Skip to main content
Log in

Chemical insight into electron density and wave functions: software developments and applications to crystals, molecular complexes and materials science

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

This paper overviews the work made by our group during the past 10–15 years on crystalline systems, semiconductor surfaces, molecular complexes and on materials of interest for technological applications, such as the defective silicon or the novel generation thermoelectric materials. Our main aim of extracting chemical insight into the analysis of electron densities and computed wave functions is illustrated through a number of examples. The recently proposed Source Function analysis is reviewed and a few of its more interesting applications are summarized. Software package developments, motivated by the need of a direct comparison with experiment or by the help these packages can provide for interpreting complex experimental outcomes, are described and future directions outlined. A particular emphasis is given to the TOPOND and TOPXD programs, which enable one to analyze theoretical and experimental crystalline densities using the rigorous framework of the Quantum Theory of Atoms in Molecules, due to Bader.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Gatti C (2005). Z Kristallogr 220:399–457

    CAS  Google Scholar 

  2. Bader RFW, Gatti C (1998). Chem Phys Lett 287:233–238

    CAS  Google Scholar 

  3. Destro R, Marsh RE, Bianchi R (1988). J Phys Chem 92:966–973

    CAS  Google Scholar 

  4. Destro R, Bianchi R, Gatti C, Merati F (1991). Chem Phys Lett 186:47–52

    CAS  Google Scholar 

  5. Coppens P (1997). X-ray charge densities and chemical bonding IUCr texts on crystallography 4. Oxford University Press, Oxford

    Google Scholar 

  6. Bader RFW (1990). Atoms in molecules: a quantum theory. International series of monographs on chemistry 22. Oxford University Press, Oxford

    Google Scholar 

  7. Gatti C, Bianchi R, Destro R, Merati F (1992). J Mol Struct (THEOCHEM) 255:409–423

    Google Scholar 

  8. Coppens P (1998). Acta Cryst A 54:779–788

    Google Scholar 

  9. Dovesi R, Saunders VR, Roetti C, Causà M, Harrison NM, Orlando R, Aprà E (1996) CRYSTAL95 User’s Manual, University of Torino, Torino

  10. Gatti C (1999) TOPOND-98: An electron density topological program for systems periodic in N (N=0–3) Dimensions, User’s Manual, CNR-ISTM, Milano

  11. Volkov A, Gatti C, Abramov Y, Coppens P (2000). Acta Cryst A 56:252–258

    Google Scholar 

  12. Koritsanszky T, Richter T, Macchi P, Volkov A, Gatti C, Howard S, Mallinson PR, Farrugia L, Su Z, Hansen NK (2003) XD: Computer program package for multipole refinement and topological analysis of electron densities from diffraction data

  13. Gatti C, Saunders VR, Roetti C (1994). J Chem Phys 101:10686–10696

    CAS  Google Scholar 

  14. Gatti C, May E, Destro R, Cargnoni F (2002). J Phys Chem A 106:2707–2720

    CAS  Google Scholar 

  15. May E, Destro R, Gatti C (2001). J Am Chem Soc 123:12248–12254

    CAS  Google Scholar 

  16. Gatti C, Silvi B, Colonna F (1995). Chem Phys Lett 247:135–141

    CAS  Google Scholar 

  17. Aray Y, Gatti C, Murgich J (1994). J Chem Phys 101:9800–9806

    CAS  Google Scholar 

  18. Jeffrey GA (1999). J Mol Struct 485–486:293–298

    Google Scholar 

  19. Bianchi R, Gatti C, Adovasio V, Nardelli M (1996). Acta Cryst B 52:471–478

    Google Scholar 

  20. Volkov A, Abramov Y, Coppens P, Gatti C (2000). Acta Cryst A 56:332–339

    Google Scholar 

  21. Hibbs DE, Overgaard J, Gatti C, Hambley TW (2003). New J Chem 27:1392–1398

    CAS  Google Scholar 

  22. Duke CB (1996). Chem Rev 96:1237–1259

    CAS  Google Scholar 

  23. Robinson IK (1998). Acta Cryst A54:772–778

    Google Scholar 

  24. Cargnoni F, Gatti C (2001). Theor Chem Acc 105:309–322

    CAS  Google Scholar 

  25. Cargnoni F, Gatti C, May E, Narducci D (2000). J Chem Phys 112:887–899

    CAS  Google Scholar 

  26. Gatti C (2007 in press) Solid state applications of QTAIM and the source function: molecular crystals, surfaces, host–guest systems and molecular complexes. In: Matta CF, Boyd R (eds) The quantum theory of atoms in molecules, Chap. 7, Wiley-VCH, Weinheim

  27. Cargnoni F, Gatti C, Colombo L (1998). Phys Rev B 57:170–177

    CAS  Google Scholar 

  28. Bongiorno A, Colombo L, Cargnoni F, Gatti C, Rosati M (2000). Europhys Lett 50:608–614

    CAS  Google Scholar 

  29. EC 5th Framework Program, Research and Technological Development Program: Competitive and Sustainable Growth, Contract number: G5RD-CT2000–00292

  30. Ziman JM (1972) Principles of the Theory of Solids. Cambridge University Press, Cambridge

    Google Scholar 

  31. Elliott S (1998) The Physics and Chemistry of Solids. Wiley, New York

    Google Scholar 

  32. Blake NP, Latturner S, Bryan JD, Stucky GD, Metiu H (2001). J Chem Phys 115:8060–8073

    CAS  Google Scholar 

  33. Saunders VR, Dovesi R, Roetti C, Causà M, Harrison NM, Orlando R, Zicovich-Wilson CM (1998) CRYSTAL98, User’s Manual, University of Torino, Torino

  34. Bertini L, Gatti C, ELTRAP, Electron Transport Properties from the Band Structure (2003), CNR-ISTM, Milano

  35. Bertini L, Gatti C (2004). J Chem Phys 121:8983–8989

    CAS  Google Scholar 

  36. Bertini L, Cargnoni F, Gatti C (2006) A Chemical approach to the first-principles modelling of novel thermoelectric materials. In: Rowe DM (ed) Thermoelectric handbook, Macro to Nano, CRC, Taylor & Francis, Boca Raton, FL, USA, Chap. 7

  37. Gatti C, Bertini L, Iversen BB, Blake NP (2003). Chem Eur J 9:4556–4568

    CAS  Google Scholar 

  38. Cargnoni F, Nishibori E, Rabiller P, Bertini L, Snyder GJ, Christensen M, Gatti C, Iversen BB (2004). Chem Eur J 10:3861–3870

    CAS  Google Scholar 

  39. Christensen M, Iversen BB, Bertini L, Gatti C, Toprak M, Muhammed M, Nishibori E (2004). J Appl Phys 96:3148–3157

    CAS  Google Scholar 

  40. Stiewe C, Bertini L, Toprak M, Christensen M, Platzek D, Williams S, Gatti C, Müller, Iversen BB, Muhammed M, Rowe M (2005). J Appl Phys 97:044317

    Google Scholar 

  41. Bader RFW, De-Cai F (2005) J Chem Theory Comp (2005) 1:403–414

    Google Scholar 

  42. Poater J, Solà M, Bickelhaupt FM (2006). Chem Eur J 12:2902–2905

    CAS  Google Scholar 

  43. Poater J, Solà M, Bickelhaupt FM (2006). Chem Eur J 12:2889–2895

    CAS  Google Scholar 

  44. Bader RFW (2006). Chem Eur J 12:2896–2901

    CAS  Google Scholar 

  45. Silvi B (2002). J Mol Struct 614:3–10

    CAS  Google Scholar 

  46. Macchi P, Sironi A (2003). Coordination Chem Rev 238–239:383–412

    Google Scholar 

  47. Bader RFW (1998). J Phys Chem A 102:7314–7323

    CAS  Google Scholar 

  48. Fradera X, Austen MA, Bader RFW (1999). J Phys Chem A103:304–314

    CAS  Google Scholar 

  49. Savin A, Silvi B, Colonna F (1996). Can J Chem 74:1088–1096

    CAS  Google Scholar 

  50. Gatti C, Cargnoni F, Bertini L (2003). J Comput Chem 24:422–436

    CAS  Google Scholar 

  51. Gatti C, Bertini L (2004). Acta Cryst A 60:438–449

    Google Scholar 

  52. Gatti C, Lasi D (2007) Faraday Discuss, DOI 10.1039/b605404h

  53. Gatti C, Cargnoni F (1997) Proceedings III Convegno Nazionale di Informatica Chimica, Napoli, Italy, pp 125–128

  54. Katan C, Rabiller P, Lecomte C, Guezo M, Oison V, Souhassou M (2003). J Appl Cryst 36:65–73

    CAS  Google Scholar 

  55. Rabiller P, Souhassou M, Katan C, Gatti C, Lecomte C (2004). J Phys Chem Solids 65:1951–1955

    CAS  Google Scholar 

  56. Becke AD, Edgecombe KE (1990). J Chem Phys 92:5397–5403

    CAS  Google Scholar 

  57. Abramov YA (1997). Acta Cryst A53:264–272

    Google Scholar 

  58. Popelier PLA (1994). Chem Phys Lett 228:160–164

    CAS  Google Scholar 

  59. Gatti C, Fantucci P, Pacchioni G (1987). Theor Chim Acta 72:433–458

    CAS  Google Scholar 

  60. Giacovazzo C (2002) Fundamentals of crystallography, IUCr texts on crystallography 7, Chap. 1, 2nd edn. Oxford Science Publications, Oxford University Press, Oxford

  61. Morse M, Cairns SS (1969) Critical point theory in global analysis and differential geometry. Academic, New York

    Google Scholar 

  62. Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1986) Numerical recipes. Cambridge University Press, Cambridge

    Google Scholar 

  63. Luaňa V, Mori-Sánchez P, Costales A, Blanco MA, Martín Pendás A (2003). J Chem Phys 119:6341–6350

    Google Scholar 

  64. Madsen GHK, Blaha P, Schwarz K (2002). J Chem Phys 117:8030–8035

    CAS  Google Scholar 

  65. Silvi B, Gatti C (2000). J Phys Chem A 104:947–953

    CAS  Google Scholar 

  66. Luaňa V, Costales A, Mori-Sánchez P, Blanco M, Martín Pendás A (2004). Acta Cryst A 60:434–437

    Google Scholar 

  67. Hô M, Smith VH, Weaver DF, Gatti C, Sagar RP, Esquivel RO (1998). J Chem Phys 108:5469–5475

    Google Scholar 

  68. Keith TA (1993) PhD Thesis, McMaster University, Hamilton, Ontario, Canada

  69. Gatti C (1997) P2DCRY97 User’s Manual, CNR-ISTM, Milano

  70. Iversen BB, Larsen FK, Souhassou M, Takata M (1995). Acta Cryst B 51:580–591

    Google Scholar 

  71. Dovesi R, Saunders VR, Roetti C, Orlando R, Zicovich-Wilson CM, Pascale F, Civalleri B, Doll K, Harrison NM, Bush IJ, D’Arco P, Llunell M (2006) CRYSTAL06 User’s Manual, University of Torino, Torino

  72. Popelier PLA (2001). Theor Chem Acc 105:393–399

    CAS  Google Scholar 

  73. Mayer I, Salvador P (2004). Chem Phys Lett 383:368–375

    CAS  Google Scholar 

  74. Koritsanszky TS, Coppens P (2001). Chem Rev 101:1583–1627

    CAS  Google Scholar 

  75. Coppens P, Iversen BB, Larsen FK (2005). Coord Chem Rev 249:179–195

    CAS  Google Scholar 

  76. Pisani C (2003). J Mol Struct (Theochem) 621:141–147

    CAS  Google Scholar 

  77. Dovesi R, Civalleri B, Orlando R, Roetti C, Saunders VR (2005). Rev Comp Chem 21:1–125

    CAS  Google Scholar 

  78. Coppens P, Volkov A (2004). Acta Cryst A60:357–364

    Google Scholar 

  79. Schiøtt B, Overgaard J, Larsen FK, Iversen BB (2004). Int J Quant Chem 96:23–31

    Google Scholar 

  80. Bader RFW, Essén H (1984). J Chem Phys 80:1943–1960

    CAS  Google Scholar 

  81. Swaminathan S, Craven BM, McMullan RK (1984) Acta Cryst B 40:300–306 and references therein

    Google Scholar 

  82. Bader RFW, Larouche A, Gatti C, Carroll MT, MacDougall PJ, Wiberg K (1987). J Chem Phys 87:1142–1152

    CAS  Google Scholar 

  83. Lunelli B, Roversi P, Ortoleva E, Destro R (1996). J Chem Soc Faraday Trans 92:3611–3623

    CAS  Google Scholar 

  84. Destro R (1997). Chem Phys Lett 275:463–468

    CAS  Google Scholar 

  85. Taylor R, Kennard O (1982). J Am Chem Soc 104:5063– 5070

    CAS  Google Scholar 

  86. Steiner T (1997). Chem Commun 727–734

  87. Koch U, Popelier PLA (1995). J Phys Chem 99:9747–9754

    CAS  Google Scholar 

  88. Espinosa E, Molins E, Lecomte C (1998). Chem Phys Lett 285:170–173

    CAS  Google Scholar 

  89. Espinosa E, Souhassou M, Lachekar H, Lecomte C (1999). Acta Cryst B 55:563–572

    Google Scholar 

  90. Espinosa E, Alkorta I, Elguero J, Molins E (2002). J Chem Phys 117:5529–5542

    CAS  Google Scholar 

  91. Spackman MA (1999). Chem Phys Lett 301:425–429

    CAS  Google Scholar 

  92. Filler MA, Bent SF (2003). Progr Surf Sci 73:1–56

    CAS  Google Scholar 

  93. Sakama H, Kawazu A (1995). Mat Sci Eng R14:255–317

    Google Scholar 

  94. Mayne AJ, Riedel D, Comtet G, Dujardin G (2006). Progr Surf Sci 81:1–51

    CAS  Google Scholar 

  95. Feidenhans’l R, Bunk O, Ciston J, Marks LD (2005). Acta Cryst A61:C96

    Google Scholar 

  96. Feder R, Mönch W (1984). Solid State Comm 50:311–313

    CAS  Google Scholar 

  97. Himpsel FJ, Marcus PM, Tromp R, Batra IP, Cook MR, Jona F, Liu H (1984). Phys Rev B30:2257–2259

    CAS  Google Scholar 

  98. Sakama H, Kawazu A, Ueda K (1986). Phys Rev B34:1367–1370

    CAS  Google Scholar 

  99. Smit L, Tromp RM, Van Der Veen JF (1985). Surf Sci 163:315–334

    CAS  Google Scholar 

  100. Himpsel FJ, Heimann P, Eastman DE (1981). Phys Rev B24:2003–2008

    CAS  Google Scholar 

  101. Uhrberg RIG, Hansson GV, Nichols JM, Flodström SA (1982). Phys Rev Lett 48:1032–1035

    CAS  Google Scholar 

  102. Martensson P, Cricenti A, Hansson GV (1985). Phys Rev B32:6959–6961

    Google Scholar 

  103. Pandey KC (1981). Phys Rev Lett 47:1913–1917

    CAS  Google Scholar 

  104. Nishiyama A, Terhorst G, Lohmeier M, Molenbroek AM, Frenken JWM (1994). Surf Sci 321:261–266

    CAS  Google Scholar 

  105. Copel M, Tromp RM, Culbertson RJ (1994). Appl Phys Lett 65:2344–2346

    CAS  Google Scholar 

  106. Jona F, Thompson WA, Marcus PM (1995). Phys Rev B52:8226–8230

    CAS  Google Scholar 

  107. Li XP, Vanderbilt D (1992). Phys Rev Lett 69:2543–2546

    CAS  Google Scholar 

  108. Ancilotto F, Selloni A (1992). Phys Rev Lett 68:2640–2643

    CAS  Google Scholar 

  109. Blasé X, Zhu X, Louie SG (1994). Phys Rev B 49:4973–4980

    Google Scholar 

  110. Van de Walle CG (1994). Phys Rev B49:4579–4585

    CAS  Google Scholar 

  111. Wolkow RA (1992). Phys Rev Lett 68:2636–2639

    CAS  Google Scholar 

  112. Felici R, Robinson IK, Ottaviani C, Imperatori P, Eng P, Perfetti P (1997). Surf Sci 375:55–62

    CAS  Google Scholar 

  113. Lauridsen EM, Baker J, Nielsen M, Feidenhans’l R, Falkenberg G, Bunk I, Zeysing JH, Johnson RL (2000). Surf Sci 453:18–24

    CAS  Google Scholar 

  114. Boland JJ (1992). Surf Sci 261:17–28

    CAS  Google Scholar 

  115. Matta CF, Hernández-Trujillo J, Tang T-H, Bader RFW (2003). Chem Eur J 9:1940–1951

    CAS  Google Scholar 

  116. Tang M, Colombo L, Zhu J, Diaz De La Rubia (1997). Phys Rev B 55:14279–14289

    CAS  Google Scholar 

  117. Averback RS, Diaz de La Rubia T (1998). Solid State Phys 51:281–402

    CAS  Google Scholar 

  118. Stich I (1991). Phys Rev B 44:4262–4274

    CAS  Google Scholar 

  119. Libertino S (1997). Appl Phys Lett 71:389–391

    CAS  Google Scholar 

  120. DiSalvo FJ (1999). Science 285:703–706

    CAS  Google Scholar 

  121. Sales BC (2002). Science 295:1248–1249

    CAS  Google Scholar 

  122. Rowe DM (2006) General Principles and Basic Considerations. In: Rowe DM (ed) Thermoelectrics handbook, macro to nano, CRC Taylor& Francis, Boca Raton, FL, USA, Chap. 1

  123. Rowe DM (ed) (2006) Thermoelectrics Handbook, Macro to Nano, CRC Taylor& Francis, Boca Raton, FL, USA, Chaps. 27–42

  124. Rogl P (2006) Formation and crystal chemistry of clathrates. In: Rowe DM (ed) Thermoelectrics handbook, macro to nano, CRC Taylor& Francis, Boca Raton, FL, USA, Chap. 32

  125. Blake NP, Bryan D, Latturner S, Möllnitz L, Stucky GD, Metiu H (2001). J Chem Phys 114:10063–10074

    CAS  Google Scholar 

  126. Bentien A, Palmqvist AEC, Bryan JD, Latturner S, Stucky GD, Furenlid L, Iversen BB (2000). Angew Chem Int Ed 39:3613–3616

    CAS  Google Scholar 

  127. Uher C (2006) General Principles and Basic Considerations. In: Rowe DM (ed) Thermoelectrics handbook, macro to nano, CRC Taylor& Francis, Boca Raton, FL, USA, Chap. 34

  128. Nolas GS, Lyon HB, Vohn JL, Tritt TM, Slack GA (1997) In: Proceedings of 16th international conference on thermoelectrics, pp 321–325

  129. Sales BC, Chakoumakos BC, Mandrus D (2000). Phys Rev B 61:2475–2481

    CAS  Google Scholar 

  130. Chen LD, Kawahara T, Tang XF, Goto T, Hirai T, Dyck JS, Chen W, Uher C (2001). J Appl Phys 90:1864–1868

    CAS  Google Scholar 

  131. Dyck JS, Chen WD, Uher C, Chen L, Tang X, Hirai T (2002) J Appl Phys (2002) 91:3698–3705

  132. Wojciechowsky KT (2002). Mat Res Bull 37:2023–2033

    Google Scholar 

  133. Bertini L, Billquist K, Christensen M, Gatti C, Holmgren L, Iversen B, Mueller E, Muhammed M, Noriega G, Palmqvist A, Platzek D, Rowe DM, Saramat A, Stiewe C, Toprak M, Williams SG, Zhang Y (2003) Theoretical modeling of Te doped 3. In: Proceedings of the 22nd international conference on thermoelectrics, IEEE Catalog Number 03TH8726, ISBN 0–7803–8301-X, ISSN 1094–2734, pp 85–88

  134. Sofo JO, Mahan GD (1998). Phys Rev B 58:15620–15623

    CAS  Google Scholar 

  135. Kawaharada Y, Kurosaki K, Uno M, Yamanaka S (2001). J Alloy Comp 315:193–197

    CAS  Google Scholar 

  136. Wojciechowsky KT, Tobola J, Leszczyński J (2003). J Alloys Comp. 361:19–27

    Google Scholar 

  137. Cenedese S, Bertini L, Gatti C (2005) In: Proceedings of the ECT 2005, Nancy, France extended abstracts, pp 164–167

  138. Cenedese S, Bertini L, Gatti C (2005) In: Proceedings of the ECT 2005, Nancy, France extended abstracts, pp 53–55

  139. Bertini L, Stiewe C, Toprak M, Williams S, Platzek D, Zhang Y, Gatti C, Mueller E, Muhammed M, Rowe M (2003). J Appl Phys 93:438–447

    CAS  Google Scholar 

  140. Fleurial J-P, Caillat T, Borshchevsky A (1997) Proceedings of the XVI international conference on thermoelectrics, Dresden, Germany, August 26–29

  141. Watcharapasorn A, DeMattei RC, Feigelson RS, Caillat T, Borshchevsky A, Snyder GJ, Fleurial J-P, Thermoelectric Properties of Some Cobalt Phosphide-Arsenide Compounds. Mat Res Soc Symp 626:Z1.4.1

  142. Singh DJ (2000). Semicond Semimetals 70:125–177

    Google Scholar 

  143. Caillat T, Fleurial J-P, Borshchevsky (1997). J Phys Chem Solids 58:1119–1125

    CAS  Google Scholar 

  144. Snyder GJ, Christensen M, Nishibori E, Caillat T, Iversen BB (2004). Nat Mater 3:458–463

    CAS  Google Scholar 

  145. Kim S-G, Mazin II, Singh DJ (1998). Phys Rev B 57: 699–6203

    Google Scholar 

  146. Mayer HW, Mikhail I, Schubert K (1978). J Less-Common Met 59:43–52

    CAS  Google Scholar 

  147. Arfken G (1985) Mathematical methods for physicists, 3rd edn. Academic, Orlando, FL

    Google Scholar 

  148. Overgaard J, Schiøtt, Larsen FK, Iversen BB (2001). Chem Eur J 7:3756–3767

    CAS  Google Scholar 

  149. Farrugia LJ, Evans C, Tegel M (2006). J Phys Chem B 110:7952–7961

    CAS  Google Scholar 

  150. Jeffrey GA (1997) An introduction to hydrogen bonding. Oxford University Press, New York

    Google Scholar 

  151. Gilli G, Gilli P (2000). J Mol Struct 552:1–15

    CAS  Google Scholar 

  152. Fuster F, Silvi B (2000). Theor Chem Acc 104:13–21

    CAS  Google Scholar 

  153. Gatti C, Bertini L, Cargnoni F (2005). Acta Cryst A61:C47–C48

    Article  Google Scholar 

  154. Cotton FA (2000) J Chem Soc Dalton Trans 1961–1968

  155. Llusar R, Beltrán A, Andrés J, Fuster F, Silvi B (2001). J Phys Chem A 105:9460–9466

    CAS  Google Scholar 

  156. Ponec R, Yuzhakov G, Carbó-Dorca R (2003). J Comput Chem 24:1829–1838

    CAS  Google Scholar 

  157. Ponec R, Yuzhakov G, Sundberg MR (2005). J Comput Chem 26:447–454

    CAS  Google Scholar 

  158. Lasi D, Gatti C (2006) European Charge Density Meeting-IV, ECDM-IV, 26–29 January, Branderburg on the Havel, Germany

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carlo Gatti.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bertini, L., Cargnoni, F. & Gatti, C. Chemical insight into electron density and wave functions: software developments and applications to crystals, molecular complexes and materials science. Theor Chem Account 117, 847–884 (2007). https://doi.org/10.1007/s00214-006-0208-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00214-006-0208-z

Keywords

Navigation