0 0

AUX 1 1 1 0 1 0 0 0

MRCI FC 1 0 0 0 1 0 0 0

FV 0 0 0 0 0 0 0 0

DOCC 2 0 1 0 1 0 1 0

ACT 0 1 0 0 0 1 0 0

AUX 1 1 1 0 1 0 0 0

INT 3 2 2 0 2 1 1 0


0 1 16 1 (Ag) (π)2

1 1 16 5 (B1u) (π)1(π∗)1

2 1 16 1 (Ag) (π∗)2

3 1 16 2 (B3u) (π)1(3s)1

4 1 16 1 (Ag) (π)1(3px)1

5 1 16 4 (B1g) (π)1(3py)1

6 1 16 6 (B2g) (π)1(3pz)1

Number of distinct row tables (DRTs): 5


SM5 – Energy and character of the ethylene spectrum (valence and Rydberg) State Symmetry Character Oscill. Strength Energy (eV)a Exp.

S0 Ag (π)2 … 0.00 …

S1 B3u π−3s 0.09 7.15 7.11b (3s)

S2 B1g π−3py 0.00 7.82 7.80b (3py)

S3 B2g π−3pz 0.00 7.83 7.90 b (3pz)

S4 B1u π−π* 0.39 7.91 7.66c (V)

S5 Ag π−3px 0.00 8.20 8.28b (3px)

S6 Ag (π*)2 0.00 12.76 … a MRCI+Q b B. A. Williams and T. A. Cool, J. Chem. Phys. 94, 6358 (1991). c R. Sension and B. S. Hudson, J. Chem. Phys. 90, 1377 (1989). Maximum of the absorption band.

SM6 – Orbital occupation of CH2NH2+ at CAS(4,3), C2

System: CH2NH2+ Point Group: C2


Level: MR-CISD/SA-3-CAS(4,3)

IRREP

a b C2 a C1

SCF DOCC 5 3 8

MCSCF DOCC 5 1 6

RAS 0 0 0

CAS 0 3 3

AUX 0 0 0

MRCI FC 2 0 2

FV 0 0 0

DOCC 3 1 4

ACT 0 3 3

AUX 0 0 0

INT 3 4 7


0 1 16 1 (A) (π)2

1 1 16 1 (A) (π)1(π∗)1

2 1 16 2 (A) (σπ∗)2

Number of distinct rows (DRTs): 1


SM7 – Geometric parameters for the CH2NH2+ (ground and excited states)

Parameter S0 S1

CN (Å) 1.284 1.319

NH (Å) 1.020 1.021

CH (Å) 1.084 1.165

HNH (°) 116.4° 116.5°

HCH (°) 120.9° 88.0°

SM8 – Topographic parameters for ethylene and CH2NH2+ (a.u.)

System sx sy dgh ∆gh

CNH4+ -0.00003 -0.03066 0.09440 0.64946

C2H4 0.01908 0.05893 0.013177 -0.44192

SM9 – Ethylene geometry (planar) Geometry (a.u.): C 6.0 0.00000000 0.00000000 -1.27572383 12.00000000 C 6.0 0.00000000 0.00000000 1.27572383 12.00000000 H 1.0 0.00000000 -1.75798067 -2.34867651 1.00782504 H 1.0 0.00000000 1.75798067 -2.34867651 1.00782504 H 1.0 0.00000000 -1.75798067 2.34867651 1.00782504 H 1.0 0.00000000 1.75798067 2.34867651 1.00782504 See file /home/cir1/SM9/geom. .


SM10 – Number of CSFs in the several spaces Space DRTs

CAS(12,12) 226512

PPMC 3012

RDP 96

RCI 64

CAS(2,2) 3

SM11 – Geometry and velocities Geometry (a.u.): N 7.0 0.05918868 -0.19931358 1.18486354 14.00307401 C 6.0 0.10770335 0.00776782 -1.22050155 12.00000000 H 1.0 0.05858956 1.28971446 2.08621050 1.00782504 H 1.0 0.16438630 -1.84831949 1.93659925 1.00782504 H 1.0 0.05068591 1.84754131 -1.90209231 1.00782504 H 1.0 0.25599617 -1.85431110 -2.49924659 1.00782504 Velocity (a.u.): -0.00003459 0.00010568 0.00003398 0.00002848 -0.00007116 -0.00004877 -0.00066462 -0.00060025 0.00073399 0.00178011 -0.00189013 -0.00114276 0.00087773 0.00158302 -0.00179383 -0.00137907 -0.00155204 0.00244732 See files geom and veloc in directory /home/cir1/SM11 .


SM12 – Character tables and direct products D2h

D2h E C2(z) C2(y) C2(x) i σ (xy)

σ (xz)

σ (yz)

Ag 1 1 1 1 1 1 1 1 x2, y2, z2 B1g 1 1 -1 -1 1 1 -1 -1 Iz xy B2g 1 -1 1 -1 1 -1 1 -1 Iy xz B3g 1 -1 -1 1 1 -1 -1 1 Ix yz Au 1 1 1 1 -1 -1 -1 -1

B1u 1 1 -1 -1 -1 -1 1 1 z B2u 1 -1 1 -1 -1 1 -1 1 y B3u 1 -1 -1 1 -1 1 1 -1 x

⊗ Ag B1g B2g B3g Au B1u B2u B3u Ag Ag B1g B2g B3g Au B1u B2u B3u B1g B1g Ag B3g B2g B1u Au B3u B2u B2g B2g B3g Ag B1g B2u B3u Au B1u B3g B3g B2g B1g Ag B3u B2u B1u Au Au Au B1u B2u B3u Ag B1g B2g B3g B1u B1u Au B3u B2u B1g Ag B3g B2g B2u B2u B3u Au B1u B2g B3g Ag B1g B3u B3u B2u B1u Au B3g B2g B1g Ag C2V C2v E C2 σ (xz) σ (yz) A1 1 1 1 1 z x2, y2, z2 B1 1 -1 1 -1 x, Iy xz B2 1 -1 -1 1 y, Ix yz A2 1 1 -1 -1 Iz xy C2

C2 E C2 A 1 1 z, Iz x2, y2, z2, xy B 1 -1 x, y, Ix, Iy xz, yz

⊗ A B A A B B B A C∞v (D∞h) ⊗ Σ+ Σ- Π ∆ Φ Σ+ Σ+, Σ- Π ∆ Φ Σ- Σ- Σ+ Π ∆ Φ Π Π Π Σ+, Σ-, ∆ Π, Φ ∆, Γ ∆ ∆ ∆ Π, Φ Σ+, Σ-, Γ Π, Η Φ Φ Φ ∆, Γ Π, Η Σ+, Σ-, I

D∞h → D2h D∞h Σg

+ Σu+ Σg

- Σu- Πg Πu ∆g ∆u Φg Φu

D2h Ag B1u B1g Au B2g+B3g B2u+B3u Ag+B1g Au+B1u B2g+B3g B2u+B3u


SM13 – Size-consistency test 1. Geometry for water Unique atoms (a.u.): O 0.00000000 0.00000000 -0.13020532 H 0.00000000 -1.48912482 1.03322649 See file /home/cir1/SM13/geom.unique . 2. Table of internal orbital occupations System: H2O Point Group: C2V


IRREP

A1 B1 B2 A2

SCF DOCC 3 1 1 0

MCSCF DOCC 2 0 1 0

RAS

CAS 2 1 1 0

AUX

MRCI FC 0 0 0 0

FV 0 0 0 0

DOCC 2 0 1 0

ACT 2 1 1 0

AUX 0 0 0 0

INT 4 1 2 0


3. Table for calculation of the size-consistency errors

method He H2O Sum dimer dimer error dimer Sum trimer trimer error trimer

SCF -2.855160 -76.004167 -78.859327 -78.859327 0.000000 -81.714487 -81.714487 0.000000

MCSCF -2.855160 -76.021719 -78.876879 -78.876879 0.000000 -81.732040 -81.732040 0.000000

MRCI -2.887365 -76.198635 -79.086000 -79.083240 -0.002761 -81.973366 -81.967485 -0.005880

DAV1 -2.887609 -76.207215 -79.094824 -79.094361 -0.000463 -81.982433 -81.981402 -0.001031

DAV2 -2.887611 -76.207651 -79.095262 -79.094993 -0.000269 -81.982873 -81.982275 -0.000598

DAV3 -2.887613 -76.208134 -79.095747 -79.095702 -0.000045 -81.983360 -81.983265 -0.000095

Pople -2.887365 -76.206071 -79.093436 -79.093415 -0.000021 -81.980801 -81.980750 -0.000052

MRAQCC -2.887365 -76.204339 -79.091704 -79.091468 -0.000236 -81.979069 -81.978595 -0.000474

MRACPF -2.887365 -76.206126 -79.093491 -79.093503 0.000012 -81.980856 -81.980875 0.000020

MRCEPA -2.887611 -76.208234 -79.095845 -79.095845 0.000000 -81.983457 -81.983456 0.000000


SM14 – Orbital occupation of C3 1. Table of internal orbital occupations System: C3 Point Group used: D2h


Level: MR-AQCC/SA-5-CAS(8,6)

IRREP

ag b3u B2u b1g b1u B2g b3g au

SCF DOCC 4 1 1 0 3 0 0 0

MCSCF DOCC 3 0 0 0 2 0 0 0

RAS 0 0 0 0 0 0 0 0

CAS 1 1 1 0 1 1 1 0

AUX 0 0 0 0 0 0 0 0

MRCI FC 2 0 0 0 1 0 0 0

FV 0 0 0 0 0 0 0 0

DOCC 1 0 0 0 1 0 0 0

ACT 1 1 1 0 1 1 1 0

AUX 0 0 0 0 0 0 0 0

INT 2 1 1 0 2 1 1 0

2. Electronic structure of C3 molecule About the spectroscopy of the C3 molecule see the paper Monninger et al. (JPC A106, 5779 (2002)). In the ground state the molecular frame is linear (experimental bond length is 1.2936 Å), therefore it belongs to the D∞h point group. The ground state is a Σg

+ state corresponding to the following configuration: 1σg

2 2σg2 1σu

2 3σg2 2σu

2 4σg2 1πu

4 3σu2. The LUMO is a πg

orbital. Therefore the relevant excited states will be of Πu, Σu+, Σu

- symmetry.


3. Determination of the states included in the calculations The states to be included in the averaging: one Σg

+ (ground state), three Πu and two Σu+ states.

DRT Multiplicity N. electrons Symmetry No. of states (full

symmetry) 1 1 18 1 (Ag) 1 (Σg

+)

2 1 18 2 (B3u) 3 (Πu)

3 1 18 3 (B2u) 3 (Πu)

4 1 18 5 (B1u) 2 (Σu+)

Number of distinct row tables (DRTs) in MCSCF calculation:

4

Number of distinct row tables (DRTs) in AQCC calculation:

3

4. Collection of the results on the excited states of C3 molecule

State MCSF MR-AQCC-LRT MR-CISD

designation Character

Excitation energy (eV)

Oscillator strength


Oscillator strength


Oscillator strength

1Πu σu → πg 3.88 0.0414 3.24 0.0187 3.38 0.0244

2Πu σgπu→πgπg 9.13 0.0028 7.91 0.0028 8.48 0.0009

3Πu (1Φu) σgπu→πgπg 9.79 0.0000 8.57 0.0002 9.02 0.0000

1Σu- πu → πg 4.74 0 4.10 0 4.26 0

1Σu+ πu → πg 10.98 1.4534 8.39 0.891 8.86 1.0573


SM15 – Nonadiabatic coupling vectors and related quantities 5. Nonadiabatic coupling vector h The non-adiabatic coupling matrix element between two states I and J is defined by the following expression:1

r

RrRrh

αα R

IJ

JI

∂Ψ∂

Ψ=);(

);( ,

whereΨ is the electronic wave function, R, the nuclear coordinates, and r indicates integration over all electron coordinates. This formula is split into two terms:

),,(),,( ααα IJIJ CSFCIJI DDh += , where:

( ) CSF

IJJI

IJCI C

RHC

EERCC

αα ∂∂

−=

∂∂

=1D ,

and

∑ ∂

∂=

ji

ji

JIji

CSF

RD

,,

α

φφD .

6. Gradient sum s and difference g vectors If GI is the gradient of the lower GJ of the upper state, then:

2

IJJI GGs +

= ,

2

IJJI GGg −

= .

7. x and y directions JIJI gg ggx == ,/ˆ ,

JIJI hh hhy == ,/ˆ .

8. Linear approximation for the energy E of the double cone By defining the topographic parameters:2

,xs ⋅= JIxs

,ys ⋅= JIys

( ),2

22

ghgh d

hg −=∆

( ) 2/122 hgd gh += .

The potential energy surfaces around the conical intersection are given approximately by:

( ) ( ) .22

12/1

2222⎟⎟⎠

⎞⎜⎜⎝

⎛−

∆++±+= yxyxdysxsE gh

ghyx

1 Lischka et al., J. Chem. Phys. 120, 7322 (2004). 2 Yarkony, J. Chem. Phys. 114, 2601 (2001).


Table of internal orbital occupation

System: C2H4 Point Group: C1


Level: CAS(2,2) CAS(12,12)

IRREP

a a

SCF DOCC 8 8

MCSCF DOCC 7 2

RAS 0 0

CAS 2 12

AUX 0 0

MRCI FC 2 2

FV 0 0

DOCC 5 0

ACT 2 12

AUX 0 0

INT 7 12


1 1 16 A

2 1 16 A

Number of distinct row tables (DRTs): 1


Table of internal orbital occupation System: Point Group:

N. Electrons: Multiplicity:

Level:

IRREP

SCF DOCC

MCSCF DOCC

RAS

CAS

AUX

MRCI FC

FV

DOCC

ACT

AUX

INT


Number of distinct row tables (DRTs):




Level:

IRREP

SCF DOCC

MCSCF DOCC

RAS

CAS

AUX

MRCI FC

FV

DOCC

ACT

AUX

INT




0 15 30 45 60 75 90-94.70

-94.65

-94.60

-94.55

-94.50

-94.45

-94.40

-94.35

Ener

gy (h

artre

e)

Torsion (°)

JOB 3A – Energy against torsional angle (MRCI+Q).

0 15 30 45 60 75 900

2

4

16

18

20 10 20 21

|hJI| (

a.u.

)

Torsion (°)

JOB 4A – Nonadiabatic coupling.


JOB 4B – g and h vectors.

JOB 4C – g and h vectors.


JOB 4B – MXS (atomic units).

JOB 4C – MXS (atomic units).


0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

Num

ber o

f tra

ject

orie

s

Time (fs)

S2

S1

S0

JOB 6B – Lifetimes.

columbus in rio.doc - univie.ac.at · marcio soares pereira [email protected] ufrj marina...

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