Exponentially correlated Gaussians for simulating of localized and autolocalized states in polar media

N. I. Kashirina ; V. D. Lakhno

Matematičeskaâ biologiâ i bioinformatika, Tome 12 (2017) no. 2, pp. 273-301.

Résumé

Localized and autolocalized states and their simplest two-electron complexes in polar media are considered in the continuum approximation. The electron-phonon interaction is taken into account in the Pekar–Fröhlich approximation. The exponentially correlated Gaussian basis is used for the calculation of the energy spectrum of two-electron systems in phonon field. Analytical expressions for effective functionals of paramagnetic centers and their simplest two-electron complexes are presented. Numerical examples are given for the calculations of the energy spectrum of localized and self-localized states in metal-ammonia solutions.

Bibliographie

[1] Boys S. F., “The integral formulae for the variational solution of the molecular many-electron wave equations in terms of gaussian functions with direct electronic correlation”, Proc. R. Soc. London Ser. A, 258:1294 (1960), 402–411 | DOI | MR

[2] Singer K., “The use of Gaussian (exponential guadratic) wave functions in molecular problems. I. General formulae for the evaluation of integrals”, Proc. R. Soc. London Ser. A, 258:1294 (1960), 412–420 | DOI | MR

[3] Komasa J., Cencek W., Rychlewski J., “Explicitly correlated Gaussian functions in variational calculations: The ground state of the beryllium atom”, Phys. Rev. A, 52:6 (1995), 4500–4507 | DOI

[4] Cencek W., Kutzelnigg W., “Accurate relativistic energies of one and twoelectron systems using Gaussian wave functions”, J. Chem. Phys., 105:14 (1996), 5878–5885 | DOI

[5] Sandberg J., Rinkevicius Z., “An algorithm for the efficient evaluation of two-electron repulsion integrals over contracted Gaussian-type basis functions”, J. Chem. Phys., 137:23 (2012), 234105 | DOI

[6] Alexander S. A., Monkhorst H. J., Roeland R., Szalewicz K., “Obtaining microhartree accuracy for two electron systems with random tempered Gaussian type geminals”, J. Chem. Phys., 93:6 (1990), 4230–4235 | DOI

[7] Wenzel K. B., “Rapidly converging high-precision He ground state energies through the use of systematically constructed Gaussian geminals”, Chem. Phys. Lett., 224:1–2 (1994), 155–159 | DOI

[8] Rybak S., Szalewicz K., Jeziorski B., Jaszunski M., “Intraatomic correlation effects for the He-He dispersion and exchange-dispersion energies using explicitly correlated Gaussian geminals”, The Journal of Chemical Physics, 86:10 (1987), 5652–5659 | DOI

[9] Rybak S., Szalewicz K., Jeziorski B., “An accurate calculation of the first order interaction energy for the helium dimer”, J. Chem. Phys., 91:8 (1989), 4779–4784 | DOI

[10] Jeziorski B., Szalewicz K., “High-accuracy Compton profile of molecular hydrogen from explicitly correlated Gaussian wave function”, Phys. Rev. A, 19:6 (1979), 2360–2365 | DOI

[11] Kolos W., Monkhorst H. J., Szalewicz K., “Energy unresolved differential cross section for electron scattering by H$_2$”, J. Chem. Phys., 77:3 (1982), 1323–1334 | DOI

[12] Moszyński R., Szalewicz K., “Accurate electron densities of the hydrogen molecule”, J. Phys. B, 20:7 (1987), 347–4365 | DOI

[13] Komasa J., Thakkar A. J., “Accurate multipole moments for H$_2$ and D$_2$ including the effects of electron correlation and molecular vibration and rotation”, Mol. Phys., 78:4 (1993), 1039–1046 | DOI

[14] Cencek W., Kutzelnigg W., “Accurate relativistic energies of one and two electron systems using Gaussian wave functions”, J. Chem. Phys., 105:14 (1998), 5878–5885 | DOI

[15] Rychlewski J., Cencek W., Komasa J., “The equivalence of explicitly correlated Slater and Gaussian functions in variational quantum chemistry computations: The ground state of H$_2$”, Chem. Phys. Lett., 229:6 (1994), 657–660 | DOI

[16] Szalewicz K., Jeziorski B., Monkhorst H. J., Zabolitzky J. G., “Atomic and molecular correlation energies with explicitly correlated Gaussian geminals. I. Secondorder perturbation treatment for He, Be, H2, and LiH”, J. Chem. Phys., 78:3 (1983), 1420–1430 | DOI

[17] Kozlowski P. M., Adamowicz L., “An effective method for generating nonadiabatic manybody wave function using explicitly correlated Gaussiantype functions”, J. Chem. Phys., 95:9 (1991), 6681–6698 | DOI

[18] Gallagher T. F., “Rydberg atoms”, Reports on Progress in Physics, 51:2 (1988), 143–188 | DOI

[19] Bendkowsky V., Butscher B., Nipper J., Shaffer J. P., Löw R., Pfau T., “Observation of ultralong-range Rydberg molecules”, Nature, 458 (2009), 1005–1008 | DOI

[20] Kazimierczuk T., Fröhlich D., Scheel S., Stolz H., Bayer M., “Giant Rydberg excitons in the copper oxide Cu$_2$O”, Nature, 514 (2014), 343–347 | DOI

[21] Pekar S. I., “Lokalnye kvantovye sostoyaniya elektronov v idealnom ionnom kristalle”, ZhETF, 16:4 (1946), 341–348

[22] Pekar S. I., Issledovaniya po elektronnoi teorii kristallov, Gostekhteoretizdat, M.–L., 1951, 256 pp.

[23] Deigen M. F., “Magnitnye svoistva metall-ammiachnykh rastvorov i ravnovesnye kontsentratsii lokalnykh tsentrov v dielektrike”, Tr. IF AN USSR, 5 (1954), 105–111

[24] Lakhno V. D., “Dynamical polaron theory of the hydrated electron”, Chem. Phys. Lett., 437:4–6 (2007), 198–202 | DOI

[25] Lakhno V. D., Volokhova A. V., Zemlyanaya E. V., Amirkhanov I. V., Puzynin I. V., Puzynina T. P., “Polyaronnaya model formirovaniya sostoyanii gidratirovannogo elektrona”, Poverkhnost. Rentgenovskie, sinkhrotronnye i neitronnye issledovaniya, 2015, no. 1, 82–87 | DOI

[26] Kashirina N. I., Lakhno V. D., “Kontinualnaya model odnomernogo bipolyarona Kholsteina v DNK”, Matematicheskaya biologiya i bioinformatika, 9:2 (2014), 430–437 | DOI

[27] Lepoutre G., “Colloque Weyl: a short history”, J. Phys. Chem., 88:17 (1984), 3772–3780 | DOI

[28] Edwards P. P., “Polarons, bipolarons, and possible high-Tc superconductivity in metal-ammonia solutions”, J. Supercond and Nov. Mag., 13:6 (2000), 933–946 | DOI

[29] Edwards P. P., “From solvated electrons to metal anions: electronic structure and dynamics”, J. Solution Chem., 14:3 (1985), 187–208 | DOI

[30] Fröhlich H., “Electrons in lattice fields”, Advan. Phys., 3:11 (1954), 325–361 | DOI

[31] Miyake S. J., “Strong-coupling limit of the polaron ground state”, J. Phys. Soc. Japan, 38:1 (1975), 181–182 | DOI

[32] Kashirina N. I., Lakhno V. D., “Vozbuzhdennye sostoyaniya svobodnogo i svyazannogo polyarona v metode silnoi i promezhutochnoi svyazi”, Matematicheskaya biologiya i bioinformatika, Sbornik dokladov II Mezhdunarodnoi konferentsii (Puschino, 7–13 sentyabrya 2008 g.), ed. Lakhno V. D., MAKS Press, M., 2008, 22–23

[33] Gabdullin R. R., “Nesfericheskie resheniya uravneniya polyarona”, DAN RAN, 333:1 (1993), 23–27

[34] Buimistrov V. M., Pekar S. I., “Kvantovye sostoyaniya chastits, vzaimodeistvuyuschikh s garminicheski koleblyuschimsya kontinuumom, pri proizvolnoi sile svyazi. 1. Sluchai otsutstviya translyatsionnoi simmetrii”, ZhETF, 32:5 (1957), 1193–1199

[35] Kashirina N. I., Lakhno V. D., Sychyov V. V., “Correlation effects and Pekar bipolaron (arbitrary electron-phonon interaction)”, Physica status solidi (b), 239:1 (2003), 174–184 | DOI

[36] Kashirina N. I., Lakhno V. D., Sychyov V. V., “Polaron effects and electron correlations in two-electron systems: Arbitrary value of electron-phonon interaction”, Physical Review B, 71:13 (2005), 134301-1–13431-14 | DOI

[37] Kashirina N. I., Lakhno V. D., Matematicheskoe modelirovanie avtolokalizovannykh sostoyanii v kondensirovannykh sredakh, Fizmatlit, M., 2013, 292 pp.

[38] Alexander S. A., Monkhorst H. J., Roeland R., Szalewicz K., “Microhartree accuracy for twoelectron systems with randomtempered Gaussiantype geminals”, The Journal of Chemical Physics, 93 (1990), 4230–4235 | DOI

[39] Baker J. D., Freund D. E., Hill R. N., Morgan III J. D., “Radius of convergence and analytic behavior of the $1/Z$ expansion”, Phys. Rev. A, 41:3 (1990), 1247–1273 | DOI | MR

[40] Gombash P., Problema mnogikh chastits v kvantovoi mekhanike (teoriya i metody resheniya), Inostrannaya literatura, M., 1953, 276 pp.

[41] Pashitskii E. A., Mashkevich S. V., Vilchynskyy S. I., “Superfluid Bose liquid with a suppressed BEC and an intensive pair coherent condensate as a model of $_4$He”, Phys. Rev. Lett., 89:7 (2002), 075301-1–075301-4 | DOI

[42] Pashitskii E. A., “Rol parnykh korrelyatsii v formirovanii osnovnogo sostoyaniya i spektra elementarnykh vozbuzhdenii sverkhtekuchei boze-zhidkosti”, FNT, 25:2 (1999), 115–140

[43] Vinetskii V. L., Pashitskii E. A., “Sverkhtekuchest zaryazhennogo Boze-gaza i bipolyaronnyi mekhanizm sverkhprovodimosti”, UFZh, 20:2 (1975), 338–341

[44] Vinetskii V. L., Pashitskii E. A., “Bipolyaronnye sostoyaniya v kristallakh s anizotropnoi effektivnoi massoi svobodnykh nositelei”, FTT, 25 (1983), 1744–1747

[45] Thompson J. S., Electrons in liquid ammonia, Clarendon Press, Oxford, 1976, 297 pp.

[46] Deigen M. F., “Teoriya magnitnykh svoistv metall-ammiachnykh rastvorov”, ZhETF, 26:3 (1954), 293–299

[47] Deigen M. F., “Opticheskie svoistva i elektroprovodnost metall-ammiachnykh rastvorov”, ZhETF, 26:3 (1954), 300–306

[48] McConnell H., Holm C. H., “Electronic structure of sodium-ammonia solutions by nuclear magnetic resonance”, J. Chem. Phys., 26:6 (1957), 1517–1521 | DOI

[49] Larsen D. M., “Giant binding of D-centers in polar crystals”, Phys. Rev. B, 23:2 (1981), 628–631 | DOI | MR

[50] Suprun S. G., Moizhes B. Ya., “O roli elektronnoi korrelyatsii v obrazovanii bipolyarona Pekara”, FTT, 24:5 (1982), 1571–1573

[51] Buimistrov V. M., Pekar S. I., “Kvantovye sostoyaniya chastits, vzaimodeistvuyuschikh s garmonicheski koleblyuschimsya kontinuumom, pri proizvolnoi sile svyazi. 2. Sluchai translyatsionnoi simmetrii”, ZhETF, 33:5 (1957), 1271–1276

[52] Ogg R. A., “Bose-Einstein condensation of trapped electron pairs. Phase separation and superconductivity of metal-ammonia solutions”, Phys. Rev., 69:5–6 (1946), 243–244 | DOI

[53] Van Vleck J. H., “Paramagnetic relaxation times for titanium and chrome alum”, Phys. Rev., 57:5 (1940), 426–447 | DOI

[54] Holstein T., “Studies of polaron motion. Part II. The “small” polaron”, Annals of Physics, 8 (1959), 343–389 | DOI