Abstract
The foundations of the two-component quantum theory of atoms in molecules (TC-QTAIM) are addressed in this contribution. In this regard, the theory is presented in an axiomatic manner and the main theorems describing regional properties of atoms in molecules are considered in detail. This is an extension of the orthodox quantum theory of atoms in molecules (QTAIM) for dealing with non-adiabatic wavefunctions of usual molecules as well as extracting the regional quantum structure of exotic species from the corresponding wavefunctions. The best examples of the latter are positronic and muonic species. The computational study of a model system consisting of a clamped lithium nucleus, four electrons, and a positively charged quantum particle carrying a unit of positive charge with a variable mass, m = 200–1013 m e, supplements the theoretical argument demonstrating unambiguously that the TC-QTAIM analysis yields reasonable results. It reveals that the contribution of the positively charged particle in the topological analysis and basin properties is non-negligible. Most importantly, it is demonstrated that by increasing the mass of the positive particle, the TC-QTAIM analysis tends toward the QTAIM analysis of the lithium hydride system considered within the clamped nucleus paradigm. This result seems to indicate that the orthodox QTAIM is just the asymptote of the TC-QTAIM, the latter encompasses the former. Thus, one may claim that the TC-QTAIM is a unified framework for the AIM analysis of vast variety of quantum systems.
Similar content being viewed by others
References
Helgaker T, Klopper W, Tew DP (2008) Mol Phys 106:2107
Schwabe T, Grimme S (2008) Acc Chem Res 41:569
Bader RWF (1990) Atoms in molecules: a quantum theory. Oxford University Press, Oxford
Popelier PLA (2000) Atoms in molecules an introduction. Pearson, London
Matta C, Boyd RJ (2007) Quantum theory of atoms in molecules: from solid state to DNA and drug design. Wiley-VCH, Weinheim
Walker DC (1985) Acc Chem Res 18:167
Horváth D (1994) Nucl Inst Meth Phys Res B 87:273
Friedman E (1998) Nucl Phys A 639:511c
Indelicato P (2004) Phys Scr T 112:20
Born M, Oppenheimer JR (1927) Ann Phys (Leipzig) 84:457
Baer M (2006) Beyond Born–Oppenheimer. Wiley-Interscience, New Jersey
Clary DC, Benoit DM, Van Mourik T (2000) Acc Chem Res 33:441
Garcia-Viloca M, Gao J, Karplus M, Truhlar DG (2004) Science 303:186
Masgrau L, Roujeinikova A, Johannissen LO, Hothi P, Basran J, Ranaghan KE, Mutholland AJ, Sutcliffe MJ, Scrutton NS, Leys D (2006) Science 312:237
Hammes-Schiffer S (2009) Acc Chem Res 42:1881
Nagel ZD, Klinman JP (2010) Chem Rev 110:PR41
Hammes-Schiffer S, Stuchebrukhov AA (2010) Chem Rev 110:6939
Nasertayoob P, Goli M, Shahbazian Sh (2011) Int J Quantum Chem 111:1970
Goli M, Shahbazian Sh (2011) Int J Quantum Chem 111:1982
Zadeh FH, Shahbazian Sh (2011) Int J Quantum Chem 111:1999
Goli M, Shahbazian Sh (2011) Theor Chem Acc 129:235
Helgaker T, Jørgenson P, Olsen J (2000) Molecular electronic-structure theory. Wiley, New York
Sutcliffe BT, Woolley RG (2005) Phys Chem Chem Phys 7:3664
Sutcliffe BT (2010) Theor Chem Acc 127:121
Kozlowski PM, Adamowicz L (1993) Chem Rev 93:2007
Cafiero M, Bubin S, Adamowicz L (2003) Phys Chem Chem Phys 5:1491
Bubin S, Cafiero M, Adamowicz L (2005) Adv Chem Phys 131:377
Kinghorn DB, Adamowicz L (1997) J Chem Phys 106:8760
Kinghorn DB (1996) Int J Quantum Chem 57:141
Kinghorn DB, Adamowicz L (1999) J Chem Phys 110:7166
Kinghorn DB, Adamowicz L (1999) Phys Rev Lett 83:2541
Kinghorn DB, Adamowicz L (2000) J Chem Phys 113:4203
Scheu CE, Kinghorn DB, Adamowicz L (2001) J Chem Phys 114:3393
Cafiero M, Adamowicz L (2002) Phys Rev Lett 88:033002
Cafiero M, Adamowicz L (2002) J Chem Phys 116:5557
Cafiero M, Adamowicz L (2002) Phys Rev Lett 89:073001
Bubin S, Adamowicz L (2003) J Chem Phys 118:3079
Cafiero M, Adamowicz L, Duran M, Luis JM (2003) J Mol Struct (Theochem) 633:113
Bubin S, Adamowicz L (2004) J Chem Phys 120:6051
Bubin S, Adamowicz L (2004) J Chem Phys 121:6249
Bubin S, Bednarz E, Adamowicz L (2005) J Chem Phys 122:041102
Bubin S, Adamowicz L (2005) Chem Phys Lett 403:185
Bednarz E, Bubin S, Adamowicz L (2005) J Chem Phys 122:164302
Pavanello M, Bubin S, Molski M, Adamowicz L (2005) J Chem Phys 123:104306
Bubin S, Adamowicz L, Molski M (2005) J Chem Phys 123:134310
Stanke M, Kędziera D, Molski M, Bubin S, Barysz M, Adamowicz L (2006) Phys Rev Lett 96:233002
Bubin S, Adamowicz L (2006) J Chem Phys 124:2243317
Bubin S, Adamowicz L (2006) J Chem Phys 125:064309
Kędziera D, Stanke M, Bubin S, Barysz M, Adamowicz L (2006) J Chem Phys 125:084303
Kędziera D, Stanke M, Bubin S, Barysz M, Adamowicz L (2006) J Chem Phys 125:014318
Bubin S, Adamowicz L (2006) Phys Rev A 74:052502
Bubin S, Adamowicz L (2007) J Chem Phys 126:214305
Bubin S, Stanke M, Kędziera D, Adamowicz L (2007) Phys Rev A 75:062504
Bubin S, Stanke M, Kędziera D, Adamowicz L (2007) Phys Rev A 76:022512
Stanke M, Kędziera D, Bubin S, Molski M, Adamowicz L (2007) Phys Rev A 76:052506
Bubin S, Adamowicz L (2008) J Chem Phys 128:114107
Stanke M, Kędziera D, Bubin S, Molski M, Adamowicz L (2008) J Chem Phys 128:114313
Bubin S, Lenoarski F, Stanke M, Adamowicz L (2009) Chem Phys Lett 477:12
Stanke M, Bubin S, Molski M, Adamowicz L (2009) Phys Rev A 79:032507
Bubin S, Lenoarski F, Stanke M, Adamowicz L (2009) J Chem Phys 130:124120
Bubin S, Stanke M, Adamowicz L (2009) J Chem Phys 131:044128
Bubin S, Stanke M, Molski M, Adamowicz L (2010) Chem Phys Lett 494:21
Bubin S, Stanke M, Adamowicz L (2010) Chem Phys Lett 500:229
Cafiero M, Adamowicz L (2004) Chem Phys Lett 387:136
Cafiero M, Adamowicz L (2005) J Chem Phys 122:184305
Cafiero M, Adamowicz L (2007) Int J Quantum Chem 107:2679
Bednarz E, Bubin S, Adamowicz L (2005) Mol Phys 103:1169
Bochevarov AD, Valeev EF, Sherrill CD (2005) Mol Phys 102:111
Thomas IL (1969) Chem Phys Lett 3:705
Thomas IL (1969) Phys Rev 185:90
Thomas IL (1970) Phys Rev A 2:72
Thomas IL (1970) Phys Rev A 2:728
Thomas IL, Joy HW (1970) Phys Rev A 2:1200
Thomas IL (1970) Phys Rev A 2:1675
Thomas IL (1970) Phys Rev A 3:565
Thomas IL (1970) Phys Rev A 3:1022
Thomas IL (1970) Phys Rev A 4:457
Thomas IL (1970) Phys Rev A 4:2120
Petitt BA (1986) Chem Phys Lett 130:399
Petitt BA, Danchura W (1987) J Phys B: At Mol Phys 20:1899
Tachikawa M, Mori K, Nakai H, Iguchi K (1998) Chem Phys Lett 290:437
Tachikawa M, Mori K, Suzuki K, Iguchi K (1998) Int J Quantum Chem 70:491
Shigeta Y, Ozaki Y, Kodama K, Nagao H, Kawabe H, Nishikawa K (1998) Int J Quantum Chem 69:629
Shigeta Y, Takahashi H, Yamanaka S, Mitani M, Nagao H, Yamaguchi K (1998) Int J Quantum Chem 70:659
Ishimoto T, Tachikawa M, Nagashima U (2009) Int J Quantum Chem 109:2677
Udagawa T, Tachikawa M (2009) Multi-component molecular orbital theory. Nova Science Publishers, New York
Tachikawa M, Osamura Y (2000) J Chem Phys 113:4942
Tachikawa M (2001) Chem Phys Lett 350:269
Tachikawa M (2002) Chem Phys Lett 360:494
Ishimoto T, Tachikawa M, Yamauchi M, KKitagawa H, Tokiwa H, Nagashima U (2003) Chem Phys Lett 372:503
Udagawa T, Tachikawa M (2006) J Chem Phys 125:244105
Ishimoto T, Tachikawa M, Nagashima U (2006) Int J Quantum Chem 106:1465
Tachikawa M, Taneda K, Mori K (1999) Int J Quantum Chem 75:497
Tachikawa M, Mori K, Osamura Y (1999) Mol Phys 96:1207
Ishida M, Tachikawa M, Tokiwa H, Mori K, Ishii A (1999) Surf Sci 438:47
Tachikawa M, Osamura Y (2000) Theor Chem Acc 104:29
Tachikawa M (2002) Mol Phys 100:881
Tachikawa M, Ishimoto T, Tokiwa H, Kasatani H, Deguchi K (2002) Ferroelectrics 268:3
Tachikawa M (2003) J Mol Struct (Theochem) 630:75
Ishimoto T, Tachikawa M, Yamauchi M, Kitagawa H, Tokiwa H, Nagashima U (2004) J Phys Soc Jpn 73:1775
Udagawa T, Ishimoto T, Tokiwa H, Tachikawa M, Nagashima U (2004) Chem Phys Lett 389:236
Ishimoto T, Tachikawa M, Tokiwa H, Nagashima U (2005) Chem Phys 314:231
Shibl MF, Tachikawa M, Kühn O (2005) Phys Chem Chem Phys 7:1368
Ishimoto T, Tachikawa M, Yamauchi M, Tokiwa H, Nagashima U (2005) J Phys Soc Jpn 74:3112
Udagawa T, Ishimoto T, Tokiwa H, Tachikawa M, Nagashima U (2006) J Phys Chem A 110:7279
Ishimoto T, Tachikawa M, Nagashima U (2006) J Chem Phys 125:144103
Itou Y, Mori S, Udagawa T, Tachikawa M, Ishimoto T, Nagashima U (2007) J Phys Chem A 111:261
Kikuta Y, Ishimoto T, Nagashima U (2008) Bull Chem Soc Jpn 81:820
Kikuta Y, Ishimoto T, Nagashima U (2008) Chem Phys 354:218
Ishimoto T, Ishihara Y, Teramae H, Baba M, Nagashima U (2008) J Chem Phys 128:184309
Tachikawa M (2008) Integr Ferroelectr 100:72
Ishimoto T, Ishihara Y, Teramae H, Baba M, Nagashima U (2008) J Chem Phys 129:214116
Udagawa T, Tachikawa M (2009) J Mol Struct (Theochem) 912:63
Ishimoto T, Tachikawa M, Nagashima U (2006) J Chem Phys 124:014112
Kita Y, Tachikawa M (2009) J Mol Struct (Theochem) 912:2
Ullah S, Ishimoto T, Williamson MP, Hansen PE (2011) J Phys Chem B 115:3208
Nakai H (2007) Int J Quantum Chem 107:2849
Nakai H, Sodeyama K, Hoshino M (2001) Chem Phys Lett 345:118
Nakai H (2002) Int J Quantum Chem 86:511
Hoshino M, Tsukamoto Y, Nakai H (2007) Int J Quantum Chem 107:2575
Nakai H, Sodeyama K (2003) J Chem Phys 118:1119
Nakai H, Hoshino M, Miyamoto K, Hyodo S (2005) J Chem Phys 122:164101
Miyamoto K, Hoshino M, Nakai H (2006) J Chem Theory Comput 2:1544
Hoshino M, Nakai H (2006) J Chem Phys 124:194110
Sodeyama K, Nishizawa H, Hoshino M, Kobayashi M, Nakai H (2007) Chem Phys Lett 433:409
Nakai H, Ikabata Y, Tsukamoto Y, Imamura Y, Miyamoto K, Hoshino M (2007) Mol Phys 105:2649
Sodeyama K, Miyamoto K, Nakai H (2006) Chem Phys Lett 421:72
Ishimoto T, Tachikawa M, Nagashima U (2006) Int J Quantum Chem 108:472
Ishimoto T, Tachikawa M, Nagashima U (2006) J Chem Phys 128:164118
Imamura Y, Kiryu H, Nakai H (2008) J Comput Chem 29:735
Imamura Y, Tsukamoto Y, Kiryu H, Nakai H (2009) Bull Chem Soc Jpn 82:1133
Sutcliffe B (2005) J Chem Phys 123:237101
Nakai H, Hoshino M, Miyamoto K, Hyodo S (2005) J Chem Phys 123:237102
Ikabata Y, Imamura Y, Nakai H (2011) J Phys Chem A 115:1433
Webb SP, Iordanov T, Hammes-Schiffer S (2002) J Chem Phys 117:4106
Iordanov T, Hammes-Schiffer S (2003) J Chem Phys 118:9489
Swalina C, Pak MV, Hammes-Schiffer S (2005) Chem Phys Lett 404:394
Skone JH, Pak MV, Hammes-Schiffer S (2005) J Chem Phys 123:134108
Pak MV, Hammes-Schiffer S (2004) Phys Rev Lett 92:103002
Pak MV, Swalina C, Webb SP, Hammes-Schiffer S (2005) Chem Phys 304:227
Swalina C, Pak MV, Hammes-Schiffer S (2005) J Chem Phys 123:041303
Hazra A, Skone JH, Hammes-Schiffer S (2005) J Chem Phys 130:054108
Hammes-Schiffer S (2002) ChemPhysChem 3:33
Swalina C, Hammes-Schiffer S (2005) J Phys Chem A 109:10410
Reyes A, Pak MV, Hammes-Schiffer S (2005) J Chem Phys 123:064104
Swalina C, Pak MV, Chakraborty A, Hammes-Schiffer S (2006) J Phys Chem A 110:9983
Chakraborty A, Pak MV, Hammes-Schiffer S (2008) J Chem Phys 129:014101
Pak MV, Chakraborty A, Hammes-Schiffer S (2009) J Phys Chem A 113:4004
Auer B, Pak MV, Hammes-Schiffer S (2010) J Phys Chem C 114:5582
Auer B, Hammes-Schiffer S (2010) J Chem Phys 132:084110
González SA, Aguirre NF, Reyes A (2008) Int J Quantum Chem 108:1742
González SA, Reyes A (2010) Int J Quantum Chem 110:689
Moreno DV, González SA, Reyes A (2010) J Phys Chem A 114:9231
Moreno DV, González SA, Reyes A (2010) J Chem Phys 134:024115
Moncada F, González SA, Reyes A (2010) Mol Phys 108:1545
Brueckner KA, Buchler JR, Clark RC, Lombard RJ (1969) Phys Rev 181:1543
Brueckner KA, Chirico JH, Meldner HW (1971) Phys Rev C 4:732
Sander LM, Shore HB, Sham LJ (1973) Phys Rev Lett 31:533
Kalia RK, Vashishta P (1978) Phys Rev B 17:2655
Nieminen RM, Boroński E, Lantto LJ (1985) Phys Rev B 32:1377
Capitani JF, Nalewajski RF, Parr RG (1982) J Chem Phys 76:568
Kryachko ES, Ludeńa EV, Mujica V (1991) Int J Quantum Chem 40:589
Gidopoulos N (1998) Phys Rev B 57:2146
Kreibich T, Gross EKU (2001) Phys Rev Lett 86:2984
van Leeuwen R (2004) Phys Rev B 69:115110. doi:10.1103/PhysRevB.69.199901
Kreibich T, van Leeuwen R, Gross EKU (2008) Phys Rev A 78:022501
Shigeta Y, Nagao H, Nishikawa K, Yamaguchi K (1999) Int J Quantum Chem 75:875
Shigeta Y, Nagao H, Nishikawa K, Yamaguchi K (1999) J Chem Phys 111:6171
Shigeta Y (2009) Bull Chem Soc Jpn 82:1323
Pak MV, Chakraborty A, Hammes-Schiffer S (2007) J Phys Chem A 111:4522
Chakraborty A, Pak MV, Hammes-Schiffer S (2008) Phys Rev Lett 101:153001
Chakraborty A, Hammes-Schiffer S (2008) J Chem Phys 129:204101
Chakraborty A, Pak MV, Hammes-Schiffer S (2009) J Chem Phys 131:124115
Matta CF, Arabi AA, Keith T (2007) J Phys Chem A 111:8864
Sutcliffe BT, Woolley RG (2005) Chem Phys Lett 408:445
Mátyus E, Hutter J, Müller-Herold U, Reiher M (2011) Phys Rev A 83:052512
Nasertayoob P, Shahbazian Sh (2008) Int J Quantum Chem 108:1477
Nasertayoob P, Shahbazian Sh (2009) Int J Quantum Chem 109:726
Nasertayoob P, Shahbazian Sh (2010) Int J Quantum Chem 110:1188
Zadeh FH, Shahbazian Sh (2011) Int J Quantum Chem 111:2788
Zadeh FH, Shahbazian Sh (2011) Theor Chem Acc 128:175
Shahbazian Sh (2011) Int J Quantum Chem 111:4497
Anderson JSM, Ayers PW, Rodriguez Hernandez JI (2010) J Phys Chem A 114:8884
Bader RFW, Popelier PLA (1993) Int J Quantum Chem 45:189
Ayers PW (2000) J Chem Phys 113:10886
Bader RFW (2001) Thero Chem Acc 105:276
Collard K, Hall GG (1977) Int J Quantum Chem 12:623
Nasertayoob P, Shahbazian S (2008) J Mol Struct Theochem 869:53
Geerlings P, De Proft F, Langenaeker W (2003) Chem Rev 103:1793
Anderson JSM, Melin J, Ayers PW (2007) J Chem Theory Comput 3:358
Anderson JSM, Melin J, Ayers PW (2007) J Chem Theory Comput 3:375
Chattaraj PK (2009) Chemical reactivity theory: a density functional view. CRC Press, New York
Evans E, Ritchie K (1997) Biophys J 72:1541
Grandbois M, Beyer M, Rief M, Clausen-Schaumann H, Gaub HE (1999) Science 283:1727
Bader RFW (2000) Phys Rev B 61:7795
Cortés-Guzman F, Bader RFW (2004) J Phys Org Chem 17:95
Bushmarinov IS, Lyssenko KA, Antipin MY (2009) Russ Chem Rev 78:283
Bader RFW (1989) J Chem Phys 91:6989
Keith TA, Bader RFW (1992) Chem Phys Lett 194:1
Keith TA, Bader RFW (1993) Chem Phys Lett 210:223
Bader RFW, Keith TA (1993) J Chem Phys 99:3669
Bader RFW, Keith TA (1993) J Chem Phys 99:3683
Bader RFW, Keith TA (1996) Int J Quantum Chem 60:373
Keith TA, Bader RFW (1996) Can J Chem 74:185
Bader RFW, Zou PF (1992) Chem Phys Lett 191:54
Biegler-König F (2000) J Comput Chem 21:1040
Biegler-König F, Schönbohm J, Bayles D (2001) J Comput Chem 22:545
Biegler-König F, Schönbohm J (2002) J Comput Chem 23:1489
McMurchie LE, Davidson ER (1978) J Comput Phys 26:218
Cancès E, Le Bris C (2000) Int J Quantum Chem 79:82
Kudin KN, Scuseria GE, Cancès E (2002) J Chem Phys 116:8255
Huber H (1981) J Mol Struct (Theochem) 76:277
Tonachini G, Schlegel HB (1987) J Chem Phys 87:514
Hurley AC (1988) J Comput Chem 9:75
Helgaker T, Almlöf J (1988) J Chem Phys 89:4889
Hashimoto K, Osamura Y (1991) J Chem Phys 95:1121
Hashimoto K, Osamura Y (1992) Can J Chem 70:547
Rao SS (2009) Engineering optimization: theory and practice. Wiley, USA
Nocedal J, Wright SJ (2006) Numerical optimization. Springer, USA
Khanna MP (2009) Introduction to particle physics. PHI Learning, New Delhi
Kato T (1957) Commun Pure Appl Math 10:151
Steiner E (1963) J Chem Phys 39:2365
Bingel WA (1963) Z Naturforsch A 18:1249
Acknowledgments
The authors are grateful to the Research Council of Shahid Beheshti University (SBU) for a grant for this project. The detailed reading of previous drafts by Prof. W.H. Eugen Schwarz, Dr. Cina Foroutan-Nejad, Miss. Farnaz Heidar Zadeh, and anonymous reviewers greatly helped the authors to improve the quality of the final draft of this paper.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Goli, M., Shahbazian, S. The two-component quantum theory of atoms in molecules (TC-QTAIM): foundations. Theor Chem Acc 131, 1208 (2012). https://doi.org/10.1007/s00214-012-1208-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00214-012-1208-9