Calculation of the Jahn-Teller parameters with DFT - Authors’ Review

Matija Zlatar, Maja Gruden

Abstract


In this review, а density functional theory (DFT) procedure is pre­sented to calculate the Jahn–Teller (JT) parameters in a non-empirical way, which does not depend on the system at hand. Moreover, the intrinsic distortion path (IDP) model that gives further insight into the mechanism of the distortion is presented. The summarized results and their comparison to experimentally estimated values and high-level ab initio calculations, not only prove the good ability of the used approach, but also provide many answers to the intriguing behavior of JT active molecules.

Keywords


vibronic coupling; density functional theory; intrinsic distortion path; distortion; transition metal complexes; organic ions and radicals

Full Text:

PDF (3,515 kB)

References


H. A. Jahn, E. Teller, Proc. R. Soc., A 161 (1937) 220 (https://dx.doi.org/10.1098/rspa.1937.0142)

O. Kahn, Structure électronique des éléments de transition: ions et molécules complexes, Presses universitaires de France, 1977

J. G. Bednorz, K. A. Müler, Perovskite-Type Oxides – The New Approach to High-Tc Superconductivity - Nobel Lecture, in Nobel Lect. Phys. 1981–1990, G. Ekspang, Ed., World Scientific Publishing Co, Singapore, 1993, pp. 424–457

I. B. Bersuker, The Jahn–Teller Effect, Cambridge University Press, Cambridge, 2006 (https://dx.doi.org/10.1017/CBO9780511524769)

R. Renner, Z. Physik 92 (1934) 172 (https://dx.doi.org/10.1007/BF01350054)

U. Öpik, M. H. L. Pryce, Proc. R. Soc., A 238 (1957) 425 (https://dx.doi.org/10.1098/rspa.1957.0010)

I. B. Bersuker, Chem. Rev. 113 (2013) 1351 (https://dx.doi.org/10.1021/cr300279n)

T. Azumi, K. Matsuzaki, Photochem. Photobiol. 25 (1977) 315 (https://dx.doi.org/10.1021/cr300279n)

H. Köppel, W. Domcke, L. S. Cederbaum, Multimode Molecular Dynamics Beyond the Born–Oppenheimer Approximation, Adv. Chem. Physics, Vol. 57, in I. Prigogine, S. A. Rice, Eds., Wiley 2007, pp. 59–246 (https://dx.doi.org/10.1002/9780470142813.ch2)

A. J. Millis, P. B. Littlewood, B. I. Shraiman, Phys. Rev. Lett. 74 (1995) 5144 (https://dx.doi.org/10.1103/PhysRevLett.74.5144)

A. J. Millis, B. I. Shraiman, R. Mueller, Phys. Rev. Lett. 77 (1996) 175 (https://dx.doi.org/10.1103/PhysRevLett.77.175)

J. G. Bednorz, K. A. Müller, Z. Physik, B: Cond. Matter 64 (1986) 189 (https://dx.doi.org/10.1007/BF01303701)

R. H. Zadik, Y. Takabayashi, G. Klupp, R. H. Colman, A. Y. Ganin, A. Potočnik, P. Jeglič, D. Arčon, P. Matus, K. Kamarás, Y. Kasahara, Y. Iwasa, A. N. Fitch, Y. Ohishi, G. Garbarino, K. Kato, M. J. Rosseinsky, K. Prassides, Sci. Adv. 1 (2015) e1500059 (https://dx.doi.org/10.1126/sciadv.1500059)

M. G. Schultz, T. S. Nunner, F. von Oppen, Phys. Rev., B 77 (2008) 075323 (https://dx.doi.org/10.1103/PhysRevB.77.075323)

I. B. Bersuker, Phys. Lett. 20 (1966) 589 (https://dx.doi.org/10.1016/0031-9163(66)91127-9)

P. Garcia-Fernandez, I. B. Bersuker, Phys. Rev. Lett. 106 (2011) 246406 (https://dx.doi.org/10.1103/PhysRevLett.106.246406)

M. Atanasov, J. M. Zadrozny, J. R. Long, F. Neese, Chem. Sci. 4 (2013) 139 (https://dx.doi.org/10.1039/c2sc21394j)

M. Gruden-Pavlović, M. Perić, M. Zlatar, P. Garcia-Fernandez, Chem. Sci. 5 (2014) 1453 (https://dx.doi.org/10.1039/C3SC52984C)

M. Perić, A. García-Fuente, M. Zlatar, C. Daul, S. Stepanović, P. García-Fernández, M. Gruden-Pavlović, Chem. Eur. J. 21 (2015) 3716 (https://dx.doi.org/10.1002/chem.201405480)

W. Domcke, H. Köppel, L. S. Cederbaum, Mol. Phys. 43 (1981) 851 (https://dx.doi.org/10.1080/00268978100101721)

M. Perić, S. D. Peyerimhoff, J. Mol. Spectrosc. 212 (2002) 153 (https://dx.doi.org/10.1006/JMSP.2002.8534)

M. Perić, S. D. Peyerimhoff, J. Chem. Phys. 102 (1995) 3685 (https://dx.doi.org/10.1063/1.468599)

M. Mitić, R. Ranković, M. Milovanović, S. Jerosimić, M. Perić, Chem. Phys. 464 (2016) 55 (https://dx.doi.org/10.1016/J.CHEMPHYS.2015.11.002)

M. Perić, Mol. Phys. 105 (2007) 59 (https://dx.doi.org/10.1080/00268970601129076)

M. Perić, B. Ostojić, J. Radić-Perić, Phys. Rep. 290 (1997) 283 (https://dx.doi.org/10.1016/S0370-1573(97)00018-5)

M. Perić, S. D. Peyerimhoff, R. J. Buenker, Mol. Phys. 49 (1983) 379 (https://dx.doi.org/10.1080/00268978300101241)

I. B. Bersuker, Spontaneous Symmetry Breaking in Matter Induced by Degeneracies and Pseudodegeneracies, in Adv. Chem. Physics, Vol. 160, S. A. Rice, A. R. Dinner, Eds., Wiley, 2016, pp. 159–208 (https://dx.doi.org/10.1002/9781119165156.ch3)

P. Garcia-Fernandez, I. B. Bersuker, Int. J. Quantum Chem. 112 (2012) 3025 (https://dx.doi.org/10.1002/qua.24204)

P. García-Fernández, J. A. Aramburu, M. Moreno, M. Zlatar, M. Gruden-Pavlovic, J. Chem. Theory Comput. (2014) 1824 (https://dx.doi.org/10.1021/ct4011097)

Y. Liu, I. B. Bersuker, P. Garcia-Fernandez, J. E. Boggs, J. Phys. Chem., A 116 (2012) 7564 (https://dx.doi.org/10.1021/jp3032836)

P. Garcia-Fernandez, J. A. Aramburu, M. Moreno, Phys. Rev., B 83 (2011) 174406 (https://dx.doi.org/10.1103/PhysRevB.83.174406)

R. F. W. Bader, Mol. Phys. 3 (1960) 137 (https://dx.doi.org/10.1103/10.1080/00268976000100161)

R. F. W. Bader, Can. J. Chem. 40 (1962) 1164 (https://dx.doi.org/10.1139/v62-178)

R. F. W. Bader, A. D. Bandrauk, J. Chem. Phys. 49 (1968) 1666 (https://dx.doi.org/10.1063/1.1670293)

R. G. Pearson, J. Am. Chem. Soc. 91 (1969) 4947 (https://dx.doi.org/10.1021/ja01046a001)

R. G. Pearson, Symmetry Rules for Chemical reactions, A Wiley-Interscience Publication, New York,1976 (https://dx.doi.org/10.1002/bbpc.19790830620)

M. Zlatar, C.-W. Schläpfer, C. Daul, A New Method to Describe Multimode Jahn–Teller Efect Using Density Functional Theory, in The Jahn–Teller-Effect Fundamentals and Implications for Physics and Chemistry, H. Koeppel, D. R. Yarkoni, H. Barentzen, Eds., Springer Series in Chemical Physics, Vol. 97, 2009, pp. 131 (https://dx.doi.org/10.1007/978-3-642-03432-9_6)

A. R. Ilkhani, N. N. Gorinchoy, I. B. Bersuker, Chem. Phys. 460 (2015) 106 (https://dx.doi.org/10.1016/J.CHEMPHYS.2015.07.015)

A. R. Ilkhani, W. Hermoso, I. B. Bersuker, Chem. Phys. 460 (2015) 75 (https://dx.doi.org/10.1016/J.CHEMPHYS.2015.02.017)

P. Garcia-Fernandez, I. B. Bersuker, J. A. Aramburu, M. T. Barriuso, M. Moreno, Phys. Rev., B 71 (2005) 184110 (https://dx.doi.org/10.1103/PhysRevB.71.184117)

Y. Liu, I. B. Bersuker, W. Zou, J. E. Boggs, J. Chem. Theory Comput. 5 (2009) 2679 (https://dx.doi.org/10.1021/ct9002515)

R. G. Parr, W. Yang, Density-Functional Theory of Atoms and Molecules, Oxford University Press, Oxford, 1989 (https://global.oup.com/academic/product/density-functional-theory-of-atoms-and-molecules-9780195092769?cc=rs〈=en&)

C. J. Cramer, D. G. Truhlar, Phys. Chem. Chem. Phys. 11 (2009) 10757 (https://dx.doi.org/10.1039/b907148b)

F. Neese, Coord. Chem. Rev. 253 (2009) 526 (https://dx.doi.org/10.1016/j.ccr.2008.05.014)

J. P. Perdew, A. Ruzsinszky, Int. J. Quantum Chem. 110 (2010) 2801 (https://dx.doi.org/10.1002/qua.22829)

K. Burke, L. O. Wagner, Int. J. Quantum Chem. 113 (2013) 96 (https://dx.doi.org/10.1002/qua.24259)

A. D. Becke, J. Chem. Phys. 140 (2014) 18A301 (https://dx.doi.org/10.1063/1.4869598)

H. S. Yu, S. L. Li, D. G. Truhlar, J. Chem. Phys. 145 (2016) 130901 (https://dx.doi.org/10.1063/1.4963168)

P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864 (https://dx.doi.org/10.1103/PhysRev.136.B864)

L. Goerigk, A. Hansen, C. Bauer, S. Ehrlich, A. Najibi, S. Grimme, Phys. Chem. Chem. Phys. 19 (2017) 32184 (https://dx.doi.org/10.1039/C7CP04913G)

I. B. I. B. Bersuker, J. Comp. Chem. 18 (1997) 260 (https://dx.doi.org/10.1002/(SICI)1096-987X(19970130)18:2<260::AID-JCC10>3.0.CO;2-M)

I. G. G. Kaplan, J. Mol. Struct. 838 (2007) 39 (https://dx.doi.org/10.1016/J.MOLSTRUC.2007.01.012)

I. B. Bersuker, J. Phys. Conf. Ser. 833 (2017) 012001 (https://dx.doi.org/10.1088/1742-6596/833/1/012001)

M. Levy, Phys. Rev., A 26 (1982) 1200 (https://dx.doi.org/10.1103/PhysRevA.26.1200)

M. Levy, Int. J. Quantum Chem. 110 (2010) 3140 (https://dx.doi.org/10.1002/qua.22895)

A. K. Theophilou, J. Phys., C: Solid State Phys. 12 (1979) 5419 (https://dx.doi.org/10.1088/0022-3719/12/24/013)

A. K. Theophilou, P. G. Papaconstantinou, Phys. Rev., A 61 (2000) 022502 (https://dx.doi.org/10.1103/PhysRevA.61.022502)

M. Filatov, J. Chem. Theory Comput. 9 (2013) 4526 (https://dx.doi.org/10.1021/ct400598b)

R. Requist, E. K. U. Gross, Phys. Rev. Lett. 117 (2016) 193001 (https://dx.doi.org/10.1103/PhysRevLett.117.193001)

R. Baer, Phys. Rev. Lett. 104 (2010) 073001 (https://dx.doi.org/10.1103/PhysRevLett.104.073001)

J. M. García-Lastra, M. T. Barriuso, J. A. Aramburu, M. Moreno, Chem. Phys. 317 (2005) 103 (https://dx.doi.org/10.1016/j.chemphys.2005.06.004)

W. L. Clinton, B. Rice, J. Chem. Phys. 30 (1959) 542 (https://dx.doi.org/10.1063/1.1729984)

H. Nakatsuji, J. Am. Chem. Soc. 96 (1974) 30 (https://dx.doi.org/10.1021/ja00808a005)

R. Bruyndonckx, C. Daul, P. T. Manoharan, E. Deiss, R. Bruyndockx, C. Daul, P. T. Manoharan, E. Deiss, Inorg. Chem. 36 (1997) 4251 (https://dx.doi.org/10.1021/ic961220+)

T. K. Kundu, R. Bruyndonckx, C. Daul, P. T. Manoharan, Inorg. Chem. 38 (1999) 3931 (https://dx.doi.org/10.1021/ic981111q)

M. Gruden-Pavlović, P. García-Fernández, L. Andjelković, C. Daul, M. Zlatar, J. Phys. Chem., A 115 (2011) 10801 (https://dx.doi.org/10.1021/jp206083j)

M. Zlatar, M. Gruden-Pavlović, C. W. Schläpfer, C. Daul, J. Mol. Struct. THEOCHEM 954 (2010) 86 (https://dx.doi.org/10.1016/j.theochem.2010.04.020)

L. Andjelković, M. Gruden-Pavlović, M. Zlatar, Chem. Phys. 460 (2015) 64 (https://dx.doi.org/10.1016/j.chemphys.2015.05.007)

M. Zlatar, M. Gruden-Pavlović, C.-W. Schläpfer, C. Daul, Chimia 64 (2010) 161 (https://dx.doi.org/10.2533/chimia.2010.161)

M. Perić, L. Andjelković, M. Zlatar, C. Daul, M. Gruden-Pavlović, Polyhedron 80 (2014) 69 (https://dx.doi.org/10.1016/j.poly.2014.02.005)

L. Andjelkovic, S. Stepanovic, F. Vlahovic, M. Zlatar, M. Gruden, L. Andjelković, S. Stepanović, F. Vlahović, M. Zlatar, M. Gruden, Phys. Chem. Chem. Phys. 18 (2016) 29122 (https://dx.doi.org/10.1039/C6CP03859J)

M. Zlatar, C.-W. Schläpfer, E. P. Fowe, C. Daul, Pure Appl. Chem. 81 (2009) 1397 (https://dx.doi.org/10.1351/PAC-CON-08-06-04)

L. Andjelković, M. Gruden-Pavlović, C. Daul, M. Zlatar, Int. J. Quantum Chem. 113 (2013) 859 (https://dx.doi.org/10.1002/qua.24245)

M. Atanasov, P. Comba, C. a Daul, A. Hauser, J. Phys. Chem., A 111 (2007) 9145 (https://dx.doi.org/10.1021/jp0731912)

M. Gruden-Pavlović, M. Zlatar, C.-W. Schläpfer, C. Daul, J. Mol. Struct. THEOCHEM 954 (2010) 80 (https://dx.doi.org/10.1016/j.theochem.2010.03.031)

M. Swart, M. Gruden, Acc. Chem. Res. 49 (2016) 2690 (https://dx.doi.org/10.1021/acs.accounts.6b00271)

H. Ramanantoanina, M. Zlatar, P. García-Fernández, C. Daul, M. Gruden-Pavlović, Phys. Chem. Chem. Phys. 15 (2013) 1252 (https://dx.doi.org/10.1039/c2cp43591h)

V. P. Khlopin, V. Z. Polinger, I. B. Bersuker, Theor. Chim. Acta 48 (1978) 87 (https://dx.doi.org/10.1007/BF02399020)

I. B. Bersuker, V. Z. Polinger, Vibronic interactions in Molecules and Crystals, Springer-

-Verlag, Berlin, 1989 (https://www.springer.com/gp/book/9783642834813)

J. H. Ammeter, L. Zoller, J. Bachmann, P. Baltzer, E. Gamp, R. Bucher, E. Deiss, Helv. Chim. Acta 64 (1981) 1063 (https://dx.doi.org/10.1002/chin.198141061)

F. A. Blankenship, R. L. Belford, J. Chem. Phys. 36 (1962) 633 (https://dx.doi.org/10.1063/1.1732585)

R. B. Johannesen, G. A. Candela, T. Tsang, J. Chem. Phys. 48 (1968) 5544 (https://doi.org/10.1063/1.1668254)

Y. Morino, H. Uehara, J. Chem. Phys. 45 (1966) 4543 (https://dx.doi.org/10.1063/1.1727535)

H. von Busch, V. Dev, H.-A. Eckel, S. Kasahara, J. Wang, W. Demtröder, P. Sebald, W. Meyer, Phys. Rev. Lett. 81 (1998) 4584 (https://dx.doi.org/10.1103/PhysRevLett.81.4584)

J. Gaus, K. Kobe, V. Bonacic-Koutecky, H. Kuehling, J. Manz, B. Reischl, S. Rutz, E. Schreiber, L. Woeste, J. Phys. Chem. 97 (1993) 12509 (https://dx.doi.org/10.1021/j100150a011)

B. E. Applegate, T. A. Miller, J. Chem. Phys. 114 (2001) 4855 (https://dx.doi.org/10.1063/1.1348275)

B. E. Applegate, T. A. Miller, J. Chem. Phys. 117 (2002) 10654 (https://dx.doi.org/10.1063/1.1520531)

V. Perebeinos, P. B. Allen, M. Pederson, Phys. Rev., A 72 (2005) 12501 (https://dx.doi.org/10.1103/PhysRevA.72.012501)

K. Tokunaga, T. Sato, K. Tanaka, J. Chem. Phys. 124 (2006) 154303 (https://dx.doi.org/10.1063/1.2184317)

I. Sioutis, V. L. Stakhursky, G. Tarczay, T. A. Miller, J. Chem. Phys. 128 (2008) 084311 (https://dx.doi.org/10.1063/1.2829471)

N. Manini, A. Dal Corso, M. Fabrizio, E. Tosatti, Philos. Mag., B 81 (2001) 793 (https://dx.doi.org/10.1080/13642810110062663)

H. Ramanantoanina, M. Gruden-Pavlovic, M. Zlatar, C. Daul, Int. J. Quantum Chem. 113 (2013) 802 (https://dx.doi.org/10.1002/qua.24080)

T. Yamabe, K. Yahara, T. Kato, K. Yoshizawa, J. Phys. Chem., A 104 (2000) 589 (https://dx.doi.org/10.1021/jp992496g)

T. Kato, K. Yoshizawa, J. Chem. Phys. 110 (1999) 249 (https://dx.doi.org/10.1063/1.478100)

R. Bucher, ESR-Untersuchungen an Jahn-Teller-Aktiven Sandwitchkomplexen, ETH Zuerich, 1977 (https://dx.doi.org/10.3929/ethz-a-000150322)

S. Stepanović, M. Zlatar, M. Swart, M. Gruden, J. Chem. Inf. Model. 59 (2019) 1806 (https://doi.org/10.1021/acs.jcim.8b00870)

J. Tóbik, E. Tosatti, J. Mol. Struct. 838 (2007) 112 (https://doi.org/10.1016/J.MOLSTRUC.2006.12.051)

M. Zlatar, M. Gruden-Pavlovic, M. Guell, M. Swart, M. Gruden-Pavlović, M. Güell, M. Swart, Phys. Chem. Chem. Phys. 15 (2013) 6631 (https://dx.doi.org/10.1039/C2CP43735J)

P. Chaudhuri, K. Oder, K. Wieghardt, J. Weiss, J. Reedijk, W. Hinrichs, J. Wood, A. Ozarowski, H. Stratemaier, D. Reinen, Inorg. Chem. 25 (1986) 2951 (https://dx.doi.org/10.1021/ic00237a007)

K. Wieghardt, W. Walz, B. Nuber, J. Weiss, A. Ozarowski, H. Stratemeier, D. Reinen, Inorg. Chem. 25 (1986) 1650 (https://dx.doi.org/10.1021/ic00230a025)

E. Gamp, ESR-Untersuchungen uber den Jahn-Teller-Effekt in oktaedrischen Kupfer(II)- Komplexen mit trigonalen dreizahnigen Liganden, ETH, Zurich, 1980 (https://dx.doi.org/10.3929/ethz-a-000215808)

A. D. Liehr, Z. Phys. Chem. 9 (1956) 338 (https://dx.doi.org/10.1524/zpch.1956.9.5_6.338)

L. C. Snyder, J. Chem. Phys. 33 (1960) 619 (https://dx.doi.org/10.1063/1.1731211)

W. D. Hobey, A. D. McLachlan, J. Chem. Phys. 33 (1960) 1703 (https://dx.doi.org/10.1063/1.1731485)

R. Meyer, F. Graf, T. Ha, H. H. Gunthard, Chem. Phys. Lett. 66 (1979) 65 (https://dx.doi.org/10.1016/0009-2614(79)80370-X)

W. T. Borden, E. R. Davidson, J. Am. Chem. Soc. 101 (1979) 3771 (https://dx.doi.org/10.1021/ja00508a012)

C. Cunha, S. Canuto, J. Molec. Struct THEOCHEM 464 (1999) 73 (https://dx.doi.org/10.1016/S0166-1280(98)00536-3)

M. J. Bearpark, M. A. Robb, N. Yamamoto, Spectrochim. Acta, A 55 (1999) 639 (https://dx.doi.org/10.1016/S1386-1425(98)00267-4)

J. H. Kiefer, R. S. Tranter, H. Wang, A. F. Wagner, Int. J. Chem. Kin. 33 (2001) 834 (https://dx.doi.org/10.1002/kin.10006)

S. Zilberg, Y. Haas, J. Am. Chem. Soc. 124 (2002) 10683 (https://dx.doi.org/10.1021/ja026304y)

T. Ichino, S. W. Wren, K. M. Vogelhuber, A. J. Gianola, W. C. Lineberger, J. F. Stanton, J. Chem. Phys. 129 (2008) 084310 (https://dx.doi.org/10.1063/1.2973631)

D. Leicht, M. Kaufmann, G. Schwaab, M. Havenith, J. Chem. Phys. 145 (2016) 074304 (https://dx.doi.org/10.1063/1.4960781)

A. D. Liehr, J. Phys. Chem. 67 (1963) 389 (https://dx.doi.org/10.1021/j100796a043)

N. Iwahara, T. Sato, K. Tanaka, L. F. Chibotaru, Phys. Rev., B 82 (2010) 245409 (https://dx.doi.org/10.1103/PhysRevB.82.245409)

J. H. Ammeter, R. Bucher, N. Oswald, J. Am. Chem. Soc. 96 (1974) 7833 (https://dx.doi.org/10.1021/ja00832a049)

I. Utke, A. Gölzhäuser, Angew. Chem. Int. Ed. 49 (2010) 9328 (https://dx.doi.org/10.1002/anie.201002677)

M. Zlatar, M. Allan, J. Fedor, J. Phys. Chem., C 120 (2016) 10667 (https://dx.doi.org/10.1021/acs.jpcc.6b02660)

K. E. R. Marriott, L. Bhaskaran, C. Wilson, M. Medarde, S. T. Ochsenbein, S. Hill, M. Murrie, Chem. Sci. 6 (2015) 6823 (https://dx.doi.org/10.1039/C5SC02854J).




DOI: https://doi.org/10.2298/JSC190510064Z

Copyright (c) 2019 J. Serb. Chem. Soc.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

IMPACT FACTOR 0.828 (140 of 172 journals)
5 Year Impact Factor 0.917 (140 of 172 journals)