Correction of residual errors in configuration interaction electronic structure calculations.

Methods for correcting residual energy errors of configuration interaction (CI) calculations of molecules and other electronic systems are discussed based on the assumption that the energy defect can be mapped onto atomic regions. The methods do not consider the detailed nature of excitations but instead define a defect energy per electron that is unique to a specific atom. Defect energy contributions are determined from calculations on diatomic and hydride molecules and then applied to other systems. Calculated energies are compared with experimental thermodynamic and spectroscopic data for a set of 41 mainly organic molecules representing a wide range of bonding environments. The most stringent test is based on a severely truncated virtual space in which higher spherical harmonic basis functions are removed. The errors of the initial CI calculations are large, but in each case, including defect corrections brings calculated CI energies into agreement with experimental values. The method is also applied to a NIST compilation of coupled cluster calculations that employ a larger basis set and no truncation of the virtual space. The corrections show excellent consistency with total energies in very good agreement with experimental values. An extension of the method is applied to dmsn states of Sc, Ti, V, Mn, Cr, Fe, Co, Ni, and Cu, significantly improving the agreement of calculated transition energies with spectroscopic values.

Understanding the electrospray ionization response factors of per- and poly-fluoroalkyl substances (PFAS).

Per- and polyfluoroalkyl substances (PFAS) are used extensively in commercial products. Their unusual solubility properties make them an ideal class of compounds for various applications. However, these same properties have led to significant contamination and bioaccumulation given their persistence in the environment. Development of analytical techniques to detect and quantify these compounds must take into account the potential for these properties to perturb these measurements, specifically the potential to bias the electrospray ionization (ESI) process. Direct injection ESI analysis of 23 different PFAS species revealed that hydrophobicity and PFAS class can predict the ESI overall response factors. In this study, a method for predicting the behavior of individual PFAS compounds, including relative retention order in chromatography, is presented which is simply based on the number of fluorine atoms in the molecule as well as the class of the compound (e.g., perfluroalkylcarboxylic acids) vs. computational estimations (e.g., non-polar surface area and logP).

Estimates of electron correlation based on density expansions.

Two methods for estimating the correlation energy of molecules and other electronic systems are discussed based on the assumption that the correlation energy can be partitioned between atomic regions. In the first method, the electron density is expanded in terms of atomic contributions using rigorous electron repulsion bounds, and in the second method, correlation contributions are associated with basis function pairs. These methods do not consider the detailed nature of localized excitations but instead define a correlation energy per electron factor that is unique to a specific atom. The correlation factors are basis function dependent and are determined by configuration interaction (CI) calculations on diatomic and hydride molecules. The correlation energy estimates are compared with the results of high-level CI calculations for a test set of 27 molecules representing a wide range of bonding environments (average error of 2.6%). An extension based on truncated CI calculations in which d-type and hydrogen p-type functions are eliminated from the virtual space combined with estimates of dynamical correlation contributions using atomic correlation factors is discussed and applied to the dissociation of several molecules.

Prediction of many-electron wavefunctions using atomic potentials: extended basis sets and molecular dissociation.

A one-electron Schrödinger equation based on special one-electron potentials for atoms is shown to exist that produces orbitals for an arbitrary molecule that are sufficiently accurate to be used without modification to construct single- and multi-determinant wavefunctions. The exact Hamiltonian is used to calculate the energy variationally and to generate configuration interaction expansions. Earlier work on equilibrium geometries is extended to larger basis sets and molecular dissociation. For a test set of molecules representing different bonding environments, a single set of invariant atomic potentials gives wavefunctions with energies that deviate from configuration interaction energies based on SCF orbitals by less than 0.04 eV per bond or valence electron pair. On a single diagonalization of the Fock matrix, the corresponding errors are reduced 0.01 eV. Atomization energies are also in good agreement with CI values based on canonical SCF orbitals. Configuration interaction applications to single bond dissociations of water and glycine, and multiple bond dissociations of ethylene and oxygen produce dissociation energy curves in close agreement with CI calculations based on canonical SCF orbitals for the entire range of internuclear distances.

Electronic and Structural Factors Controlling the Spin Orientations of Magnetic Ions.

Magnetic ions M in discrete molecules and extended solids form MLn complexes with their first-coordinate ligand atoms L. The spin moment of M in a complex MLn prefers a certain direction in coordinate space because of spin-orbit coupling (SOC). In this minireview, we examine the structural and electronic factors governing the preferred spin orientations. Elaborate experimental measurements and/or sophisticated computational efforts are required to find the preferred spin orientations of magnetic ions, largely because the energy scale of SOC is very small. The latter is also the very reason why one can readily predict the preferred spin orientation of M by analyzing the SOC-induced highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) interactions of the MLn complexes in terms of qualitative perturbation theory. The strength of this HOMO-LUMO interaction depends on the spin orientation, which is governed by the selection rules based on the minimum |ΔLz| value (i.e., the minimum difference in the magnetic quantum numbers) between the HOMO and LUMO. With the local z axis of MLn chosen as its n-fold rotational axis, the preferred spin orientation is parallel to the z axis (∥z) when |ΔLz| = 0 but perpendicular to the z axis (⊥z) when |ΔLz| = 1.

Prediction of many-electron wavefunctions using atomic potentials: Refinements and extensions to transition metals and large systems.

For a given many-electron molecule, it is possible to define a corresponding one-electron Schrödinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-determinant and multideterminant wavefunctions for the molecule. The energy is not predicted and must be evaluated by calculating Coulomb and exchange interactions over the predicted orbitals. Transferable potentials for first-row atoms and transition metal oxides that can be used without modification in different molecules are reported. For improved accuracy, molecular wavefunctions can be refined by slightly scaling nuclear charges and by introducing potentials optimized for functional groups. The accuracy is further improved by a single diagonalization of the Fock matrix constructed from the predicted orbitals. For a test set of 20 molecules representing different bonding environments, the transferable potentials with scaling give wavefunctions with energies that deviate from exact self-consistent field or configuration interaction energies by less than 0.05 eV and 0.02 eV per bond or valence electron pair, respectively. On diagonalization of the Fock matrix, the corresponding errors are reduced by a factor of three to less than 0.016 eV and 0.006 eV, respectively. Applications to the ground and excited states of a Ti18O36 nanoparticle and chlorophyll-a are reported.

Prediction of many-electron wavefunctions using atomic potentials.

For a given many-electron molecule, it is possible to define a corresponding one-electron Schrödinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single- and multi-determinant wavefunctions for the molecule. The energy is not predicted and must be evaluated by calculating Coulomb and exchange interactions over the predicted orbitals. Potentials are found by minimizing the energy of predicted wavefunctions. There exist slightly less accurate average potentials for first-row atoms that can be used without modification in different molecules. For a test set of molecules representing different bonding environments, these average potentials give wavefunctions with energies that deviate from exact self-consistent field or configuration interaction energies by less than 0.08 eV and 0.03 eV per bond or valence electron pair, respectively.

Electron correlation by polarization of interacting densities.

Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize dynamically, thereby reducing the magnitude of the interaction. Exchange integrals of molecular orbitals are not correlated. The modified Coulomb interactions are used in single-determinant or configuration interaction calculations. The objective is to account for dynamical correlation effects without explicitly introducing higher spherical harmonic functions into the molecular orbital basis. Molecular orbital densities are decomposed into a distribution of spherical components that conserve the charge and each of the interacting components is considered as a two-electron wavefunction embedded in the system acted on by an average field Hamiltonian plus r12-1. A method of avoiding redundancy is described. Applications to atoms, negative ions, and molecules representing different types of bonding and spin states are discussed.

Configuration interaction study of the ground and excited states of TiO2 ring structures.

Theoretical studies of the ground and lowest excited singlet and triplet states of a series of titanium dioxide ring structures, (TiO(2))(2n), n = 3-9, are reported. Calculations are based on many-electron configuration theory, where energies of states and geometrical structures are determined by variational energy minimization. The lowest energy excited states correspond to excitations from oxygen 2p levels to unoccupied 3d orbitals on titanium. For each ring system, two types of excited state solutions are investigated: those that maintain periodic symmetry for individual orbitals and solutions that allow the symmetry to be broken. The latter solutions which correspond to localized states or excitons are found to be significantly lower in energy than the symmetric solutions. We compare the vertical excitation energy of these well-defined geometrical structures with size effects reported in experimental studies.

Improving limits of detection for B-type natriuretic peptide using PC-IDMS: an application of the ALiPHAT strategy.

Hydrophobic tagging of biomolecules has been reported by our group and others to increase their ionization efficiency during electrospray ionization and facilitate their detection by mass spectrometry. As such, hydrophobic tagging should provide a viable method for augmenting MS-based quantification of low abundance proteins by decreasing their detection limits. Herein we have evaluated two commercial alkylation reagents and several newly synthesized hydrophobic alkylation reagents for their utility in quantifying B-type Natriuretic Peptide, a low abundance cardiac biomarker, by protein cleavage isotope dilution mass spectrometry. For the cysteine containing tryptic peptide evaluated, a approximately 3.5-fold decrease in the detection limit was observed for the best performing hydrophobic reagent, 2-iodo-N-octylacetamide, relative to the commonly used alkylation reagent, iodoacetamide. Additionally, we have evaluated the use of nonpolar surface areas as a metric for assessing the effectiveness of the alkylation reagents in improving ESI response.

Evaluation of the ALiPHAT method for PC-IDMS and correlation of limits-of-detection with nonpolar surface area.

PC-IDMS experiments for two peptides, laminin nonapeptide and the N-terminal tryptic peptide of prostate specific antigen, were performed utilizing a variety of alkylating reagents. These experiments were conducted to investigate how hydrophobicity influences the limits-of-detection (LOD) by altering their electrospray ionization response. Nonpolar surface areas were calculated for both peptides and all alkylating reagents to provide an estimate of the hydrophobicity of the differently alkylated peptides. Decreases in LOD by 2-fold were observed for both peptides between the best and worst performing combination of alkylating reagent. However, while an increase in hydrophobicity was found to aid in decreasing LOD to an extent, beyond a certain hydrophobicity, we observed a decrease.

Photoinduced dissociation of water and transport of hydrogen between silver clusters.

Theoretical electronic structure calculations are reported for the dissociation of water adsorbed on a 31-atom silver cluster, Ag31, and subsequent transfer of a H to a second Ag31 cluster leaving OH on the first cluster. Both ground and excited electronic state processes are considered for two choices of Ag cluster separation, 6.35 and 7.94 A, on the basis of preliminary calculations for a range of separation distances. The excited electronic state of interest is formed by photoemission of an electron from one Ag cluster and transient attachment of the photoemitted electron to the adsorbed water molecule. A very large energy barrier is found for the ground-state process (3.53 eV at a cluster separation of 6.35 A), while the barrier in the excited state is small (0.38 eV at a cluster separation of 6.35 A). In the excited state, partial occupancy of an OH antibonding orbital facilitates OH stretch and concomitant movement of the negatively charged OH toward the electron-hole in the metal cluster. The excited-state pathway for dissociation of water and transfer of H begins with the formation of an excited electronic state at 3.59-3.82 eV. Stretch of the OH bond occurs with little change in energy (0.38-0.54 eV up to a stretch of 1.96 A). In this region of OH stretch the molecule must return to the ground-state potential energy surface to fully dissociate and to transfer H to the other Ag cluster. Geometry optimizations are carried out using a simplex algorithm and a semigrid method. These methods allow the total energy to be calculated directly using configuration interaction theory.

Weak hydrogen bonding can initiate alkane C-H bond activation in acidic zeolites.

Ab initio calculations at the Hartree-Fock self-consistent field/single determinant (SCF) and configuration interaction multi-determinant (CI) expansion levels have been used to show that isobutane primary C-H bond activation occurs via direct protium exchange with the zeolite surface via a weakly hydrogen-bonded complex. The calculated 15 kcal/mol activation barrier agrees with the 13.7 kcal/mol value from a recently reported experimental study (J. Am. Chem. Soc. 2006, 128, 1847-1852). Overall, the mechanism described in this contribution demonstrates that weak C-H to O hydrogen bonding leads to complexes at the zeolite acid site that can facilitate C-H bond activation.

CO adsorption on Ag(100) and Ag/MgO(100).

Theoretical studies of CO adsorption on a two-layer Ag(100) film and on a two-layer Ag film on a MgO(100) support are reported. Ab initio calculations are carried at the configuration interaction level of theory using embedding methods to treat the metal-adsorbate region and the extended ionic solid. The metal overlayer is considered in two different structures: where Ag-Ag distances are equal to the value in the bulk solid, and for a slightly expanded lattice in which the Ag-Ag distances are equal to the O-O distance on the MgO(100) surface. The calculated adsorption energy of Ag(100) on MgO(100) is 0.58 eV per Ag interfacial atom; the Ag-O distance is 2.28 A. A small transfer of electrons from MgO to Ag occurs on deposition of the silver overlayer. CO adsorption at an atop Ag site is found to be the most stable for adsorption on the two-layer Ag film and also for adsorption on Ag deposited on the oxide; CO adsorption energies range from 0.12 to 0.19 eV. The CO adsorption energy is reduced for the Ag/MgO system compared to adsorption on the unsupported metal film thereby providing evidence for a direct electronic effect of the oxide support at the metal overlayer surface. Expansion of the Ag-Ag distance in the two-layer system also reduces the adsorption energy.

Adsorption of O, H, OH, and H2O on Ag(100).

The adsorption of H(2)O and its dissociation products, O, H, and OH, on Ag(100) has been studied using an ab initio embedding method. Results at different sites (atop, bridge, and hollow) are presented. The four-fold hollow site is found to be the most stable adsorption site for O, H, and OH, and the calculated adsorption energies are 87.1, 42.7, and 76.2 kcal mol(-1), respectively. The adsorption energy of water at the atop and bridge sites is almost identical with values of 11.1 and 12.0 kcal mol(-1), respectively. The formation of adsorbed OH species by adsorption of water on oxygen-precovered Ag(100) is predicted to be exothermic by 36 kcal mol(-1).

Theoretical study of the CH2 + O photodissociation of formaldehyde adsorbed on the Ag(111) surface.

Configuration interaction calculations of the ground and excited states of the H2CO molecule adsorbed on the Ag(111) surface have been carried out to study the photoinduced dissociation process leading to polymerization of formaldehyde. The metal-adsorbate system has been described by the embedded cluster and multireference configuration interaction methods. The pi electron-attachment H2CO- and n-pi* internally excited H2CO* states have been considered as possible intermediates. The calculations have shown that H2CO* is only very weakly bound on Ag(111), and thus that the dissociation of adsorbed formaldehyde due to internal excitation is unlikely. By contrast, the H2CO- anion is strongly bound to Ag(111) and gains additional vibrational energy along the C-O stretch coordinate via Franck-Condon excitation from the neutral molecule. Computed energy variations of adsorbed H2CO and H2CO- at different key geometries along the pathway for C-O bond cleavage make evident, however, that complete dissociation is very difficult to attain on the potential energy surface of either of these states. Instead, reneutralization of the vibrationally excited anion by electron transfer back to the substrate is the most promising means of breaking the C-O bond, with subsequent formation of the coadsorbed O and CH2 fragments. Furthermore, it has been demonstrated that the most stable state for both dissociation fragments on Ag(111) is a closed-shell singlet, with binding energies relative to the gas-phase products of approximately 3.2 and approximately 1.3 eV for O and CH2, respectively. Further details of the reaction mechanism for the photoinduced C-O bond cleavage of H2CO on the Ag(111) surface are also given.