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The effective electric field experienced by the unpaired electron in the ground state of PbF, which is a potential candidate in the search of electron electric dipole moment due to some special characteristics, is calculated using Z-vector method in the coupled cluster single- and double- excitation approximation with four component Dirac spinor. This is an important quantity to set the upper bound limit of the electron electric dipole moment. Further, we have calculated molecular dipole moment and parallel magnetic hyperfine structure constant (A$_\|$) of $^{207}$Pb in PbF to test the accuracy of the wave function obtained in the Z-vector method. The outcome of our calculations clearly suggests that the core electrons have significant contribution to the "atom in compound (AIC)" properties., Comment: 6 pages, 1 figure

The article considers the successful implementation of relativistic equation-of-motion coupled cluster method for the electron attachment problem (EA-EOMCC) at the level of single- and double- excitation approximation. The implemented relativistic EA-EOMCC method is employed to calculate ionization potential values of alkali metal atoms (Li, Na, K, Rb, Cs, Fr) and the vertical electron affinity values of LiX (X = H, F, Cl, Br), NaY (Y = H, F, Cl) starting from their closed-shell configuration. Both four-component and exact two-component calculations are done for all the opted systems. Further, we have shown the effect of spin-orbit interaction considering the atomic systems. The results of our atomic calculations are compared with the values from the NIST database and the results are found to be very accurate (< 1 %)., Comment: 26 Pages, 3 figures, 6 Tables. Comments are welcome

A triple of commuting operators for which the closed tetrablock $\overline{\mathbb E}$ is a spectral set is called a tetrablock contraction or an $\mathbb E$-contraction. The set $\mathbb E$ is defined as \[ \mathbb E = \{ (x_1,x_2,x_3)\in\mathbb C^3\,:\, 1-zx_1-wx_2+zwx_3\neq 0 \textup{ whenever } |z|\leq 1, |w|\leq 1 \}. \] We show that every $\mathbb E$-contraction can be uniquely written as a direct sum of an $\mathbb E$-unitary and a completely non-unitary $\mathbb E$-contraction. It is analogous to the canonical decomposition of a contraction operator into a unitary and a completely non-unitary contraction. We produce a concrete operator model for such a triple satisfying some conditions., Comment: To appear in Journal of Mathematical Analysis and Applications

The molecular dipole moment and magnetic hyperfine structure constant demand an accurate wavefunction far from the nucleus and in near nuclear region, respectively. We, therefore, employ the so-called Z-vector method in the domain of relativistic coupled cluster theory to calculate the first order property of molecular systems in their open-shell ground state configuration. The implemented method is applied to calculate molecular dipole moment and parallel component of the magnetic hyperfine structure constant of SrF molecule. The results of our calculation are compared with the experimental and other available theoretically calculated values. We are successful in achieving good accordance with the experimental results. The result of our calculation of molecular dipole moment is in the accuracy of ~? 0.5 %, which is clearly an improvement over the previous calculation based on the expectation value method in the four component coupled cluster framework [V. S. Prasannaa et al, Phys. Rev. A 90, 052507 (2014)] and it is the best calculated value till date. Thus, it can be inferred that the Z vector method can provide an accurate wavefunction in both near and far nuclear region, which is evident from our calculated results., Comment: 5 pages, 1 figure, Comments are welcome

This article deals with the general implementation of 4-component spinor relativistic extended coupled cluster (ECC) method to calculate first order property of atoms and molecules in their open-shell ground state configuration. The implemented relativistic ECC is employed to calculate hyperfine structure (HFS) constant of alkali metals (Li, Na, K, Rb and Cs), singly charged alkaline earth metal atoms (Be+, Mg+, Ca+ and Sr+) and molecules (BeH, MgF and CaH). We have compared our ECC results with the calculations based on restricted active space configuration interaction (RAS-CI) method. Our results are in better agreement with the available experimental values than those of the RAS-CI values., Comment: 14 pages, 6 figures

We report the implementation of 4-component spinor relativistic equation-of-motion coupledcluster method within the single- and double- excitation approximation to calculate ionization potential (EOM-CCSD) of molecules. We have applied this method to calculate vertical ionization potentials of the molecules, XH(X=F, Cl, Br, I) along with Cl2 and Br2 in their closed-shell configuration. We have also presented intermediate results using 2-nd order many-body perturbation theory level in the EOM framework (EOM-MBPT(2)) to understand the role of electron correlation. All the calculated values are compared with the available experimental results. Our results are found to be in well agreement with the sophisticated experiments and relative deviation of less than 1% achieved for all the considered systems., Comment: Accepted in Physical Review A

We report a benchmark theoretical investigation of both adiabatic and vertical electron affinities of five DNA and RNA nucleobases: adenine, guanine, cytosine, thymine and uracil using state-of-the-art equation of motion coupled cluster (EOMCC) method. We have calculated the vertical electron affinity values of first five electron attached states of the DNA and RNA nucleobases and only the first electron attached state is found to be energetically accessible in gas phase. An analysis of the natural orbitals shows that the first electron attached states of uracil and thymine are valence-bound type and undergo significant structural changes on attachment of excess electron, which is reflected in the deviation of the adiabatic electron affinity from the vertical one. On the other hand, the first electron attached state of cytosine, adenine and guanine are dipole-bound type and their structure remain unaffected on attachment of an extra electron, which results in small deviation of adiabatic electron affinity from that of the vertical one. Vertical and adiabatic electron affinity values of all the DNA and RNA nucleobases are negative implying that the first electron attached state are not stable, but rather resonance states. Previously, reported theoretical studies had shown scattered results for electron affinities of DNA and RNA bases, with large deviations from experimental values. Our EOMCC computed values are in very good agreement with experimental values and can be used as a reliable benchmark for calibrating new theoretical methods.

We employ four-component spinor relativistic equation-of-motion coupled-cluster (EOMCC) method within the single- and double- excitation approximation to calculate the single ionization potentials (IPs) and double ionization potentials (DIPs) of the He and Be isoelectronic sequences up to Ne. The obtained results are compared with the available results from the National Institute of Standards and Technology (NIST) database to test the performance of the EOMCC method. We also present intermediate results at different level of approximations in the EOMCC framework to gain insight of the effect of electron correlation. Furthermore, we investigate the dependence of the IPs and DIPs of these ions on the ionic charge and observe that these follow parabolic trends. Comparison between the trends of IPs and DIPs in both the classes of considered systems are categorically demonstrated., Comment: 8 pages, 3 figures

We show by a counter example the failure of rational dilation on the tetrablock, a polynomially convex and non-convex domain in $\mathbb C^3$, defined as $$ \mathbb E = \{ (x_1,x_2,x_3)\in\mathbb C^3\,:\, 1-zx_1-wx_2+zwx_3\neq 0 \textup{ whenever } |z|\leq 1, |w|\leq 1 \}. $$ A commuting triple of operators $(T_1,T_2,T_3)$ for which the closed tetrablock $\overline{\mathbb E}$ is a spectral set, is called an $\mathbb E$-contraction. For an $\mathbb E$-contraction $(T_1,T_2,T_3)$, the two operator equations $$ T_1-T_2^*T_3=D_{T_3}X_1D_{T_3} \textup{ and } T_2-T_1^*T_3= D_{T_3}X_2D_{T_3}, \quad D_{T_3}=(I-T_3^*T_3)^{\frac{1}{2}},$$ have unique solutions $A_1,A_2$ on $\mathcal D_{T_3}=\overline{Ran} D_{T_3}$ and they are called the fundamental operators of $(T_1,T_2,T_3)$. For a particular class of $\mathbb E$-contractions, we prove it necessary for the existence of rational dilation that the corresponding fundamental operators $A_1,A_2$ satisfy the conditions \begin{equation}\label{abstract} A_1A_2=A_2A_1 \textup{ and } A_1^*A_1-A_1A_1^*=A_2^*A_2-A_2A_2^*. \end{equation} Then we construct an $\mathbb E$-contraction from that particular class which fails to satisfy (\ref{abstract}). We produce a concrete functional model for pure $\mathbb E$-isometries, a class of $E$-contractions analogous to the pure isometries in one variable. The fundamental operators play the main role in this model., Comment: Final version - 23 pages, To appear in Journal of Functional Analysis

We show an interplay between the complex geometry of the tetrablock $\mathbb E$ and the commuting triples of operators having $\overline{\mathbb E}$ as a spectral set. We prove that every distinguished variety in the tetrablock is one-dimensional and can be represented as \begin{equation}\label{eqn:1} \Omega=\{ (x_1,x_2,x_3)\in \mathbb E \,:\, (x_1,x_2) \in \sigma_T(A_1^*+x_3A_2\,,\, A_2^*+x_3A_1) \}, \end{equation} where $A_1,A_2$ are commuting square matrices of the same order satisfying $[A_1^*,A_1]=[A_2^*,A_2]$ and a norm condition. The converse also holds, i.e, a set of the form (\ref{eqn:1}) is always a distinguished variety in $\mathbb E$. We show that for a triple of commuting operators $\Upsilon = (T_1,T_2,T_3)$ having $\overline{\mathbb E}$ as a spectral set, there is a one-dimensional subvariety $\Omega_{\Upsilon}$ of $\overline{\mathbb E}$ depending on $\Upsilon$ such that von-Neumann's inequality holds, i.e, \[ f(T_1,T_2,T_3)\leq \sup_{(x_1,x_2,x_3)\in\Omega_{\Upsilon}}\, |f(x_1,x_2,x_3)|, \] for any holomorphic polynomial $f$ in three variables, provided that $T_3^n\rightarrow 0$ strongly as $n\rightarrow \infty$. The variety $\Omega_\Upsilon$ has been shown to have representation like (\ref{eqn:1}), where $A_1,A_2$ are the unique solutions of the operator equations \begin{gather*} T_1-T_2^*T_3=(I-T_3^*T_3)^{\frac{1}{2}}X_1(I-T_3^*T_3)^{\frac{1}{2}} \text{ and } \\ T_2-T_1^*T_3=(I-T_3^*T_3)^{\frac{1}{2}}X_2(I-T_3^*T_3)^{\frac{1}{2}}. \end{gather*} We also show that under certain condition, $\Omega_{\Upsilon}$ is a distinguished variety in $\mathbb E$. We produce an explicit dilation and a concrete functional model for such a triple $(T_1,T_2,T_3)$ in which the unique operators $A_1,A_2$ play the main role. Also, we describe a connection of this theory with the distinguished varieties in the bidisc and in the symmetrized bidisc., Comment: 28 pages, A new reference added, To appear in Indiana Univ. Math. J

We report the general implementation of the relativistic equation-of-motion coupled-cluster method to calculate double ionization spectra (DI-EOMCC) of atomic and molecular systems. As a first application, this method is employed to calculate the principal valence double ionization potential values of He and alkaline earth metal (Be, Mg, Ca, Sr and Ba) atoms. Our results are compared with the results available from the national institute of standards and technology (NIST) database and other ab initio calculations. We have achieved an accuracy of ~ 0.1%, which is an improvement over the first principles T-matrix calculations [J. Chem. Phys. 123, 144112 (2005)]. We also present results using the second-order many-body perturbation theory and the random- phase approximation in the equation-of-motion framework and these results are compared with the DI-EOMCC results., Comment: 5 pages, 4 figure

The spectroscopic properties of Li atom and Li-like Ca and Ti ions in the plasma environment are investigated using a relativistic coupled-cluster (RCC) method. Assuming the plasma is of low density and very hot, we consider the Debye model with two approximations by accounting the screening effects: (i) in the nuclear potential alone and (ii) in both the nuclear and the electron-electron interaction potentials. First, the calculations for the energies and the lifetimes of the atomic states are carried out for the plasma free systems in order to check their accuracies following which they are investigated in the plasma environment. It is observed that screenings in the electron-electron interaction potentials stabilize the systems more than the case when the screenings present only in the nuclear potential. Similarly, the earlier predicted blue and red shifts in the $\Delta n=0$ and $\Delta n \ne 0$ transition lines (with the principal quantum number $n$) of the Li-like ions change significantly in the case (ii) approximation. The level-crossings among the energy levels are observed for the large screening effects which seem to be prominent in the states of higher orbital angular momentum. The lifetimes of many low-lying states and the relative line-intensities of the allowed transitions are estimated considering different plasma screening strengths., Comment: 5 tables and 10 figures

We report our successful implementation of the full fledged relativistic equation of motion coupled cluster (EOMCC) method. This method is employed to compute the principal ionization potentials (IPs) of closed-shell rare gas atoms, He-like ions, Be-like ions along with Na+, Al+, K+, Be, and Mg. Four component Dirac spinors are used in the calculations and the one and two electron integrals are evaluated using the Dirac Coulomb Hamiltonian. Our results are in excellent agreement with those available measurements, which are taken from the National Institute of Science and Technology database (NIST). We also present results using the second order many-body perturbation theory (MBPT(2)) and random phase approximation (RPA) in the EOMCC framework. These results are compared with those of EOMCC at the level of single and double excitations in order to assess the role of the electron correlation effects in the intermediate schemes considered in our calculations .

We provide an explicit normal distinguished boundary dilation to a pair of commuting operators $(S,P)$ having the closed symmetrized bidisc $\Gamma$ as a spectral set. This is called Sz.-Nagy dilation of $(S,P)$. The operator pair that dilates $(S,P)$ is obtained by an application of Stinespring dilation of $(S,P)$ given by Agler and Young. We further prove that the dilation is minimal and the dilation space is no bigger than the dilation space of the minimal unitary dilation of the contraction $P$. We also describe model space and model operators for such a pair $(S,P)$.

We show that for every pair of matrices (S,P), having the closed symmetrized bidisc $\Gamma$ as a spectral set, there is a one dimensional complex algebraic variety $\Lambda$ in $\Gamma$ such that for every matrix valued polynomial f, the norm of f(S,P) is less then the sup norm of f on $\Lambda$. The variety $\Lambda$ is shown to have a particular determinantal representation, related to the so-called "fundamental operator" of the pair (S,P). When (S,P) is a strict $\Gamma$-contraction, then $\Lambda$ is a distinguished variety in the symmetrized bidisc, i.e., a one dimensional algebraic variety that exits the symmetrized bidisc through its distinguished boundary. We characterize all distinguished varieties of the symmetrized bidisc by a determinantal representation as above., Comment: 18 pages. Slightly revised

A pair of commuting operators $(S,P)$ defined on a Hilbert space $\mathcal H$ for which the closed symmetrized bidisc $$ \Gamma= \{(z_1+z_2,z_1z_2):: |z_1|\leq 1,\, |z_2|\leq 1 \}\subseteq \mathbb C^2, $$ is a spectral set is called a $\Gamma$-contraction in the literature. A $\Gamma$-contraction $(S,P)$ is said to be pure if $P$ is a pure contraction, i.e, ${P^*}^n \rightarrow 0$ strongly as $n \rightarrow \infty $. Here we construct a functional model and produce a complete unitary invariant for a pure $\Gamma$-contraction. The key ingredient in these constructions is an operator, which is the unique solution of the operator equation $$ S-S^*P=D_PXD_P, \textup{where} X\in \mathcal B(\mathcal D_P), $$and is called the fundamental operator of the $\Gamma$-contraction $(S,P)$. We also discuss some important properties of the fundamental operator., Comment: Journal of Operator Theory, 71 (2014), 327-339

For a contraction P and a bounded commutant S of P, we seek a solution X of the operator equation S-S*P = (I-P*P)^1/2 X(I-P*P) 1/2, where X is a bounded operator on Ran(I-P*P) 1/2 with numerical radius of X being not greater than 1. A pair of bounded operators (S,P) which has the domain \Gamme = {(z 1 +z 2, z 1z 2) : |z1|{\leq} 1, |z2| {\leq}1} {\subseteq} C2 as a spectral set, is called a \Gamme-contraction in the literature. We show the existence and uniqueness of solution to the operator equation above for a \Gamma-contraction (S,P). This allows us to construct an explicit \Gamma-isometric dilation of a \Gamma-contraction (S,P). We prove the other way too, i.e, for a commuting pair (S,P) with |P|| {\leq} 1 and the spectral radius of S being not greater than 2, the existence of a solution to the above equation implies that (S,P) is a \Gamma-contraction. We show that for a pure \Gamma-contraction (S,P), there is a bounded operator C with numerical radius not greater than 1, such that S = C +C*P. Any \Gamma-isometry can be written in this form where P now is an isometry commuting with C and C*. Any \Gamma-unitary is of this form as well with P and C being commuting unitaries. Examples of \Gamma-contractions on reproducing kernel Hilbert spaces and their \Gamma-isometric dilations are discussed., Comment: Advances in Mathematics, 230 (2012), 577-606

Reactivity of Aluminum Clusters has been found to exhibit size sensitive variations. This work is motivated by a recent report1 predicting higher reactivity of melted Aluminum clusters towards the N2 molecule as compared to the non-melted Al clusters. We attempt to understand the underlying electronic and structural factors influencing the adsorption of N2 molecule (a prerequisite for the reactivity) on ground state geometry (a non-melted structure) of various Al clusters. The results show that the adsorption energy is of the order of 8-10 kcal/mol and does not vary with respect to the cluster size and the electronic properties of the ground state geometry. The structural and electronic properties of high energy conformations of Al clusters (a melted cluster) are also analyzed to explain their higher reactivity towards N2 molecule.

A new electronic structure principle, viz. the minimum magnetizability principle (MMP) has been proposed and also has been verified through ab initio calculations, to extend the domain of applicability of the conceptual density functional theory (DFT) in explaining the magnetic interactions and magnetochemistry. This principle may be stated as, "A stable configuration/conformation of a molecule or a favorable chemical process is associated with a minimum value of the magnetizability". It has also been shown that a soft molecule is easily polarizable and magnetizable than a hard one., Comment: 2 Pages, 3 Figures

Periodic density functional theory has been employed to characterize the differences in the structural, Lewis acidic and hydrophobic properties of Sn--BEA and Ti--BEA. We show that the incorporation of Sn increases the Lewis acidity of BEA compared to the incorporation of Ti. Hence, the present work gives an insight into the role of Sn in increasing the efficiency of the oxidation reactions. The results also justify that the percentage of Sn substituted in BEA is less than Ti. The structural analysis shows that the first coordination shell of Sn is larger than that of Ti. However, the second coordination of both sites remains the same. Moreover, the water resistant properties of these substituted zeolites are quantified., Comment: 1 figure

Local reactivity descriptors such as the condensed local softness and Fukui function have been employed to investigate the inter-cluster reactivity of the metallo-aromatic (Al4Li- and Al4Na-) and anti-aromatic (Al4Li4 and Al4Na4) compounds. We use the concept of group softness and group Fukui function to study the strength of the nucleophilicity of the Al4 unit in these compounds. Our analysis shows that the trend of nucleophilicity of the Al4 unit in the above clusters is as follows; Al4Li- > Al4Na- > Al4Li4 > Al4Na 4 For the first time we have used the reactivity descriptors to show that these clusters can act as electron donating systems and thus can be used as a molecular cathode., Comment: 23 pages, 1 figure and 1 table of content

The structural, electronic and the bonding properties of the Sn-BEA are investigated by using the periodic density functional theory. Each of the 9 different T-sites in the BEA were substituted by the Sn atom and all the 9 geometries were completely optimized using the plane wave basis set in conjunction with the ultra-soft pseudopotential. On the basis of the structural and the electronic properties, it has been demonstrated that the substitution of the Sn atom in the BEA framework is an endothermic process and hence the incorporation of the Sn in the BEA is limited. The lowest unoccupied molecular orbitals (LUMO) energies have been used to characterize the Lewis acidity of each T-site. On the basis of the relative cohesive energy and the LUMO energy, T2 site is shown to be the most favorable site for the substitution of Sn atom in the BEA framework., Comment: 17 pages, 5 figures, 2 Tables

We have performed ab initio molecular dynamics simulations to study the nature of the synchronous double proton transfer in formic acid dimer. In order to understand the evolution of the bonding during the double proton transfer, we have used the electron localization function and the molecular orbital isosurfaces. During the dynamics of the double proton transfer in formic acid dimer the two formic acid monomers approach each other, forming Speakman-Hadzi type, of short strong hydrogen bonds at the transition state. The Speakman-Hadzi type of short strong hydrogen bonds are also shown to be polar covalent bonds. Based on the concept of resonance assisted hydrogen bond proposed by Gilli et al (Gilli P, Bertolasi V, Ferretti V & G. Gilli, J. Am. Chem. Soc., 116 (1994). 909-915), we show that the proton at the transition state is connected by a conjugated O-C-O structures, indicating a resonance assisted hydrogen bond. On this basis the double proton transfer process in the formic acid dimer can be termed as a resonance assisted double proton transfer. Our finding on the above analysis suggest that the synchronous double proton transfer in the formic acid dimer is due to the formation of (a) Speakman-Hadzi type of short strong hydrogen bonds and (b) Resonance assisted hydrogen bond at the transition state., Comment: 19 pages, 7 figures

We propose a theoretical investigation in this paper to understand the bonding and structural properties of neutral Al4Na4 and anion Al4Na3- clusters. We show that the Al4 species in Al4Na4 and Al4Na3- clusters is a rectangular planar structure with alternate pi-bonds and hence satisfying the basic criteria for anti-aromaticity. We prove that the Al4Na4 and Al4Na3- clusters are metallo-anti-aromatic compounds.