ABSTRACT
The chaotic ionization of hydrogen atoms [1-3] in highly excited states by microwave fi elds has become an important area of research for both experimentalists [1-7] and theoreticians [4]. In 1974 Bayfi eld and Koch [8] fi rst studied the chaotic ionization of hydrogen atoms which has been considered to be very important in atomic theory [1,2,4,5,9-28]. Sanders and Jensen [4] have studied the chaotic ionization of hydrogen and helium using classical mechanics [4]. When the hydrogen atom is promoted to a highly excited state it gets ionized in case the fi eld intensity is above some threshold value and the ionization probability depends on the fi eld intensity [4,6,7]. Standard diagnostics used for the present study include electronegativity ( χ ), hardness (η ), polarizability (α ), phase-volume (Vps), electrophilicity index (ω ), nucleophilicity index (
1 ), Shannon entropy (S), quantum
Lyapunov exponent (Λ ) and Kolmogorov-Sinai entropy (H) defi ned in terms of the distance between two initially close Bohmian trajectories. In this paper we have generated the higher-order harmonics [3,29,30]. The response of the atom when it interacts with the external fi eld vis-á-vis the variation of its reactivity is an important area of research. Electornegativity ( χ ) [31] and hardness (η ) [32] are two cardinal indices of chemical reactivity. Pauling [33] introduced the concept of electronegativity as the power of an atom in a molecule to attract electrons to itself. The concept of hardness was given by Pearson [34] in his hard-soft acid-base (HSAB) principle which states that, “hard likes hard and soft likes soft”. These popular qualitative chemical reactivity concepts have been quantifi ed in density functional theory (DFT) [35]. Another important hardness-related principle is the maximum hardness principle (MHP) [36,37], which states that, “ there seems to be a rule of nature that molecules arrange themselves so as to be as hard as possible”. The quantitative defi nitions for electronegativity [38] and hardness [39] for an N-electron system with total energy E can respectively be given as
−=−= (1)
and
= (2)
In eqs.(1) and (2)μ and ⎟ ⎠
with the normalization constraint of DFT [34,36]) and external potential respectively. An equivalent expression [40,41] for hardness is
∫∫ (3)
where )(ρF is the Hohenberg-Kohn universal functional of DFT [35]. The complete characterization of an N-particle system acted on by an external potential
the infl uence of the weak electric fi eld, polarizability (α ) takes care of the corresponding response. During molecule formation the electronegativities of the pertinent atoms get equalized [42,43]. A stable confi guration or a favorable process is generally associated with maximum hardness [36,37], minimum polarizability [44-47] and maximum entropy [48] values. The conditions for maximum hardness and entropy and minimum polarizability complement the usual minimum energy criterion for stability.
