The Experts below are selected from a list of 9978 Experts worldwide ranked by ideXlab platform
G Benedek - One of the best experts on this subject based on the ideXlab platform.
-
inelastic Helium Atom scattering from sb2te3 111 phonon dispersion focusing effects and surfing
Physical Chemistry Chemical Physics, 2021Co-Authors: Adrian Ruckhofer, Martin Bremholm, Marco Bianchi, Philip Hofmann, G Benedek, Simon Halbritter, Henriette Lund, Ann Julie Holt, Wolfgang ErnstAbstract:We present an experimental study of inelastic scattering processes on the (111) surface of the topological insulator Sb2Te3 using Helium Atom scattering. In contrast to other binary topological insulators such as Bi2Se3 and Bi2Te3, Sb2Te3 is much less studied and the as-grown Sb2Te3 sample turns out to be p-doped, with the Fermi-level located below the Dirac-point as confirmed by angle-resolved photoemission spectroscopy. We report the surface phonon dispersion along both high symmetry directions in the energy region below 11 meV, where the Rayleigh mode exhibits the strongest intensity. The experimental data is compared with a study based on density functional perturbation theory calculations, providing good agreement except for a set of additional peculiar inelastic events below the Rayleigh mode. In addition, an analysis of angular scans with respect to a number of additional inelastic events is presented, including resonance enhancement, kinematical focusing, focused inelastic resonance and surfing. In the latter case, phonon-assisted adsorption of the incident Helium Atom gives rise to a bound state where the Helium Atom rides the created Rayleigh wave.
-
electron phonon coupling constant of 2h mos2 0001 from Helium Atom scattering
Journal of Physical Chemistry C, 2019Co-Authors: Gloria Anemone, G Benedek, Amjad Al Taleb, Andres Castellanosgomez, D FariasAbstract:We have studied the (0001) surface of 2H-MoS2 by means of Helium-Atom scattering (HAS). The electron–phonon coupling constant, λ, of this system has been determined by measuring the thermal attenua...
-
history of surface phonons and Helium Atom scattering
2018Co-Authors: G Benedek, J P ToenniesAbstract:The chapter starts with an overview of the history of the theory of surface phonons. Next the history of Helium Atom and electron inelastic scattering experiments are briefly reviewed. Present day Helium Atom scattering experiments are described next and some important related concepts are introduced. The chapter closes with a short history of the classical and quantum theory of inelastic surface scattering.
-
electron phonon coupling strength at metal surfaces directly determined from the Helium Atom scattering debye waller factor
Journal of Physical Chemistry Letters, 2016Co-Authors: G Benedek, J R Manson, Salvador MiretartesAbstract:A new quantum-theoretical derivation of the elastic and inelastic scattering probability of He Atoms from a metal surface, where the energy and momentum exchange with the phonon gas can occur only through the mediation of the surface free-electron density, shows that the Debye-Waller exponent is directly proportional to the electron-phonon mass coupling constant λ. The comparison between the values of λ extracted from existing data on the Debye-Waller factor for various metal surfaces and the λ values known from literature indicates a substantial agreement, which opens the possibility of directly extracting the electron-phonon coupling strength in quasi-2D conducting systems from the temperature or incident energy dependence of the elastic Helium Atom scattering intensities.
-
Atomic surface structure of ch3 ge 111 characterized by Helium Atom diffraction and density functional theory
Journal of Physical Chemistry C, 2015Co-Authors: Zachary M Hund, G Benedek, M Bernasconi, Davide Campi, Nathan S Lewis, Kevin J Nihill, Keith Tatseun Wong, S J SibenerAbstract:The Atomic-scale surface structure of methyl-terminated germanium (111) has been characterized by using a combination of Helium Atom scattering and density functional theory. High-resolution Helium diffraction patterns taken along both the ⟨121⟩ and the ⟨011⟩ azimuthal directions reveal a hexagonal packing arrangement with a 4.00 ± 0.02 A lattice constant, indicating a commensurate (1 × 1) methyl termination of the primitive Ge(111) surface. Taking advantage of Bragg and anti-Bragg diffraction conditions, a step height of 3.28 ± 0.02 A at the surface has been extracted using variable de Broglie wavelength specular scattering; this measurement agrees well with bulk values from CH3-Ge(111) electronic structure calculations reported herein. Density functional theory showed that methyl termination of the Ge(111) surface induces a mild inward relaxation of 1.66% and 0.60% from bulk values for the first and second Ge–Ge bilayer spacings, respectively. The DFT-calculated rotational activation barrier of a sin...
Hiroshi Nakatsuji - One of the best experts on this subject based on the ideXlab platform.
-
how accurately does the free complement wave function of a Helium Atom satisfy the schrodinger equation
Physical Review Letters, 2008Co-Authors: Hiroyuki Nakashima, Hiroshi NakatsujiAbstract:The local energy defined by $H\ensuremath{\psi}/\ensuremath{\psi}$ must be equal to the exact energy $E$ at any coordinate of an Atom or molecule, as long as the $\ensuremath{\psi}$ under consideration is exact. The discrepancy from $E$ of this quantity is a stringent test of the accuracy of the calculated wave function. The $H$-square error for a normalized $\ensuremath{\psi}$, defined by ${\ensuremath{\sigma}}^{2}\ensuremath{\equiv}⟨\ensuremath{\psi}|(H\ensuremath{-}E{)}^{2}|\ensuremath{\psi}⟩$, is also a severe test of the accuracy. Using these quantities, we have examined the accuracy of our wave function of a Helium Atom calculated using the free complement method that was developed to solve the Schr\"odinger equation. Together with the variational upper bound, the lower bound of the exact energy calculated using a modified Temple's formula ensured the definitely correct value of the Helium fixed-nucleus ground state energy to be $\mathbf{\ensuremath{-}}\mathbf{2.903}\text{ }\mathbf{724}\text{ }\mathbf{377}\text{ }\mathbf{034}\text{ }\mathbf{119}\text{ }\mathbf{598}\text{ }\mathbf{311}\text{ }\mathbf{159}\text{ }\mathbf{245}\text{ }\mathbf{194}\text{ }\mathbf{4}\text{ }\mathrm{a}.\mathrm{u}.$, which is correct to 32 digits.
-
solving the electron nuclear schrodinger equation of Helium Atom and its isoelectronic ions with the free iterative complement interaction method
Journal of Chemical Physics, 2008Co-Authors: Hiroyuki Nakashima, Hiroshi NakatsujiAbstract:Our previous paper [J. Chem. Phys. 127, 224104 (2007)] revealed that the Schrodinger equation in the fixed-nucleus approximation could be very accurately solved for Helium Atom and its isoelectronic ions (Z=1-10) with the free iterative-complement-interaction (ICI) method combined with the variation principle. In this report, the quantum effect of nuclear motion has further been variationally considered by the free ICI formalism for the Hamiltonian including mass-polarization operator. We obtained -2.903 304 557 729 580 294 733 816 943 892 697 752 659 273 965 a.u. for Helium Atom, which is over 40 digits in accuracy, similarly to the previous result for the fixed-nucleus level. Similar accuracy was also obtained for the Helium isoelectronic ions. The present results may be regarded to be the nonrelativistic limits. We have further analyzed the physics of the free ICI wave function by applying it to an imaginary Atom called "eneon," [e(-)e(10+)e(-)](8+), in which both of the quantum effect of nuclear motion and the three-particle collisions are differently important from the Helium and its isoelectronic ions. This revealed the accurate physics automatically generated by the free ICI formalism.
-
solving the electron and electron nuclear schrodinger equations for the excited states of Helium Atom with the free iterative complement interaction method
Journal of Chemical Physics, 2008Co-Authors: Hiroyuki Nakashima, Yuh Hijikata, Hiroshi NakatsujiAbstract:Very accurate variational calculations with the free iterative-complement-interaction ICI method for solving the Schrodinger equation were performed for the 1sNs singlet and triplet excited states of Helium Atom up to N = 24. This is the first extensive applications of the free ICI method to the calculations of excited states to very high levels. We performed the calculations with the fixed-nucleus Hamiltonian and moving-nucleus Hamiltonian. The latter case is the Schrodinger equation for the electron-nuclear Hamiltonian and includes the quantum effect of nuclear motion. This solution corresponds to the nonrelativistic limit and reproduced the experimental values up to five decimal figures. The small differences from the experimental values are not at all the theoretical errors but represent the physical effects that are not included in the present calculations, such as relativistic effect, quantum electrodynamic effect, and even the experimental errors. The present calculations constitute a small step toward the accurately predictive quantum chemistry. © 2008 American Institute of Physics. DOI: 10.1063/1.2904871
-
solving the electron nuclear schrodinger equation of Helium Atom and its isoelectronic ions with the free iterative complement interaction method
Journal of Chemical Physics, 2008Co-Authors: Hiroyuki Nakashima, Hiroshi NakatsujiAbstract:Our previous paper [J. Chem. Phys. 127, 224104 (2007)] revealed that the Schrodinger equation in the fixed-nucleus approximation could be very accurately solved for Helium Atom and its isoelectronic ions (Z=1–10) with the free iterative-complement-interaction (ICI) method combined with the variation principle. In this report, the quantum effect of nuclear motion has further been variationally considered by the free ICI formalism for the Hamiltonian including mass-polarization operator. We obtained −2.903304557729580294733816943892697752659273965a.u. for Helium Atom, which is over 40 digits in accuracy, similarly to the previous result for the fixed-nucleus level. Similar accuracy was also obtained for the Helium isoelectronic ions. The present results may be regarded to be the nonrelativistic limits. We have further analyzed the physics of the free ICI wave function by applying it to an imaginary Atom called “eneon,” [e−e10+e−]8+, in which both of the quantum effect of nuclear motion and the three-particl...
-
solving the schrodinger equation for Helium Atom and its isoelectronic ions with the free iterative complement interaction ici method
Journal of Chemical Physics, 2007Co-Authors: Hiroyuki Nakashima, Hiroshi NakatsujiAbstract:The Schrodinger equation was solved very accurately for Helium Atom and its isoelectronic ions (Z=1-10) with the free iterative complement interaction (ICI) method followed by the variational principle. We obtained highly accurate wave functions and energies of Helium Atom and its isoelectronic ions. For Helium, the calculated energy was -2.903,724,377,034,119,598,311,159,245,194,404,446,696,905,37 a.u., correct over 40 digit accuracy, and for H(-), it was -0.527,751,016,544,377,196,590,814,566,747,511,383,045,02 a.u. These results prove numerically that with the free ICI method, we can calculate the solutions of the Schrodinger equation as accurately as one desires. We examined several types of scaling function g and initial function psi(0) of the free ICI method. The performance was good when logarithm functions were used in the initial function because the logarithm function is physically essential for three-particle collision area. The best performance was obtained when we introduce a new logarithm function containing not only r(1) and r(2) but also r(12) in the same logarithm function.
J P Toennies - One of the best experts on this subject based on the ideXlab platform.
-
Helium Atom scattering studies of the structure and vibrations of h physisorbed on mgo 001 single crystals
Physical Review B, 2003Co-Authors: J G Skofronick, J P Toennies, F Traeger, H WeissAbstract:The surface structure and vibrations of normal-H 2 , para-H 2 , HD, and normal-D 2 films physisorbed on in situ cleaved single crystal MgO(001) surfaces, have been investigated at surface temperatures 7-12 K using high-resolution Helium Atom scattering. The He-diffraction patterns agree with the sequence of c(2×2)-c(4×2)-c(6×2) structures previously determined by neutron scattering. For the H 2 monolayer three different adsorbate frequencies, two Einstein modes around 10 meV and a dispersive mode between 2 and 7 meV, are found. HD and D 2 show the expected isotopomer shifts. A second probably ordered H 2 layer is formed upon further adsorption and exhibits one dispersionless mode at 5 meV.
-
a Helium Atom scattering study of the structure and phonon dynamics of the ice surface
Journal of Chemical Physics, 2000Co-Authors: A Glebov, A P Graham, J P Toennies, Andreas M Menzel, Patrick SenetAbstract:The structure and phonons of an ordered ice surface, prepared in situ under ultra high vacuum conditions, have been studied by high resolution Helium Atom scattering. The angular distributions are dominated by sharp hexagonal (1×1) diffraction peaks characteristic of a full bilayer terminated ice Ih crystal. Additional, very broad and weak, p(2.1×2.1) peaks may indicate the presence of small domains of antiphase oriented molecules. An eikonal analysis of the 1×1 peaks is compatible with either a proton disordered or a proton ordered surface with corrugations of 0.76 A and 0.63 A, respectively. Inelastic time-of-flight spectra reveal not only a dispersionless phonon branch reported previously at 5.9 meV, but also the first evidence for the surface Rayleigh phonons, which are reproduced well by a Born–von Karman simulation of a full bilayer terminated ice surface using the unmodified force constants derived from neutron scattering bulk phonon measurements. Since the lattice dynamics simulations do not repro...
-
Helium Atom scattering from isolated co molecules on a pt 111 surface experiment versus close coupling calculations for a realistic he co potential
Journal of Chemical Physics, 2000Co-Authors: B H Choi, A P Graham, K T Tang, J P ToenniesAbstract:The angular dependence of the elastic scattering of Helium Atoms from a low coverage (ΘCO=0.03) of randomly distributed isolated CO molecules adsorbed on a Pt(111) surface has been measured over a wide range of incident Helium Atom beam energies between Ei=5.25 and 62.1 meV. The results are compared with a close-coupling theory for a realistic He–CO potential. From a best fit of the experimental results the distance of the molecule from the surface and a modified gas phase He–CO potential are obtained.
-
observation of the second ordered phase of water on the mgo 100 surface low energy electron diffraction and Helium Atom scattering studies
Journal of Chemical Physics, 1996Co-Authors: Daniel Ferry, J P Toennies, A Glebov, V Senz, J Suzanne, H WeissAbstract:The interaction of water with MgO (100) single crystal surfaces cleaved in situ has been studied by low energy electron diffraction and Helium Atom scattering in the temperature range 80 K–230 K. At Tcrystal=100–180 K water forms a layer with a c(4×2) symmetry in good agreement with previous spot profile analysis of low energy electron diffraction experiments. Adsorption at Tcrystal=185–221 K leads to the formation of a new ordered phase. The results of the low energy electron diffraction and elastic Helium Atom scattering experiments show that this high‐temperature phase has a (3×2) symmetry, and that the unit cell contains a glide plane. The isosteric heat of adsorption at half coverage Qst=85.3 kJ/mol has been determined from equilibrium adsorption isotherms measured between 210 and 221 K.
-
organ pipe modes of sodium epitaxial multilayers on cu 001 observed by inelastic Helium Atom scattering
Physical Review Letters, 1992Co-Authors: G Benedek, John Ellis, A Reichmuth, Paolo Ruggerone, H Schief, J P ToenniesAbstract:Inelastic Helium-Atom scattering from epitaxial films (2-20 monolayers) of sodium on Cu(001) reveals a large number of nearly dispersionless phonon modes whose frequencies depend on the thickness and scale as the lower harmonics of an open-ended organ pipe. These data provideevidence for confined acoustic resonances, corresponding to longitudinal standing waves normal to the surface with frequencies about 20% larger than in the bulk
S J Sibener - One of the best experts on this subject based on the ideXlab platform.
-
Atomic surface structure of ch3 ge 111 characterized by Helium Atom diffraction and density functional theory
Journal of Physical Chemistry C, 2015Co-Authors: Zachary M Hund, G Benedek, M Bernasconi, Davide Campi, Nathan S Lewis, Kevin J Nihill, Keith Tatseun Wong, S J SibenerAbstract:The Atomic-scale surface structure of methyl-terminated germanium (111) has been characterized by using a combination of Helium Atom scattering and density functional theory. High-resolution Helium diffraction patterns taken along both the ⟨121⟩ and the ⟨011⟩ azimuthal directions reveal a hexagonal packing arrangement with a 4.00 ± 0.02 A lattice constant, indicating a commensurate (1 × 1) methyl termination of the primitive Ge(111) surface. Taking advantage of Bragg and anti-Bragg diffraction conditions, a step height of 3.28 ± 0.02 A at the surface has been extracted using variable de Broglie wavelength specular scattering; this measurement agrees well with bulk values from CH3-Ge(111) electronic structure calculations reported herein. Density functional theory showed that methyl termination of the Ge(111) surface induces a mild inward relaxation of 1.66% and 0.60% from bulk values for the first and second Ge–Ge bilayer spacings, respectively. The DFT-calculated rotational activation barrier of a sin...
-
hybridization of surface waves with organic adlayer librations a Helium Atom scattering and density functional perturbation theory study of methyl si 111
Physical Review Letters, 2013Co-Authors: Ryan D Brown, G Benedek, M Bernasconi, Davide Campi, Zachary M Hund, Leslie E Oleary, Nathan S Lewis, S J SibenerAbstract:The interplay of the librations of a covalently bound organic adlayer with the lattice waves of an underlying semiconductor surface was characterized using Helium Atom scattering in conjunction with analysis by density functional perturbation theory. The Rayleigh wave dispersion relation of CH3- and CD3-terminated Si(111) surfaces was probed across the entire surface Brillouin zone by the use of inelastic Helium Atom time-of-flight experiments. The experimentally determined Rayleigh wave dispersion relations were in agreement with those predicted by density functional perturbation theory. The Rayleigh wave for the CH3- and CD3-terminated Si(111) surfaces exhibited a nonsinusoidal line shape, which can be attributed to the hybridization of overlayer librations with the vibrations of the underlying substrate. This combined synthetic, experimental, and theoretical effort clearly demonstrates the impact of hybridization between librations of the overlayer and the substrate lattice waves in determining the overall vibrational band structure of this complex interface.
-
Helium Atom diffraction measurements of the surface structure and vibrational dynamics of ch3 si 111 and cd3 si 111 surfaces
Journal of Chemical Physics, 2010Co-Authors: James S Becker, Ryan D Brown, Nathan S Lewis, Erik Johansson, S J SibenerAbstract:The surface structure and vibrational dynamics of CH_3–Si(111) and CD_3–Si(111) surfaces were measured using Helium Atom scattering. The elastic diffraction patterns exhibited a lattice constant of 3.82 A, in accordance with the spacing of the silicon underlayer. The excellent quality of the observed diffraction patterns, along with minimal diffuse background, indicated a high degree of long-range ordering and a low defect density for this interface. The vibrational dynamics were investigated by measurement of the Debye–Waller attenuation of the elastic diffraction peaks as the surface temperature was increased. The angular dependence of the specular (θ_i=θ_f) decay revealed perpendicular mean-square displacements of 1.0 x 10^(−5) A^2 K^(−1) for the CH_3–Si(111) surface and 1.2 x 10^(−5) A^2 K^(−1) for the CD_3–Si(111) surface, and a He-surface attractive well depth of ~7 meV. The effective surface Debye temperatures were calculated to be 983 K for the CH_3–Si(111) surface and 824 K for the CD_3–Si(111) surface. These relatively large Debye temperatures suggest that collisional energy accommodation at the surface occurs primarily through the Si–C local molecular modes. The parallel mean-square displacements were 7.1 x 10^(−4) and 7.2 x 10^(−4) A^2 K^(−1) for the CH_3–Si(111) and CD_3–Si(111) surfaces, respectively. The observed increase in thermal motion is consistent with the interaction between the Helium Atoms and Si–CH_3 bending modes. These experiments have thus yielded detailed information on the dynamical properties of these robust and technologically interesting semiconductor interfaces.
Hiroyuki Nakashima - One of the best experts on this subject based on the ideXlab platform.
-
how accurately does the free complement wave function of a Helium Atom satisfy the schrodinger equation
Physical Review Letters, 2008Co-Authors: Hiroyuki Nakashima, Hiroshi NakatsujiAbstract:The local energy defined by $H\ensuremath{\psi}/\ensuremath{\psi}$ must be equal to the exact energy $E$ at any coordinate of an Atom or molecule, as long as the $\ensuremath{\psi}$ under consideration is exact. The discrepancy from $E$ of this quantity is a stringent test of the accuracy of the calculated wave function. The $H$-square error for a normalized $\ensuremath{\psi}$, defined by ${\ensuremath{\sigma}}^{2}\ensuremath{\equiv}⟨\ensuremath{\psi}|(H\ensuremath{-}E{)}^{2}|\ensuremath{\psi}⟩$, is also a severe test of the accuracy. Using these quantities, we have examined the accuracy of our wave function of a Helium Atom calculated using the free complement method that was developed to solve the Schr\"odinger equation. Together with the variational upper bound, the lower bound of the exact energy calculated using a modified Temple's formula ensured the definitely correct value of the Helium fixed-nucleus ground state energy to be $\mathbf{\ensuremath{-}}\mathbf{2.903}\text{ }\mathbf{724}\text{ }\mathbf{377}\text{ }\mathbf{034}\text{ }\mathbf{119}\text{ }\mathbf{598}\text{ }\mathbf{311}\text{ }\mathbf{159}\text{ }\mathbf{245}\text{ }\mathbf{194}\text{ }\mathbf{4}\text{ }\mathrm{a}.\mathrm{u}.$, which is correct to 32 digits.
-
solving the electron nuclear schrodinger equation of Helium Atom and its isoelectronic ions with the free iterative complement interaction method
Journal of Chemical Physics, 2008Co-Authors: Hiroyuki Nakashima, Hiroshi NakatsujiAbstract:Our previous paper [J. Chem. Phys. 127, 224104 (2007)] revealed that the Schrodinger equation in the fixed-nucleus approximation could be very accurately solved for Helium Atom and its isoelectronic ions (Z=1-10) with the free iterative-complement-interaction (ICI) method combined with the variation principle. In this report, the quantum effect of nuclear motion has further been variationally considered by the free ICI formalism for the Hamiltonian including mass-polarization operator. We obtained -2.903 304 557 729 580 294 733 816 943 892 697 752 659 273 965 a.u. for Helium Atom, which is over 40 digits in accuracy, similarly to the previous result for the fixed-nucleus level. Similar accuracy was also obtained for the Helium isoelectronic ions. The present results may be regarded to be the nonrelativistic limits. We have further analyzed the physics of the free ICI wave function by applying it to an imaginary Atom called "eneon," [e(-)e(10+)e(-)](8+), in which both of the quantum effect of nuclear motion and the three-particle collisions are differently important from the Helium and its isoelectronic ions. This revealed the accurate physics automatically generated by the free ICI formalism.
-
solving the electron and electron nuclear schrodinger equations for the excited states of Helium Atom with the free iterative complement interaction method
Journal of Chemical Physics, 2008Co-Authors: Hiroyuki Nakashima, Yuh Hijikata, Hiroshi NakatsujiAbstract:Very accurate variational calculations with the free iterative-complement-interaction ICI method for solving the Schrodinger equation were performed for the 1sNs singlet and triplet excited states of Helium Atom up to N = 24. This is the first extensive applications of the free ICI method to the calculations of excited states to very high levels. We performed the calculations with the fixed-nucleus Hamiltonian and moving-nucleus Hamiltonian. The latter case is the Schrodinger equation for the electron-nuclear Hamiltonian and includes the quantum effect of nuclear motion. This solution corresponds to the nonrelativistic limit and reproduced the experimental values up to five decimal figures. The small differences from the experimental values are not at all the theoretical errors but represent the physical effects that are not included in the present calculations, such as relativistic effect, quantum electrodynamic effect, and even the experimental errors. The present calculations constitute a small step toward the accurately predictive quantum chemistry. © 2008 American Institute of Physics. DOI: 10.1063/1.2904871
-
solving the electron nuclear schrodinger equation of Helium Atom and its isoelectronic ions with the free iterative complement interaction method
Journal of Chemical Physics, 2008Co-Authors: Hiroyuki Nakashima, Hiroshi NakatsujiAbstract:Our previous paper [J. Chem. Phys. 127, 224104 (2007)] revealed that the Schrodinger equation in the fixed-nucleus approximation could be very accurately solved for Helium Atom and its isoelectronic ions (Z=1–10) with the free iterative-complement-interaction (ICI) method combined with the variation principle. In this report, the quantum effect of nuclear motion has further been variationally considered by the free ICI formalism for the Hamiltonian including mass-polarization operator. We obtained −2.903304557729580294733816943892697752659273965a.u. for Helium Atom, which is over 40 digits in accuracy, similarly to the previous result for the fixed-nucleus level. Similar accuracy was also obtained for the Helium isoelectronic ions. The present results may be regarded to be the nonrelativistic limits. We have further analyzed the physics of the free ICI wave function by applying it to an imaginary Atom called “eneon,” [e−e10+e−]8+, in which both of the quantum effect of nuclear motion and the three-particl...
-
solving the schrodinger equation for Helium Atom and its isoelectronic ions with the free iterative complement interaction ici method
Journal of Chemical Physics, 2007Co-Authors: Hiroyuki Nakashima, Hiroshi NakatsujiAbstract:The Schrodinger equation was solved very accurately for Helium Atom and its isoelectronic ions (Z=1-10) with the free iterative complement interaction (ICI) method followed by the variational principle. We obtained highly accurate wave functions and energies of Helium Atom and its isoelectronic ions. For Helium, the calculated energy was -2.903,724,377,034,119,598,311,159,245,194,404,446,696,905,37 a.u., correct over 40 digit accuracy, and for H(-), it was -0.527,751,016,544,377,196,590,814,566,747,511,383,045,02 a.u. These results prove numerically that with the free ICI method, we can calculate the solutions of the Schrodinger equation as accurately as one desires. We examined several types of scaling function g and initial function psi(0) of the free ICI method. The performance was good when logarithm functions were used in the initial function because the logarithm function is physically essential for three-particle collision area. The best performance was obtained when we introduce a new logarithm function containing not only r(1) and r(2) but also r(12) in the same logarithm function.