A Hessian-Free Method to Prevent Zero-Point Energy Leakage in Classical Trajectories

The problem associated with the zero-point energy (ZPE) leak in classical trajectory calculations is well known. Since ZPE is a manifestation of the quantum uncertainty principle, there are no restrictions on energy during the classical propagation of nuclei. This phenomenon can lead to unphysical results, such as forming products without the ZPE in the internal vibrational degrees of freedom (DOFs). The ZPE leakage also permits reactions below the quantum threshold for the reaction. We have developed a new Hessian-free method, inspired by the Lowe-Andersen thermostat model, to prevent energy dipping below a threshold in the local-pair (LP) vibrational DOFs. The idea is to pump the leaked energy to the corresponding local vibrational mode taken from the other vibrational DOFs. We have applied the new correction protocol on the ab-initio ground-state molecular dynamics simulation of the water dimer (H2O)2, which dissociates due to unphysical ZPE spilling from high-frequency OH modes. The LP-ZPE method has been able to prevent the ZPE spilling of the OH stretching modes by pumping back the leaked energy into the corresponding modes, while this energy is taken from the other modes of the dimer itself, keeping the system as a microcanonical ensemble

pH-Sensitive Nanoaggregates for Site-Specific Drug-Delivery as Well as Cancer Cell Imaging

Multifunctional polymeric nanoaggregates could enable targeted cancer therapy and imaging, which eventually facilitate monitoring of the therapeutic effect. A fluorescent nanoaggregate is constructed for theranostic application. Chlorambucil (Chl), a fluorescent inactive chemotherapeutic agent, is covalently attached to the nanoaggregate for therapeutic action. The pyrene (Py) motif is also covalently attached to the nanoaggregates, with the motivation of cancer cell imaging. This nanoaggregate is further functionalized with biotin (Btn) for receptor-mediated drug delivery. The efficiency of this system is evaluated by in vitro cell studies to prove its receptor-mediated internalization as well as theranostic capabilities. This newly designed nanocarrier, Nor–Chl–Py–Btn (Nor, norbornene), has the ability to combine both therapeutic and diagnostic capabilities into a single polymer that offers existing prospects for the development of nanomedicine

pH-Sensitive Nanoaggregates for Site-Specific Drug-Delivery as Well as Cancer Cell Imaging

Multifunctional polymeric nanoaggregates could enable targeted cancer therapy and imaging, which eventually facilitate monitoring of the therapeutic effect. A fluorescent nanoaggregate is constructed for theranostic application. Chlorambucil (Chl), a fluorescent inactive chemotherapeutic agent, is covalently attached to the nanoaggregate for therapeutic action. The pyrene (Py) motif is also covalently attached to the nanoaggregates, with the motivation of cancer cell imaging. This nanoaggregate is further functionalized with biotin (Btn) for receptor-mediated drug delivery. The efficiency of this system is evaluated by in vitro cell studies to prove its receptor-mediated internalization as well as theranostic capabilities. This newly designed nanocarrier, Nor–Chl–Py–Btn (Nor, norbornene), has the ability to combine both therapeutic and diagnostic capabilities into a single polymer that offers existing prospects for the development of nanomedicine

pH-Sensitive Nanoaggregates for Site-Specific Drug-Delivery as Well as Cancer Cell Imaging

Multifunctional polymeric nanoaggregates could enable targeted cancer therapy and imaging, which eventually facilitate monitoring of the therapeutic effect. A fluorescent nanoaggregate is constructed for theranostic application. Chlorambucil (Chl), a fluorescent inactive chemotherapeutic agent, is covalently attached to the nanoaggregate for therapeutic action. The pyrene (Py) motif is also covalently attached to the nanoaggregates, with the motivation of cancer cell imaging. This nanoaggregate is further functionalized with biotin (Btn) for receptor-mediated drug delivery. The efficiency of this system is evaluated by in vitro cell studies to prove its receptor-mediated internalization as well as theranostic capabilities. This newly designed nanocarrier, Nor–Chl–Py–Btn (Nor, norbornene), has the ability to combine both therapeutic and diagnostic capabilities into a single polymer that offers existing prospects for the development of nanomedicine

pH-Sensitive Nanoaggregates for Site-Specific Drug-Delivery as Well as Cancer Cell Imaging

Multifunctional polymeric nanoaggregates could enable targeted cancer therapy and imaging, which eventually facilitate monitoring of the therapeutic effect. A fluorescent nanoaggregate is constructed for theranostic application. Chlorambucil (Chl), a fluorescent inactive chemotherapeutic agent, is covalently attached to the nanoaggregate for therapeutic action. The pyrene (Py) motif is also covalently attached to the nanoaggregates, with the motivation of cancer cell imaging. This nanoaggregate is further functionalized with biotin (Btn) for receptor-mediated drug delivery. The efficiency of this system is evaluated by in vitro cell studies to prove its receptor-mediated internalization as well as theranostic capabilities. This newly designed nanocarrier, Nor–Chl–Py–Btn (Nor, norbornene), has the ability to combine both therapeutic and diagnostic capabilities into a single polymer that offers existing prospects for the development of nanomedicine

ADT: A Generalized Algorithm and Program for Beyond Born–Oppenheimer Equations of “<i>N</i>” Dimensional Sub-Hilbert Space

The major bottleneck of first principle based beyond Born–Oppenheimer (BBO) treatment originates from large number and complicated expressions of adiabatic to diabatic transformation (ADT) equations for higher dimensional sub-Hilbert spaces. In order to overcome such shortcoming, we develop a generalized algorithm, “ADT” to generate the nonadiabatic equations through symbolic manipulation and to construct highly accurate diabatic surfaces for molecular processes involving excited electronic states. It is noteworthy to mention that the nonadiabatic coupling terms (NACTs) often become singular (removable) at degenerate point(s) or along a seam in the nuclear configuration space (CS) and thereby, a unitary transformation is required to convert the kinetically coupled (adiabatic) Hamiltonian to a potentially (diabatic) one to avoid such singularity­(ies). The “ADT” program can be efficiently used to (a) formulate analytic functional forms of differential equations for ADT angles and diabatic potential energy matrix and (b) solve the set of coupled differential equations numerically to evaluate ADT angles, residue due to singularity­(ies), ADT matrices, and finally, diabatic potential energy surfaces (PESs). For the numerical case, user can directly provide ab initio data (adiabatic PESs and NACTs) as input files to this software or can generate those input files through in-built python codes interfacing MOLPRO followed by ADT calculation. In order to establish the workability of our program package, we selectively choose six realistic molecular species, namely, NO2 radical, H3+, F + H2, NO3 radical, C6H6+ radical cation, and 1,3,5-C6H3F3+ radical cation, where two, three, five and six electronic states exhibit profound nonadiabatic interactions and are employed to compute diabatic PESs by using ab initio calculated adiabatic PESs and NACTs. The “ADT” package released under the GNU General Public License v3.0 (GPLv3) is available at https://github.com/AdhikariLAB/ADT-Program and also as the Supporting Information of this article

Construction of Diabatic Hamiltonian Matrix from ab Initio Calculated Molecular Symmetry Adapted Nonadiabatic Coupling Terms and Nuclear Dynamics for the Excited States of Na₃ Cluster

We present the molecular symmetry (MS) adapted treatment of nonadiabatic coupling terms (NACTs) for the excited electronic states (2²E′ and 1²A₁^′) of Na₃ cluster, where the adiabatic potential energy surfaces (PESs) and the NACTs are calculated at the MRCI level by using an ab initio quantum chemistry package (MOLPRO). The signs of the NACTs at each point of the configuration space (CS) are determined by employing appropriate irreducible representations (IREPs) arising due to MS group, and such terms are incorporated into the adiabatic to diabatic transformation (ADT) equations to obtain the ADT angles. Since those sign corrected NACTs and the corresponding ADT angles demonstrate the validity of curl condition for the existence of three-state (2²E′ and 1²A₁^′) sub-Hilbert space, it becomes possible to construct the continuous, single-valued, symmetric, and smooth 3 × 3 diabatic Hamiltonian matrix. Finally, nuclear dynamics has been carried out on such diabatic surfaces to explore whether our MS-based treatment of diabatization can reproduce the pattern of the experimental spectrum for system <b>B</b> of Na₃ cluster

ADT: A Generalized Algorithm and Program for Beyond Born–Oppenheimer Equations of “<i>N</i>” Dimensional Sub-Hilbert Space

The major bottleneck of first principle based beyond Born–Oppenheimer (BBO) treatment originates from large number and complicated expressions of adiabatic to diabatic transformation (ADT) equations for higher dimensional sub-Hilbert spaces. In order to overcome such shortcoming, we develop a generalized algorithm, “ADT” to generate the nonadiabatic equations through symbolic manipulation and to construct highly accurate diabatic surfaces for molecular processes involving excited electronic states. It is noteworthy to mention that the nonadiabatic coupling terms (NACTs) often become singular (removable) at degenerate point(s) or along a seam in the nuclear configuration space (CS) and thereby, a unitary transformation is required to convert the kinetically coupled (adiabatic) Hamiltonian to a potentially (diabatic) one to avoid such singularity­(ies). The “ADT” program can be efficiently used to (a) formulate analytic functional forms of differential equations for ADT angles and diabatic potential energy matrix and (b) solve the set of coupled differential equations numerically to evaluate ADT angles, residue due to singularity­(ies), ADT matrices, and finally, diabatic potential energy surfaces (PESs). For the numerical case, user can directly provide ab initio data (adiabatic PESs and NACTs) as input files to this software or can generate those input files through in-built python codes interfacing MOLPRO followed by ADT calculation. In order to establish the workability of our program package, we selectively choose six realistic molecular species, namely, NO2 radical, H3+, F + H2, NO3 radical, C6H6+ radical cation, and 1,3,5-C6H3F3+ radical cation, where two, three, five and six electronic states exhibit profound nonadiabatic interactions and are employed to compute diabatic PESs by using ab initio calculated adiabatic PESs and NACTs. The “ADT” package released under the GNU General Public License v3.0 (GPLv3) is available at https://github.com/AdhikariLAB/ADT-Program and also as the Supporting Information of this article

Recommendations for Velocity Adjustment in Surface Hopping

This study investigates velocity adjustment directions after hopping in surface hopping dynamics. Using fulvene and a protonated Schiff base (PSB4) as case studies, we investigate the population decay and reaction yields of different sets of dynamics with the velocity adjusted in either the nonadiabatic coupling, gradient difference, or momentum directions. For the latter, in addition to the conventional algorithm, we investigated the performance of a reduced kinetic energy reservoir approach recently proposed. Our evaluation also considered velocity adjustment in the directions of approximate nonadiabatic coupling vectors. While results for fulvene are susceptible to the adjustment approach, PSB4 is not. We correlated this dependence to the topography near the conical intersections. When nonadiabatic coupling vectors are unavailable, the gradient difference direction is the best adjustment option. If the gradient difference is also unavailable, a semiempirical vector direction or the momentum direction with a reduced kinetic energy reservoir becomes an excellent option to prevent an artificial excess of back hoppings. The precise velocity adjustment direction is less crucial for describing the nonadiabatic dynamics than the kinetic energy reservoir’s size

Site-Specific Amphiphilic Magnetic Copolymer Nanoaggregates for Dual Imaging

Molecular imaging along with combinations of imaging modalities can provide a thorough understanding of disease, in particular, tumors. Magnetic resonance imaging (MRI) offers exceptional tissue contrast and resolution; whereas optical imaging provides high sensitivity. Hence a norbornene based copolymer (<b>Nor-Cob-Py-Fol</b>) is reported in this paper as a dual-imaging agent. <b>Nor-Cob-Py-Fol</b> having Co²⁺ complex, pyrene and poly­(ethylene glycol) derived folate, have been synthesized using ring-opening metathesis polymerization (<b>ROMP</b>). All the monomers and polymers are characterized by ¹H NMR, IR, GPC, and TGA techniques. The morphology of the copolymer nanoaggregates has been evaluated with DLS, TEM, and SEM techniques. The functionalization of Co²⁺ to the polymer is monitored by FTIR, ¹H NMR, and ¹³C NMR spectroscopy. Furthermore, the presence of Co²⁺ in the nanoaggregates is confirmed by the EDX (SEM) technique. To prove the MRI capabilities nature of copolymer nanoaggregates, NMR experiment is performed at room temperature. Cell viability studies suggest the biocompatibility nature of the copolymer. Flow cytometry as well as epifluoroscence microscope experiments clearly demonstrate the dual-imaging ability of the newly designed copolymer. The much higher relaxivity ratio (<i>r</i>₂/<i>r</i>₁) of the present method clearly establishes the superiority of our system as one of the best contrast agents known to the practitioners of magnetic resonance imaging