IG-UY -INITIO OVITIONL SPETOSOPY Gábor zakó a Edit Mátyus b ttila G. sászár b astiaa J. raas a ad Joel M. owa a a Eory Uiversity tlata US b Eötvös Uiversity udapest ugary D 7 7 5 8 Eergy / c - SET May 7 8
Overview Quatu heistry or Oppeheier approxiatio No-or Oppeheier quatu cheistry Electroic structure coputatios e e ( r; ) E( ) ψ ( r; ) e Nuclear otio coputatios ψ ( T ( ) E( ) ) χ ( ) ε χ ( ) PES DMS v Variatioal solutio v v diabatic DO J Noadiabatic Iteral coordiates DOPI Noral coordiates DEWE MULTIMODE
Variatioal calculatio of (ro)vibratioal eergies ad averaged properties of triatoic olecules The DOPI algorith ( ) ( ) ( ) { } cos Φ L N N l l χ χ G. zakó T. Furtebacher. G. sászár ad V. Szalay Mol. Phys. 4 (4) DV ailtoia i orthogoal (O) iteral coordiates Direct-product (P) basis fuctios Iterative (I) Láczos eigesolver ) cos ( cot V
Why do we eed theory? ighly accurate PES VQD PES of O V : ore-valece correctio el : elativistic correctio QED : Quatu electrodyaics DO : Diagoal or-oppeheier correctio O. L. Polyasky. G. sászár S. V. Shiri N. F. Zobov P. arletta J. Teyso D. W. Schweke P. J. Kowles Sciece 99 539 (3) Exact uerical solutio of the uclear otio proble DOPI algorith G. zakó T. Furtebacher. G. sászár ad V. Szalay Mol. Phys. 4 (4) Experiet Icoplete lielist Theory oplete lielist Vibratioal levels of 7 O 3 DOPI(VQD) MVEL 463.367 59.644 59. 35648 345.535 344. 98447 3653.38 3653. 468 3748.5 3748. 387 3 4657.888 58.4 57. 7568 538 53. 597 4 6.69 6765.588 6857.887 6857. 777 79.896 793. 4668 738.6 738. 736 743.98 743. 768 5 758.957 3 86.877 3 8357.439 875.35 879.566 879. 5443 6 8855.488 8983.9 898. 8698 4 979.883 4 984.54 7 7. 793 7. 377 3. 63 3.5. G. sászár G. zakó T. Furtebacher ad E. Mátyus. ep. op. he. 3 55 (7) 3 DOPI(VQD) MVEL 463.367 59.644 59.35648 345.535 344.98447 3653.38 3653.468 3748.5 3748.387 3 4657.888 58.4 57.7568 538 53.597 4 6.69 6765.588 6857.887 6857.777 79.896 793.4668 738.6 738.736 743.98 743.768 5 758.957 3 86.877 3 8357.439 875.35 879.566 879.5443 6 8855.488 8983.9 898.8698 4 979.883 4 984.54 7 7.793 7.377 3.63 3.5 5.67 3 584.956 597.44 598.4756 853.4 853.5538 3 6 5 8.44 5.33 8 35.5 3 75.948 3 793.487 79.87 3 985.47 3.97 3.557 6 36.56 389.3 9 5.995 3 54.86 6 56.935 4 386.44 4 334.9 4 348.499 3 36.79 363.364 363.4998 7 364.75 4 387.77 3 389.863 7 38.86 389.43 389.37 3 439.7 4.553 3 495.39 496.795
Sigularities: ad si Treatig the sigularities Direct-prodact basis Treatig sigularities i variatioal triatoic (ro)vibratioal calculatios ( ) ) cos ( si cot V j J j J j J J j z z z Nodirect-product basis ( ) ( ) ( ) ( ) ψ χ ϕ χ χ cos Jp MK K l Φ ( ) ( ) ( ) ( ) ψ χ ϕ χ cos Jp MK K P F l l G. zakó et al. J. he. Phys. 4 (5) G. zakó et al. J. he. Phys. 4 4 (6) G. zakó et al. Phys. he. he. Phys. 9 347 (7)
Toward coplete vibratioal spectroscopy of 3 eferece results (6) PES with correct dissociative behaviour 3 D 34 9.6 c Nuber of vibratioal states below D : 687 eve-parity 599 odd-parity DV3D coputatios o a large parallel supercoputer (a couple of hudred processors) This work essel-dv o a sigle 3-bit P J. J. Muro J. aalal J. Teyso ad. Y. Mussa Mol. Phys. 4 5 (6) G. zakó PhD dissertatio (7) Near-dissociatio eve vibratioal bad origis for 3 i Jacobi coordiates Nube r asis I e f. a sis I a sis II e f. a sis II e f. 66 3464.83 436.6.96. 3466.6 436.6.73. 3466.79 436.6 66 3468.7 56.98. 3468.4 56.. 3469.5 56 66 3 34633.66 378.78.3. 34633.8 378.78.5. 34633.69 378.78 663 4 3464.89 4777.5 4.64. 34646.4 4777.5.3. 34646.54 4777.5 664 5 34665.84 4996.96.5. 34667.3 4996.96 5. 34667.98 4996.96 6656 34666.48 5554..68. 34667.66 5554..5. 34668.6 5554. 666 7 34675.54 663.5.67. 34676.68 663.5.53. 34677. 663.5 667 8 3468.88 74.7.9. 34684.49 74.7.59. 34685.8 74.7 668 9 3475.75 783.73.. 3475.6 783.73.5. 3476.85 783.73 669 3475.38 7768.69.58. 3476.3 7768.7 4. 3476.96 7768.69 67 3474.98 7869.47 3.6. 34744.7 7869.47.3. 34744.4 7869.47 67 34744.7 8488... 34745. 8488.. 34745.8 8488. 67 3 34749.8 8999..9. 3475.36 8999..38. 3475.74 8999. 673 4 3476. 9.4. 3476.7 9.7. 34763.43 9 674 5 34767.67 953.4.99. 34769. 953.4 6. 34769.66 953.4 675 6 34789.95 965.78.9. 3479.7 965.78.59. 34796 965.78 676 7 34795.38 9967.5.8. 34794.34 9967.5.. 34795.46 9967.5 677 8 3485.43 9995.99 3.7. 3489.5 9995.99.9. 348.7 9995.99 678 9 3484.5 59.76.9. 3483. 59.76 -..95 3483.96 59.76 679 3487.3 644.6.. 3483.65 644.6.57. 3485. 644.6 68 34839.7 859.7 3.8. 34834.9 859.8.6. 34836.53 859.8 68 34856.93 99.8 4.93. 34855 99.8.6. 3485. 99.8 68 3 34859.7 33.37.7. 34857.79 33.37.3. 34858. 33.37 683 4 34868.7 655.64.65. 34865.58 655.64.5. 34865.4 655.65 684 5 34885.7 8.54.73. 34883.63 8.54 5. 3488.98 8.54 685 6 76.83. 76.84. 3489.35 76.83 686 7 34897.6 47.87.38. 34897.6 47.87.74. 34898. 47.87 687 8 99.7. 99.8. 349. 99.8
Geeral variatioal (ro)vibratioal progra packages MULTIMODE F DEWE DV Eckart-Watso ailtoia 3N 6 h π P α αβ π β αα 8 αβ α k V -ode represetatio of the potetial Exact iclusio of the potetial Vibratioal ofiguratio Iteractio (VI) asis set: trucated direct-product basis Matrix: odest size stored eleets Eigepairs: usually direct diagoalizatio S. arter J. M. owa ad N.. ady Theor. he. cc. 9 (998) Grid represetatio Grid poits: direct-product grid Matrix: o stored eleets o-the-fly Eigepairs: iterative eigesolver E. Mátyus G. zakó. T. Sutcliffe ad. G. sászár J. he. Phys. 7 84 (7)
First-priciples vibratioal spectroscopy of the F 4 aio coplex PES SD(T)/aug-cc-pVTZ Nuber of eergy poits: 546 Nuber of coefficiets: 36 DMS MP/aug-cc-pVTZ Nuber of dipole oets: 3 586 Nuber of coefficiets: 56 Itesity / k ol - 5 4 3 5 5 5 3 Frequecy / c - 4 F - - 4 Ex pt. a r. VI Expt. ar. v ω v I v ω v I v (a ) 984 9677 v (a ) 9967 9795 v s (a ) 79 v b (e ) 76 3 v s (a ) 4 39 5 v 4 (t ) 3 357 35 7 v 4 (a ) 96 44 v 4 (e ) 395 353 4 v (e ) 533 565 53 v (e ) 57 53 [v b (e )v 4 (e )](a ) 67 649 9 [v b (e )v (e )](a ) 846 87 5 v 4 (a ) 587 74 59 v 4 (a ) 59 464 v 4 (t ) 64 74 6 v 4 (a )v 4 (e ) 69 599 v 4 (e ) 65 74 63 [v 4 (e )](e ) 79 697 9 [v 4 (e )](a ) 79 75 v (a ) 97 38 96 4 v hb (a ) 535 78 59 489 v s (a )v hb (a ) 745 98 755 5 [v (e )v 4 (t )](t ) 83 9 83 7 v (e )v 4 (a ) 866 773 3 [v (e )v 4 (t )](t ) 846 9 849 [v (e )v 4 (e )](e ) 965 893 7 [v (e )v 4 (e )](a ) 965 894 v 3 (t ) 3 343 36 8 v 3 (a ) 34 859 7 G. zakó. J. raas ad J. M. owa J. Phys. he. subitted (8) VI v 3 (e ) 956 374 937 6
eyod the or Oppeheier approxiatio ( ) V cos ) ( ± ± ± ± V V ctg diabatic Jacobi correctio (J) G. zakó. G. sászár V. Szalay ad. T. Sutcliffe J. he. Phys. 6 4 (7). Fábri G. zakó G. Tasi ad. G. sászár J. he. Phys. to be subitted (8)
syetry i the D olecular io v r pd.55 bohr v r pd.95 bohr. cos cos... 5 4 3 3 4 5 p e.688 d e. 688.6 cos cos.4.4.... 8 6 4 4 6 8 p e.38 d e. v 8 r pd 6.7 bohr v r pd 8.6 bohr cos cos.. 8 7 6 5 4 3 3 4 5 6 p e 3.887 d e 3. 863.5 cos. cos.5.5 cos cos.8.8.5.6.6.75.4.75.4.5.5...5.5 5 5 5 5 5 5 5 5 5 p e 8.65 d e. 5
Suary Toward coplete (ro)vibratioal spectroscopy of triatoics siple variatioal strategy: DOPI pplicatios for O (eergy levels ad effective structures) Treatig the sigularities: essel-dv approaches pplicatios for 3 Geeral variatioal (ro)vibratioal progra packages MULTIMODE pplicatio for F 4 DEWE No-or Oppeheier coputatios diabatic Jacobi correctio (J)