Quantum phase transitions in skewed ladder systems.

In this brief review, we introduce a new spin ladder system called skewed spin ladders and discuss the exotic quantum phases of this system. The spin ladders studied are the 5/7, 3/4 and 3/5 systems corresponding to alternately fused 5 and 7 membered rings; 3 and 4 membered rings; and 3 and 5 membered rings. These ladders show completely different behaviour as the Hamiltonian model parameter is changed. When the Hamiltonian parameter is increased the 5/7 ladder switches from an initial singlet ground state to progressively higher spin ground state and then to a reentrant singlet state before finally settling to the highest spin ground state whose spin equals the number of unit cells in the system. The 3/4 ladder goes from a singlet ground state to a high spin ground state with each unit cell contributing spin 1 to the state, as the model parameter is increased. The 3/5 ladder shows a singlet ground state for small parameters and high spin ground state for intermediate values of the parameter and for still higher parameters, a reentrant singlet ground state. They can also show interesting magnetization plateaus as illustrated by studies on a specific spin ladder.

A simple scheme for finding magnetic aromatic hydrocarbon molecules.

Polycyclic aromatic hydrocarbon (PAH) molecules such as quasi-unidimensional oligo-acene and fused azulene display interesting properties for increasing chain length. However, these molecules can be hard to explore computationally due to the number of atoms involved and the fast-increasing numerical cost when using many-body methods. The identification of magnetic PAH molecules is most relevant for technological applications and hence it would be of particular interest to develop rapid preliminary checks to identify likely candidates for both theoretical and experimental pursuits. In this article, we show that an analysis based on a second-order perturbation treatment of electronic correlations for the Hubbard model qualitatively predicts the outcome of more extensive and accurate methods. Based on these results we propose a simple computational protocol for screening molecules and identifying those worthy of a more sophisticated analysis on the magnetic nature of their ground states. Using this protocol we were able to identify two new magnetic molecules made from the combination of only two naphthalene monomers and two azulene ones (both isomers with formula C34H20). For further confirmation of this result, these molecules were also studied by means of density matrix renormalization group and density functional theory.

Correlated Electronic States of a Few Polycyclic Aromatic Hydrocarbons: A Computational Study.

In recent years, polycyclic aromatic hydrocarbons (PAHs) have been studied for their electronic properties as they are viewed as nanodots of graphene. They have also been of interest as functional molecules for applications such as light-emitting diodes and solar cells. Since the last few years, varying structural and chemical properties corresponding to the size and geometry of these molecules have been studied both theoretically and experimentally. Here, we carry out a systematic study of the electronic states of several PAHs using the Pariser-Parr-Pople model, which incorporates long-range electron correlations. In all of the molecules studied by us, we find that the 2A state is below the 1B state and hence none of them will be fluorescent in the gaseous phase. The singlet-triplet gap is more than half of the singlet-singlet gap in all cases, and hence, none of these PAHs can be candidates for improved solar cell efficiencies in a singlet fission. We discuss in detail the properties of the electronic states, which include bond orders and spin densities (in triplets) of these systems.

Correlated Electronic Properties of a Graphene Nanoflake: Coronene.

We report studies of the correlated excited states of coronene and substituted coronene within the Pariser⁻Parr⁻Pople (PPP) correlated π -electron model employing the symmetry-adapted density matrix renormalization group technique. These polynuclear aromatic hydrocarbons can be considered as graphene nanoflakes. We review their electronic structures utilizing a new symmetry adaptation scheme that exploits electron-hole symmetry, spin-inversion symmetry, and end-to-end interchange symmetry. The study of the electronic structures sheds light on the electron correlation effects in these finite-size graphene analogues, which diminishes going from one-dimensional to higher-dimensional systems, yet is significant within these finite graphene derivatives.

A Model Exact Study of the Properties of Low-Lying Electronic States of Perylene and Substituted Perylenes.

There is a resurgence of interest in the electronic structure of perylene for its applications in molecular devices such as organic photovoltaics and organic light-emitting diodes. In this study, we have obtained the low-lying singlet states of perylene by exactly solving the Parisar-Parr-Pople model Hamiltonian of this system with 20 sites and 20 electrons in the VB basis where dimensionality is ∼5.92 billion. The triplet states of perylene are obtained using a DMRG scheme with symmetry adaptation. The one- and two-photon states are very close in energy ∼3.2 eV while the lowest triplet state is slightly below 1.6 eV indicating that perylene is a good candidate for singlet fission. To explore the tunability of the electronic states, we have studied donor-acceptor substituted perylenes. The two donors and two acceptors are substituted symmetrically at either the four bay sites or four peri sites. In all the bay substitution and one peri substitution at moderate D/A strength, the optical gap is lowered to about 2.8 eV. These molecules can be used as blue emitters. We have also reported bond orders in all the cases, and perylene as well as substituted perylenes can be viewed as two weakly coupled naphthalenes in the singlet states, but in triplets these bonds tend to be comparable to other bonds in strength. The charge densities in substituted perylenes are mostly localized around the substitution sites in the ground state. The positive spin densities in triplets are concentrated around the peri and bay sites with the remaining sites having small spin densities of either sign.

Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets.

Pentagonal bipyramid FeII complexes have been investigated to evaluate their potential as Ising-spin building units for the preparation of heteropolynuclear complexes that are likely to behave as single-molecule magnets (SMMs). The considered monometallic complexes were prepared from the association of a divalent metal ion with pentadentate ligands that have a 2,6-diacetylpyridine bis(hydrazone) core (H2 LN3O2R ). Their magnetic anisotropy was established by magnetometry to reveal their zero-field splitting (ZFS) parameter D, which ranged between -4 and -13 cm-1 and was found to be modulated by the apical ligands (ROH versus Cl). The alteration of the D value by N-bound axial CN ligands, upon association with cyanometallates, was also assessed for heptacoordinated FeII as well as for related NiII and CoII derivatives. In all cases, N-coordinated cyanide ligands led to large magnetic anisotropy (i.e., -8 to -18 cm-1 for Fe and Ni, +33 cm-1 for Co). Ab initio calculations were performed on three FeII complexes, which enabled one to rationalize the role of the ligand on the nature and magnitude of the magnetic anisotropy. Starting from the pre-existing heptacoordinated complexes, a series of pentanuclear compounds were obtained by reactions with paramagnetic [W(CN)8 ]3- . Magnetic studies revealed the occurrence of ferromagnetic interactions between the spin carriers in all the heterometallic systems. Field-induced slow magnetic relaxation was observed for mononuclear FeII complexes (Ueff /kB up to 53 K (37 cm-1 ), τ0 =5×10-9  s), and SMM behavior was evidenced for a heteronuclear [Fe3 W2 ] derivative (Ueff /kB =35 K and τ0 =4.6 10-10  s), which confirmed that the parent complexes were robust Ising-type building units. High-field EPR spectroscopic investigation of the ZFS parameters for a Ni derivative is also reported.

Single-ion magnet behaviour of heptacoordinated Fe(II) complexes: on the importance of supramolecular organization.

Supramolecular organization of a metal complex may significantly contribute to the magnetization dynamics of mononuclear SMMs. This is illustrated for a heptacoordinated Fe(II) complex with rather moderate Ising-type anisotropy for which a slow magnetization relaxation with significant energy barrier was reached when this complex was properly organized in the crystal lattice. Incidentally, it is the first example of single-ion magnet behaviour of Fe(II) in a pentagonal bipyramid surrounding.

Hetero-tri-spin [2p-3d-4f] chain compounds based on nitronyl nitroxide lanthanide metallo-ligands: synthesis, structure, and magnetic properties.

Employing nitronyl nitroxide lanthanide(III) complexes as metallo-ligands allowed the efficient and highly selective preparation of three series of unprecedented hetero-tri-spin (Cu-Ln-radical) one-dimensional compounds. These 2p-3d-4f spin systems, namely [Ln3Cu(hfac)11(NitPhOAll)4] (Ln(III) = Gd 1Gd, Tb 1Tb, Dy 1Dy; NitPhOAll = 2-(4'-allyloxyphenyl)-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide), [Ln3Cu(hfac)11(NitPhOPr)4] (Ln(III) = Gd 2Gd, Tb 2Tb, Dy 2Dy, Ho 2Ho, Yb 2Yb; NitPhOPr = 2-(4'-propoxyphenyl)-4,4,5,5-tetramethyl-imidazoline-1-oxyl-3-oxide) and [Ln3Cu(hfac)11(NitPhOBz)4] (Ln(III) = Gd 3Gd, Tb 3Tb, Dy 3Dy; NitPhOBz=2-(4'-benzyloxyphenyl)-4,4,5,5-tetramethyl-imidazoline-1-oxyl-3-oxide) involve O-bound nitronyl nitroxide radicals as bridging ligands in chain structures with a [Cu-Nit-Ln-Nit-Ln-Nit-Ln-Nit] repeating unit. The dc magnetic studies show that ferromagnetic metal-radical interactions take place in these hetero-tri-spin chain complexes, these and the next-neighbor interactions have been quantified for the Gd derivatives. Complexes 1Tb and 2Tb exhibit frequency dependence of ac magnetic susceptibilities, indicating single-chain magnet behavior.

Model for triplet state engineering in organic light emitting diodes.

Engineering the position of the lowest triplet state (T1) relative to the first excited singlet state (S1) is of great importance in improving the efficiencies of organic light emitting diodes and organic photovoltaic cells. We have carried out model exact calculations of substituted polyene chains to understand the factors that affect the energy gap between S1 and T1. The factors studied are backbone dimerisation, different donor-acceptor substitutions, and twisted geometry. The largest system studied is an 18 carbon polyene which spans a Hilbert space of about 991 × 10(6). We show that for reverse intersystem crossing process, the best system involves substituting all carbon sites on one half of the polyene with donors and the other half with acceptors.

Studies on a frustrated Heisenberg spin chain with alternating ferromagnetic and antiferromagnetic exchanges.

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J(F)(1)) and antiferromagnetic (J(A)(1)) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction (J(F)(2)). In this model frustration is present due to the non-zero J(F)(2). The model with site spin s behaves like a Haldane spin chain, with site spin 2s in the limit of vanishing J(F)(2)and large J(F)(1)/J(A)(1). We show that the exact ground state of the model can be found along a line in the parameter space. For fixed J(F)(1), the phase diagram in the space of J(A)(1)-J(F)(2) is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

Exact solution of the PPP model for correlated electronic states of tetracene and substituted tetracene.

Tetracene is an important conjugated molecule for device applications. We have used the diagrammatic valence bond method to obtain the desired states, in a Hilbert space of about 450 million singlets and 902 million triplets. We have also studied the donor/acceptor (D/A)-substituted tetracenes with D and A groups placed symmetrically about the long axis of the molecule. In these cases, by exploiting a new symmetry, which is a combination of C2 symmetry and electron-hole symmetry, we are able to obtain their low-lying states. In the case of substituted tetracene, we find that optically allowed one-photon excitation gaps reduce with increasing D/A strength, while the lowest singlet-triplet gap is only weakly affected. In all the systems we have studied, the excited singlet state, S1, is at more than twice the energy of the lowest triplet state and the second triplet is very close to the S1 state. Thus, donor-acceptor-substituted tetracene could be a good candidate in photovoltaic device application as it satisfies energy criteria for singlet fission. We have also obtained the model exact second harmonic generation (SHG) coefficients using the correction vector method, and we find that the SHG responses increase with the increase in D/A strength.

Linear and nonlinear optical properties of expanded porphyrins: a DMRG study.

We study absorption spectra and two photon absorption coefficient of expanded porphyrins (EPs) by the density matrix renormalization group (DMRG) technique. We employ the Pariser-Parr-Pople (PPP) Hamiltonian which includes long-range electron-electron interactions. We find that, in the 4n+2 EPs, there are two prominent low-lying one-photon excitations, while in 4n EPs, there is only one such excitation. We also find that 4n+2 EPs have large two-photon absorption cross sections compared to 4n EPs. The charge density rearrangement in the one-photon excited state is mostly at the pyrrole nitrogen site and at the meso carbon sites. In the two-photon states, the charge density rearrangement occurs mostly at the aza-ring sites. In the one-photon state, the C-C bond length in aza rings shows a tendency to become uniform. In the two-photon state, the bond distortions are on C-N bonds of the pyrrole ring and the adjoining C-C bonds which connect the pyrrole ring to the aza or meso carbon sites.

Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study.

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J2) and dimerization (δ). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J2-δ plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

Influence of anion on the quadratic nonlinearity and depolarization ratios of scattered second harmonic light from cation-π complexes.

We have investigated quadratic nonlinearity (ß(HRS)) and linear and circular depolarization ratios (D and D('), respectively) of a series of 1:1 complexes of tropyliumtetrafluoroborate as a cation and methyl-substituted benzenes as π-donors by making polarization resolved hyper-Rayleigh scattering measurements in solution. The measured D and D(') values are much lower than the values expected from a typical sandwich or a T-shaped geometry of a complex. In the cation-π complexes studied here, the D value varies from 1.36 to 1.46 and D(') from 1.62 to 1.72 depending on the number of methyl substitutions on the benzene ring. In order to probe it further, ß, D and D(') were computed using the Zerner intermediate neglect of differential overlap-correction vector self-consistent reaction field technique including single and double configuration interactions in the absence and presence of BF(4) (-) anion. In the absence of the anion, the calculated value of D varies from 4.20 to 4.60 and that of D(') from 2.45 to 2.72 which disagree with experimental values. However, by arranging three cation-π BF(4)(-) complexes in a trigonal symmetry, the computed values are brought to agreement with experiments. When such an arrangement was not considered, the calculated ß values were lower than the experimental values by more than a factor of two. This unprecedented influence of the otherwise "unimportant" anion in solution on the ß value and depolarization ratios of these cation-π complexes is highlighted and emphasized in this paper.

Exact entanglement studies of strongly correlated systems: role of long-range interactions and symmetries of the system.

We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople model with long-range interactions. We compare the results for this model with those obtained for the Hubbard and Heisenberg models with short-range interactions. This study helps us to understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions. To better understand the behavior of long-range interactions and why the DMRG works well with it, we study the entanglement spectrum of the ground state and a few excited states of finite chains. We also investigate if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, we make an interesting observation on the entanglement profiles of different states (across the energy spectrum) in comparison with the corresponding profile of the density of states. We use isotropic chains and a molecule with non-Abelian symmetry for these numerical investigations.

A density matrix renormalization group method study of optical properties of porphines and metalloporphines.

The symmetrized density matrix renormalization group method is used to study linear and nonlinear optical properties of free base porphine and metalloporphine. Long-range interacting model, namely, Pariser-Parr-Pople model is employed to capture the quantum many-body effect in these systems. The nonlinear optical coefficients are computed within the correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modeled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have D(4h) symmetry and hence have more degenerate excited states. The ground state of metalloporphines shows 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients.

Structure of the pyridine-chloranil complex in solution: a surprise from depolarized hyper-Rayleigh scattering measurements.

In this article, we report the structure of a 1:1 charge transfer complex between pyridine (PYR) and chloranil (CHL) in solution (CHCl(3)) from the measurement of hyperpolarizability (ß(HRS)) and linear and circular depolarization ratios, D and D', respectively, by the hyper-Rayleigh scattering technique and state-of-the-art quantum chemical calculations. Using linearly (electric field vector along X) and circularly polarized incident light, respectively, we have measured two macroscopic depolarization ratios D = I(X,X)(2ω)/I(X,Z)(2ω) and D' = I(X,C)(2ω)/I(Z,C)(2ω) in the laboratory fixed XYZ frame by detecting the second harmonic (SH) scattered light in a polarization resolved fashion. The stabilization energy and the optical gap calculated through the MP2/cc-pVDZ method using Gaussian09 were not significantly different to distinguish between the cofacial and T-shape structures. Only when the experimentally obtained ß(HRS) and the depolarization ratios, D and D', were matched with the theoretically computed values from single and double configuration interaction (SDCI) calculations performed using the ZINDO-SCRF technique, we concluded that the room temperature equilibrium structure of the complex is cofacial. This is in sharp contrast to an earlier theoretical prediction of the T-shape structure of the complex.

Geometry and quadratic nonlinearity of charge transfer complexes in solution: a theoretical study.

In this paper, we have computed the quadratic nonlinear optical (NLO) properties of a class of weak charge transfer (CT) complexes. These weak complexes are formed when the methyl substituted benzenes (donors) are added to strong acceptors like chloranil (CHL) or di-chloro-di-cyano benzoquinone (DDQ) in chloroform or in dichloromethane. The formation of such complexes is manifested by the presence of a broad absorption maximum in the visible range of the spectrum where neither the donor nor the acceptor absorbs. The appearance of this visible band is due to CT interactions, which result in strong NLO responses. We have employed the semiempirical intermediate neglect of differential overlap (INDO∕S) Hamiltonian to calculate the energy levels of these CT complexes using single and double configuration interaction (SDCI). The solvent effects are taken into account by using the self-consistent reaction field (SCRF) scheme. The geometry of the complex is obtained by exploring different relative molecular geometries by rotating the acceptor with respect to the fixed donor about three different axes. The theoretical geometry that best fits the experimental energy gaps, ß(HRS) and macroscopic depolarization ratios is taken to be the most probable geometry of the complex. Our studies show that the most probable geometry of these complexes in solution is the parallel displaced structure with a significant twist in some cases.

Geometry and quadratic nonlinearity of charge transfer complexes in solution using depolarized hyper-Rayleigh scattering.

We report large quadratic nonlinearity in a series of 1:1 molecular complexes between methyl substituted benzene donors and quinone acceptors in solution. The first hyperpolarizability, ß(HRS), which is very small for the individual components, becomes large by intermolecular charge transfer (CT) interaction between the donor and the acceptor in the complex. In addition, we have investigated the geometry of these CT complexes in solution using polarization resolved hyper-Rayleigh scattering (HRS). Using linearly (electric field vector along X direction) and circularly polarized incident light, respectively, we have measured two macroscopic depolarization ratios D=I(2ω,X,X)/I(2ω,Z,X) and D(')=I(2ω,X,C)/I(2ω,Z,C) in the laboratory fixed XYZ frame by detecting the second harmonic scattered light in a polarization resolved fashion. The experimentally obtained first hyperpolarizability, ß(HRS), and the value of macroscopic depolarization ratios, D and D('), are then matched with the theoretically deduced values from single and double configuration interaction calculations performed using the Zerner's intermediate neglect of differential overlap self-consistent reaction field technique. In solution, since several geometries are possible, we have carried out calculations by rotating the acceptor moiety around three different axes keeping the donor molecule fixed at an optimized geometry. These rotations give us the theoretical ß(HRS), D and D(') values as a function of the geometry of the complex. The calculated ß(HRS), D, and D(') values that closely match with the experimental values, give the dominant equilibrium geometry in solution. All the CT complexes between methyl benzenes and chloranil or 1,2-dichloro-4,5-dicyano-p-benzoquinone investigated here are found to have a slipped parallel stacking of the donors and the acceptors. Furthermore, the geometries are staggered and in some pairs, a twist angle as high as 30° is observed. Thus, we have demonstrated in this paper that the polarization resolved HRS technique along with theoretical calculations can unravel the geometry of CT complexes in solution.

Enhanced ion anisotropy by nonconventional coordination geometry: single-chain magnet behavior for a [{Fe(II)L}2{Nb(IV)(CN)8}] helical chain compound designed with heptacoordinate Fe(II).

Nonconventional heptacoordination in combination with efficient magnetic exchange coupling is shown to yield a 1-D heteronuclear {Fe(II)Nb(IV)} compound with remarkable magnetic features when compared to other Fe(II)-based single chain magnets (SCM). Cyano-bridged heterometallic {3d-4d} and {3d-5d} chains are formed upon assembling Fe(II) bearing a pentadentate macrocycle as the blocking ligand with octacyano metallates, [M(CN)(8)](4-) (M = Nb(IV), Mo(IV), W(IV)). X-ray diffraction (single-crystal and powder) measurements reveal that the [{(H(2)O)Fe(L(1))}{M(CN)(8)}{Fe(L(1))}](infinity) architectures consist of isomorphous 1-D polymeric structures based on the alternation of {Fe(L(1))}(2+) and {M(CN)(8)}(4-) units (L(1) stands for the pentadentate macrocycle). Analysis of the magnetic susceptibility behavior revealed cyano-bridged {Fe-Nb} exchange interaction to be antiferromagnetic with J = -20 cm(-1) deduced from fitting an Ising model taking into account the noncollinear spin arrangement. For this ferrimagnetic chain a slow relaxation of its magnetization is observed at low temperature revealing a SCM behavior with Delta/k(B) = 74 K and tau(0) = 4.6 x 10(-11) s. The M versus H behavior exhibits a hysteresis loop with a coercive field of 4 kOe at 1 K and reveals at 380 mK magnetic avalanche processes, i.e., abrupt reversals in magnetization as H is varied. The origin of these characteristics is attributed to the combination of efficient {Fe-Nb} exchange interaction and significant anisotropy of the {Fe(L(1))} unit. High field EPR and magnetization experiments have revealed for the parent compound [Fe(L(1))(H(2)O)(2)]Cl(2) a negative zero field splitting parameter of D approximately = -17 cm(-1). The crystal structure, magnetic behavior, and Mossbauer data for [Fe(L(1))(H(2)O)(2)]Cl(2) are also reported.