CONTROLLED BY QUANTUM COMPUTING LOGIC GATES

Transcription

1 Quantum QUANTUM Mechanical MECHANICAL Modeling of Self-Reproducible MODELING OF Living SELF-REPRODUCIBLE PNA Chip Immersed in the LIVING Lipid PNA Bilayer CHIP Vesicle IMMERSED Controlled IN by Quantum THE LIPID Computing BILAYER Logic VESICLE Gates CONTROLLED BY QUANTUM COMPUTING LOGIC GATES Arvydas Tamulis, Vykintas Tamulis, Jelena Tamuliene Institute of Theoretical Physics and Technology of Vilnius University A. Gostauto 12, Vilnius 2600, Lithuania; 1. Theoretical methods and original software In order to better understand the origin of life and the production of artificial living organisms and programmable nano-biorobots we used ab initio quantum mechanical (QM) Hartree-Fock (HF), density functional theory (DFT), QM semiempirical PM3 [1, 2} and molecular dynamics (MD) NAMD, GROMACS and CHARMM simulations [3-5] to investigate various bioorganic systems of artificial minimal living organisms based on peptide nucleic acid (PNA), photo-sensitizer, lipid precursor and SH anion molecules [6]. Quantum modeling of nano-structures self-assembly in PNA based minimal living organisms were performed using our developed software for building PNA double helix [7] and additionally our implemented code in quantum chemical program packages for the calculations of extended DFT [8-10] for accurate descriptions of hydrogen bonding and Van der Waals interactions. Our originally developed codes for electron charge and spin density tunneling calculations and visualization in electronic and magnetic excited states we used for quantum mechanical search of new light harvesting sensitizers in artificial living organisms and for quantum modeling of molecular electronics and spintronics logical elements in PNA based minimal living organisms [11, 12]. 2. Research stages of quantum mechanical modeling of self-reproducible and logically controlled living PNA chip Quantum mechanical modelings of self-reproducible and logically controlled living PNA chips were divided into five research stages: 1) Elementary acts of PNA chip computing are self assembling of supramolecules adenine::thymine and guanine::thymine. Systematic exact QM investigations of self-assembly energy of formation for supramolecules adenine::thymine and guanine::thymine were performed using ab initio HF and non local gradient and extended DFT models including electron correlations: B3PW91, B3LYP, PBELYP, PBEPBE [1, 2], X3LYP [9] in addition with base set superposition error methodology [10]. The best result for G-C pair energy of formation was obtained using X3LYP model using diffusion and polarization basis sets is equal to 61 kcal/mol [13]. 2) Self-formation of large fragments of PNA suitable for construction of PNA chips possessing the protogene information was done by Vykintas Tamulis developed software for building PNA double helix [13]. 3) Self-assembly of fragment of PNA chip: twelve nucleobases PNA double helix -tree 1,4- bis(n,n-dimethylamino)naphthalene sensitizers and lipid precursor molecules surrounding by

2 water molecules immersed in lipid molecules bilayer was modeled by QM HF, DFT, PM3 methods and MD NAMD, GROMACS and CHARMM simulations (see figure bellow) [14]. Water molecules in this image are omitted for the better seeing all details. The lipid bilayer vesicles surrounding the PNA chip possessing artificial photo-synthetic system including 1,4-bis(N,N-dimethylamino)naphthalene sensitizer and lipid precursor molecules were modeled by DFT, PM3 and molecular dynamics NAMD and GROMACS methods. Vesicle composed from around atoms was built starting from exact quantum mechanical studies of separate molecules, later were performed DFT investigations of self-assembling to nucleobases dimers and photosynthetic supramolecules and finally was done molecular dynamics processing of self-formation of entire artificial minimal living vesicle [13]. 4) Quantum mechanical processes of self-reproduction of PNA chip possessing artificial photosynthetic system were systematically investigated using time dependent (TD) DFT method. Absorption spectra and relative positions of the HOMO and LUMO eigenvalues of lipid precursor and sensitizers: 1,4-bis(N,N-dimethylamino)naphthalene, 1,4- dihydroquinoxaline and 7,8-dimethylisoalloxazine molecules show that our new investigated sensitizers 1,4-dihydroquinoxaline and 7,8-dimethylisoalloxazine molecules are good for usage them in the PNA chips because their HOMO are enough high relatively LUMO of lipid precursor molecule and absorption spectra are in the visible region [15]. It was calculated and visualized electron tunneling in our optimized self-assembled supramolecule: cytosinepna fragment-sensitizer 1,4-bis(N,N-dimethylamino)naphthalene and lipid precursor molecules using TD DFT method. HOMO-LUMO (first excited state) transition is equal to nm wavelength in absorption spectrum of this supramolecule. HOMO-LUMO transition leads with electron tunneling from sensitizer molecule to lipid precursor molecule. The same electron tunneling is in the third excited state [13]. The applying of extended TD DFT for

3 accurate descriptions of hydrogen bonding and Van der Waals interactions, the usage of diffusion basis set and surrounding this self-assembled supramolecule by water molecules gives the HOMO-LUMO (first excited state) transition equal to nm [13]. 5) We have also explored the possibility of using programmable PNA chip possessing photosynthetic systems in molecular electronics and spintronics installing classical Boolean and quantum logics gates and logically controlled molecular machines. For this were done detailed quantum mechanical investigations of electronic and spintronic structure and NMR spectra of biliverdin Cu, Co, Zn dimers and ESR spectra of endohedral fullerene ErSc 80 and neutral radical molecules: beta-diketone and dodecyl syringate [16]. It was suggested recently that self-assembling systems could be used to create a macroscopic ensemble of quantum entangled 3-spin groups, as a first step in quantum information processing. The spins of such a group could be connected by dipole-dipole interaction. Application of a nonuniform external magnetic field would allow selective excitation of every spin inside the group. The proper sequence of resonant electromagnetic pulses would drive all spin groups into the 3-spin entangled state. In the suggested proposal the spins were associated with a single unpaired electron spin of a neutral radical molecule in the self-assembled systems. One of the key elements of this strategy is the proper choice of molecules for experimental implementation of the proposal. Involved in this choice are four criteria for the chemical structure of these molecules: 1) A specific group or structural elements to provide self-organization characteristics; 2) A specific group to provide an attachment of the molecule to a substrate in SAM; 3) An unpaired, spatially localized electronic spin representing an elementary qubit; 4) Strong non-compensated valence bonds, which are responsible for the unpaired electron spin, to provide the chemical stability of a qubit. Modern quantum chemical methods provide powerful tools for theoretical modeling and analysis of molecular electronic structure and may be used to guide the synthetic effort. In particular, the small carbon-centered π-radical molecules (8-14 atoms) possessing a β- diketone structure have been investigated in the scope of unrestricted Hartree-Fock (UHF) and unrestricted density functional theory (UDFT) methods. It was shown that an unpaired, spatially localized electronic spin representing an elementary qubit and strong noncompensated valence bonds, which are responsible for the unpaired electron spin, to provide the chemical stability of a quantum bit (qubit). Electronic g-tensor shift along the long axis of our investigated β-diketone neutral radical molecule is close to free-electron g-factor and therefore entirely determined by first order contributions to electronic g-tensor shift, i.e. can be influenced only slightly by environment due to the fact that first order contributions to g- tensor shift solely determined by spin density distribution in radical. Rotation of the radical around the long axis will not change g-factor of molecule along the long axis as well due to the orientation of it g-tensor principal axes. The neutral dodecyl syringate radical molecule is suggested as a candidate for molecular ESR quantum computers. First principles quantum chemical calculations indicates that this molecule with a stable delocalized electron spin may represent a qubit in quantum information processing. The spin density analysis exhibits that unpaired spin of radical molecule is delocalized in the region of entire hexagonal ring where the non-compensated

4 valence bond is delocalized. The spin density shifts are investigated in five electronic excited states using configuration interaction (CI) unrestricted Hartree-Fock (UHF) time dependent (TD) method with EPR-II basis. The spin density shifts are more essential in first, fourth and fifth excited states that might be used for designing of controlling gates in quantum information processing. It was found that exist internal local spin density flips in the first and fifth electronic excited states. Isotropic Fermi contact couplings constants and anisotropic spin dipole couplings were investigated and indicated the largest hyperfine splittings (HFS) of electron spin resonance (ESR) spectra on atoms of above mentioned region of delocalized not-compensated valence bonds. The investigated qubits in biliverdin dimers, endohedral fullerene and neutral radical molecule allowed us to design and implement a set of molecular electronics AND, OR, XOR, ControlNOT logically controlled molecular machines to the PNA in order to control processes of self-replication and photosynthesis in the artificial living organisms. References 1. M. J. Frisch, et al, Gaussian 03, RevC.01, Gaussian, Inc., Pittsburgh PA, GAMESS US license agreement: M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Kosecki, N. Matsunaga, K.A. Nguyen, S.J.Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comput. Chem. 14, ( S. Rasmussen, L. Chen, M. Nilsson, and S. Abe; Artificial Life, vol 9, , 2003). 7. Vykintas Tamulis developed software for building PNA double helix. 8. Perdew, J. P., Burke, K. & Ernzerhof, M. (1996) Phys. Rev. Lett. 77, Xin Xu, William A. Goddard III, "The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and termochemical properties", PNAS, March 2, 2004, vol. 101, no. 9, A. Bende, A. Vibok, J. Halasz, S. Suhai, BSSE-Free Description of the Formamide Dimers, International J. Quantum Chemistry, vol. 84, (2001). 11. A. Tamulis, J. Tamuliene, V. Tamulis, "Quantum Mechanical Design of Photoactive Molecular Machines and Logical Devices", 11th chapter in "Handbook of Photochemistry and Photobiology", Vol. 3 "Supramolecular Photochemistry", Ed. H.S. Nalwa, American Scientific Publishers, p.p , J. Tamuliene, A. Tamulis, J. Kulys, Electronic Structure of Dodecyl Syringate Radical Suitable for ESR Molecular Quantum Computers", Nonlinear Analysis: Modelling and Control, Vol. 9, No. 2, 2004, p Arvydas Tamulis, Vykintas Tamulis, Andrzej Graja, Quantum mechanical modelling of photosynthetic system self-assembly in PNA based artificial living organisms, article prepared for publication to the Journal of Structural Chemistry, March Arvydas Tamulis, Vykintas Tamulis, Steen Rasmussen, Quantum Molecular Dynamics Self- Assembly of PNA Artificial Photosynthetic System on Lipid Bilayer, paper completing for

5 publication. 15. J. Tamuliene, A. Tamulis, Quantum Mechanical Investigations of 1,4-dihidrochinoksaline and 7,8-dimetilizoaloksazine for sensibilization of self-assembled system consist of PNA and Lipid Molecules, article submitted to the Journal of Structural Chemistry, November Arvydas Tamulis, Jelena Tamuliene, Vykintas Tamulis, Quantum Mechanical Investigations of Electronic Structure, Spectra, Electron Charge and Spin Density Transfer and Magnetically Features of Syringate Radical Molecule Based Logical Gates of ESR Molecular Quantum Computers, article prepared for publication in the Journal of Structural Chemistry, March 2005.