Bond order quantifies the number of electrons dressed-exchanged between two atoms in a material and is important for understanding many chemical properties. Diatomic molecules are the smallest molecules possessing chemical bonds and play key roles in atmospheric chemistry, biochemistry, lab chemistry, and chemical manufacturing. Here we quantum-mechanically calculate bond orders for 288 diatomic molecules and ions. For homodiatomics, we show bond orders correlate to bond energies for elements within the same chemical group. We quantify and discuss how semicore electrons weaken bond orders for elements having diffuse semicore electrons. Lots of chemistry is effected by this. We introduce a first-principles method to represent orbital-independent bond order as a sum of orbital-dependent bond order components. This bond order component analysis (BOCA) applies to any spin-orbitals that are unitary transformations of the natural spin-orbitals, with or without periodic boundary conditions, and to non-magnetic and (collinear or non-collinear) magnetic materials. We use this BOCA to study all period 2 homodiatomics plus Mo 2 , Cr 2 , ClO, ClO − , and Mo 2 (acetate) 4 . Using Manz's bond order equation with DDEC6 partitioning, the Mo–Mo bond order was 4.12 in Mo 2 and 1.46 in Mo 2 (acetate) 4 with a sum of bond orders for each Mo atom of ∼4. Our study informs both chemistry research and education. As a learning aid, we introduce an analogy between bond orders in materials and message transmission in computer networks. We also introduce the first working quantitative heuristic model for all period 2 homodiatomic bond orders. This heuristic model incorporates s–p mixing to give heuristic bond orders of ¾ (Be 2 ), 1¾ (B 2 ), 2¾ (C 2 ), and whole number bond orders for the remaining period 2 homodiatomics.
more »
« less
Introducing DDEC6 atomic population analysis: part 4. Efficient parallel computation of net atomic charges, atomic spin moments, bond orders, and more
The DDEC6 method is one of the most accurate and broadly applicable atomic population analysis methods. It works for a broad range of periodic and non-periodic materials with no magnetism, collinear magnetism, and non-collinear magnetism irrespective of the basis set type. First, we show DDEC6 charge partitioning to assign net atomic charges corresponds to solving a series of 14 Lagrangians in order. Then, we provide flow diagrams for overall DDEC6 analysis, spin partitioning, and bond order calculations. We wrote an OpenMP parallelized Fortran code to provide efficient computations. We show that by storing large arrays as shared variables in cache line friendly order, memory requirements are independent of the number of parallel computing cores and false sharing is minimized. We show that both total memory required and the computational time scale linearly with increasing numbers of atoms in the unit cell. Using the presently chosen uniform grids, computational times of ∼9 to 94 seconds per atom were required to perform DDEC6 analysis on a single computing core in an Intel Xeon E5 multi-processor unit. Parallelization efficiencies were usually >50% for computations performed on 2 to 16 cores of a cache coherent node. As examples we study a B-DNA decamer, nickel metal, supercells of hexagonal ice crystals, six X@C 60 endohedral fullerene complexes, a water dimer, a Mn 12 -acetate single molecule magnet exhibiting collinear magnetism, a Fe 4 O 12 N 4 C 40 H 52 single molecule magnet exhibiting non-collinear magnetism, and several spin states of an ozone molecule. Efficient parallel computation was achieved for systems containing as few as one and as many as >8000 atoms in a unit cell. We varied many calculation factors ( e.g. , grid spacing, code design, thread arrangement, etc. ) and report their effects on calculation speed and precision. We make recommendations for excellent performance.
more »
« less
- Award ID(s):
- 1555376
- NSF-PAR ID:
- 10055288
- Date Published:
- Journal Name:
- RSC Advances
- Volume:
- 8
- Issue:
- 5
- ISSN:
- 2046-2069
- Page Range / eLocation ID:
- 2678 to 2707
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Developing a comprehensive method to compute bond orders is a problem that has eluded chemists since Lewis's pioneering work on chemical bonding a century ago. Here, a computationally efficient method solving this problem is introduced and demonstrated for diverse materials including elements from each chemical group and period. The method is applied to non-magnetic, collinear magnetic, and non-collinear magnetic materials with localized or delocalized bonding electrons. Examples studied include the stretched O 2 molecule, 26 diatomic molecules, 3d and 5d transition metal solids, periodic materials with 1 to 8748 atoms per unit cell, a biomolecule, a hypercoordinate molecule, an electron deficient molecule, hydrogen bound systems, transition states, Lewis acid–base complexes, aromatic compounds, magnetic systems, ionic materials, dispersion bound systems, nanostructures, and other materials. From near-zero to high-order bonds were studied. Both the bond orders and the sum of bond orders for each atom are accurate across various bonding types: metallic, covalent, polar-covalent, ionic, aromatic, dative, hypercoordinate, electron deficient multi-centered, agostic, and hydrogen bonding. The method yields similar results for correlated wavefunction and density functional theory inputs and for different S Z values of a spin multiplet. The method requires only the electron and spin magnetization density distributions as input and has a computational cost scaling linearly with increasing number of atoms in the unit cell. No prior approach is as general. The method does not apply to electrides, highly time-dependent states, some extremely high-energy excited states, and nuclear reactions.more » « less
-
We present a new implementation for computing spin–orbit couplings (SOCs) within a time-dependent density-functional theory (TD-DFT) framework in the standard spin-conserving formulation as well in the spin–flip variant (SF-TD-DFT). This approach employs the Breit–Pauli Hamiltonian and Wigner–Eckart’s theorem applied to the reduced one-particle transition density matrices, together with the spin–orbit mean-field treatment of the two-electron contributions. We use a state-interaction procedure and compute the SOC matrix elements using zero-order non-relativistic states. Benchmark calculations using several closed-shell organic molecules, diradicals, and a single-molecule magnet illustrate the efficiency of the SOC protocol. The results for organic molecules (described by standard TD-DFT) show that SOCs are insensitive to the choice of the functional or basis sets, as long as the states of the same characters are compared. In contrast, the SF-TD-DFT results for small diradicals (CH 2 , [Formula: see text], SiH 2 , and [Formula: see text]) show strong functional dependence. The spin-reversal energy barrier in a Fe(III) single-molecule magnet computed using non-collinear SF-TD-DFT (PBE0, ωPBEh/cc-pVDZ) agrees well with the experimental estimate.more » « less
-
The discovery of singular organic radical ligands is a formidable challenge due to high reactivity arising from the unpaired electron. Matching radical ligands with metal ions to engender magnetic coupling is crucial for eliciting preeminent physical properties such as conductivity and magnetism that are crucial for future technologies. The metal-radical approach is especially important for the lanthanide ions exhibiting deeply buried 4f-orbitals. The radicals must possess a high spin density on the donor atoms to promote strong coupling. Combining diamagnetic 89 Y ( I = 1/2) with organic radicals allows for invaluable insight into the electronic structure and spin-density distribution. This approach is hitherto underutilized, possibly owing to the challenging synthesis and purification of such molecules. Herein, evidence of an unprecedented bisbenzimidazole radical anion (Bbim 3− ˙) along with its metalation in the form of an yttrium complex, [K(crypt-222)][(Cp* 2 Y) 2 (μ-Bbim˙)] is provided. Access of Bbim 3− ˙ was feasible through double-coordination to the Lewis acidic metal ion and subsequent one-electron reduction, which is remarkable as Bbim 2− was explicitly stated to be redox-inactive in closed-shell complexes. Two molecules containing Bbim 2− (1) and Bbim 3− ˙ (2), respectively, were thoroughly investigated by X-ray crystallography, NMR and UV/Vis spectroscopy. Electrochemical studies unfolded a quasi-reversible feature and emphasize the role of the metal centre for the Bbim redox-activity as neither the free ligand nor the Bbim 2− complex led to analogous CV results. Excitingly, a strong delocalization of the electron density through the Bbim 3− ˙ ligand was revealed via temperature-dependent EPR spectroscopy and confirmed through DFT calculations and magnetometry, rendering Bbim 3− ˙ an ideal candidate for single-molecule magnet design.more » « less
-
more » « less
This data set for the manuscript entitled "Design of Peptides that Fold and Self-Assemble on Graphite" includes all files needed to run and analyze the simulations described in the this manuscript in the molecular dynamics software NAMD, as well as the output of the simulations. The files are organized into directories corresponding to the figures of the main text and supporting information. They include molecular model structure files (NAMD psf or Amber prmtop format), force field parameter files (in CHARMM format), initial atomic coordinates (pdb format), NAMD configuration files, Colvars configuration files, NAMD log files, and NAMD output including restart files (in binary NAMD format) and trajectories in dcd format (downsampled to 10 ns per frame). Analysis is controlled by shell scripts (Bash-compatible) that call VMD Tcl scripts or python scripts. These scripts and their output are also included.
Version: 2.0
Changes versus version 1.0 are the addition of the free energy of folding, adsorption, and pairing calculations (Sim_Figure-7) and shifting of the figure numbers to accommodate this addition.
Conventions Used in These Files
===============================Structure Files
----------------
- graph_*.psf or sol_*.psf (original NAMD (XPLOR?) format psf file including atom details (type, charge, mass), as well as definitions of bonds, angles, dihedrals, and impropers for each dipeptide.)- graph_*.pdb or sol_*.pdb (initial coordinates before equilibration)
- repart_*.psf (same as the above psf files, but the masses of non-water hydrogen atoms have been repartitioned by VMD script repartitionMass.tcl)
- freeTop_*.pdb (same as the above pdb files, but the carbons of the lower graphene layer have been placed at a single z value and marked for restraints in NAMD)
- amber_*.prmtop (combined topology and parameter files for Amber force field simulations)
- repart_amber_*.prmtop (same as the above prmtop files, but the masses of non-water hydrogen atoms have been repartitioned by ParmEd)Force Field Parameters
----------------------
CHARMM format parameter files:
- par_all36m_prot.prm (CHARMM36m FF for proteins)
- par_all36_cgenff_no_nbfix.prm (CGenFF v4.4 for graphene) The NBFIX parameters are commented out since they are only needed for aromatic halogens and we use only the CG2R61 type for graphene.
- toppar_water_ions_prot_cgenff.str (CHARMM water and ions with NBFIX parameters needed for protein and CGenFF included and others commented out)Template NAMD Configuration Files
---------------------------------
These contain the most commonly used simulation parameters. They are called by the other NAMD configuration files (which are in the namd/ subdirectory):
- template_min.namd (minimization)
- template_eq.namd (NPT equilibration with lower graphene fixed)
- template_abf.namd (for adaptive biasing force)Minimization
-------------
- namd/min_*.0.namdEquilibration
-------------
- namd/eq_*.0.namdAdaptive biasing force calculations
-----------------------------------
- namd/eabfZRest7_graph_chp1404.0.namd
- namd/eabfZRest7_graph_chp1404.1.namd (continuation of eabfZRest7_graph_chp1404.0.namd)Log Files
---------
For each NAMD configuration file given in the last two sections, there is a log file with the same prefix, which gives the text output of NAMD. For instance, the output of namd/eabfZRest7_graph_chp1404.0.namd is eabfZRest7_graph_chp1404.0.log.Simulation Output
-----------------
The simulation output files (which match the names of the NAMD configuration files) are in the output/ directory. Files with the extensions .coor, .vel, and .xsc are coordinates in NAMD binary format, velocities in NAMD binary format, and extended system information (including cell size) in text format. Files with the extension .dcd give the trajectory of the atomic coorinates over time (and also include system cell information). Due to storage limitations, large DCD files have been omitted or replaced with new DCD files having the prefix stride50_ including only every 50 frames. The time between frames in these files is 50 * 50000 steps/frame * 4 fs/step = 10 ns. The system cell trajectory is also included for the NPT runs are output/eq_*.xst.Scripts
-------
Files with the .sh extension can be found throughout. These usually provide the highest level control for submission of simulations and analysis. Look to these as a guide to what is happening. If there are scripts with step1_*.sh and step2_*.sh, they are intended to be run in order, with step1_*.sh first.
CONTENTS
========The directory contents are as follows. The directories Sim_Figure-1 and Sim_Figure-8 include README.txt files that describe the files and naming conventions used throughout this data set.
Sim_Figure-1: Simulations of N-acetylated C-amidated amino acids (Ac-X-NHMe) at the graphite–water interface.
Sim_Figure-2: Simulations of different peptide designs (including acyclic, disulfide cyclized, and N-to-C cyclized) at the graphite–water interface.
Sim_Figure-3: MM-GBSA calculations of different peptide sequences for a folded conformation and 5 misfolded/unfolded conformations.
Sim_Figure-4: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 370 K.
Sim_Figure-5: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 295 K.
Sim_Figure-5_replica: Temperature replica exchange molecular dynamics simulations for the peptide cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) with 20 replicas for temperatures from 295 to 454 K.
Sim_Figure-6: Simulation of the peptide molecule cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) in free solution (no graphite).
Sim_Figure-7: Free energy calculations for folding, adsorption, and pairing for the peptide CHP1404 (sequence: cyc(GTGSGTG-GPGG-GCGTGTG-SGPG)). For folding, we calculate the PMF as function of RMSD by replica-exchange umbrella sampling (in the subdirectory Folding_CHP1404_Graphene/). We make the same calculation in solution, which required 3 seperate replica-exchange umbrella sampling calculations (in the subdirectory Folding_CHP1404_Solution/). Both PMF of RMSD calculations for the scrambled peptide are in Folding_scram1404/. For adsorption, calculation of the PMF for the orientational restraints and the calculation of the PMF along z (the distance between the graphene sheet and the center of mass of the peptide) are in Adsorption_CHP1404/ and Adsorption_scram1404/. The actual calculation of the free energy is done by a shell script ("doRestraintEnergyError.sh") in the 1_free_energy/ subsubdirectory. Processing of the PMFs must be done first in the 0_pmf/ subsubdirectory. Finally, files for free energy calculations of pair formation for CHP1404 are found in the Pair/ subdirectory.
Sim_Figure-8: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) where the peptides are far above the graphene–water interface in the initial configuration.
Sim_Figure-9: Two replicates of a simulation of nine peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 370 K.
Sim_Figure-9_scrambled: Two replicates of a simulation of nine peptide molecules with the control sequence cyc(GGTPTTGGGGGGSGGPSGTGGC) at the graphite–water interface at 370 K.
Sim_Figure-10: Adaptive biasing for calculation of the free energy of the folded peptide as a function of the angle between its long axis and the zigzag directions of the underlying graphene sheet.
This material is based upon work supported by the US National Science Foundation under grant no. DMR-1945589. A majority of the computing for this project was performed on the Beocat Research Cluster at Kansas State University, which is funded in part by NSF grants CHE-1726332, CNS-1006860, EPS-1006860, and EPS-0919443. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562, through allocation BIO200030.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/c7ra11829e
