Quantum Computing for Molecular Biology.

Molecular biology and biochemistry interpret microscopic processes in the living world in terms of molecular structures and their interactions, which are quantum mechanical by their very nature. Whereas the theoretical foundations of these interactions are well established, the computational solution of the relevant quantum mechanical equations is very hard. However, much of molecular function in biology can be understood in terms of classical mechanics, where the interactions of electrons and nuclei have been mapped onto effective classical surrogate potentials that model the interaction of atoms or even larger entities. The simple mathematical structure of these potentials offers huge computational advantages; however, this comes at the cost that all quantum correlations and the rigorous many-particle nature of the interactions are omitted. In this work, we discuss how quantum computation may advance the practical usefulness of the quantum foundations of molecular biology by offering computational advantages for simulations of biomolecules. We not only discuss typical quantum mechanical problems of the electronic structure of biomolecules in this context, but also consider the dominating classical problems (such as protein folding and drug design) as well as data-driven approaches of bioinformatics and the degree to which they might become amenable to quantum simulation and quantum computation.

Expansive Quantum Mechanical Exploration of Chemical Reaction Paths.

Quantum mechanical methods have been well-established for the elucidation of reaction paths of chemical processes and for the explicit dynamics of molecular systems. While they are usually deployed in routine manual calculations on reactions for which some insights are already available (typically from experiment), new algorithms and continuously increasing capabilities of modern computer hardware allow for exploratory open-ended computational campaigns that are unbiased and therefore enable unexpected discoveries. Highly efficient and even automated procedures facilitate systematic approaches toward the exploration of uncharted territory in molecular transformations and dynamics. In this work, we elaborate on such explorative approaches that range from reaction network explorations with (stationary) quantum chemical methods to explorative molecular dynamics and migrant wave packet dynamics. The focus is on recent developments that cover the following strategies. (i) Pruning search options for elementary reaction steps by heuristic rules based on the first-principles of quantum mechanics: Rules are required for reducing the combinatorial explosion of potentially reactive atom pairings, and rooting them in concepts derived from the electronic wave function makes them applicable to any molecular system. (ii) Enforcing reactive events by external biases: Inducing a reaction requires constraints that steer and direct elementary-step searches, which can be formulated in terms of forces, velocities, or supplementary potentials. (iii) Manual steering facilitated by interactive quantum mechanics: As ultrafast quantum chemical methods allow for real-time manual interactions with molecular systems, human-intuition-guided paths can be easily explored with suitable human-machine interfaces. (iv) New approaches for transition-state optimization with continuous curve representations can provide stable schemes to be driven in an automated way by allowing for an efficient tuning of the curve's parameters (instead of a manipulation of a collection of structures along the path), and (v) reactive molecular dynamics and direct wave packet propagation exploit the equations of motion of an underlying mechanical theory (usually, classical Newtonian mechanics or Schrödinger quantum mechanics). Explorative approaches are likely to replace the current state of the art in computational chemistry, because they reduce the human effort to be invested in reaction path elucidations, they are less prone to errors and bias-free, and they cover more extensive regions of the relevant configuration space. As a result, computational investigations that rely on these techniques are more likely to deliver surprising discoveries.

Symmetry-Projected Nuclear-Electronic Hartree-Fock: Eliminating Rotational Energy Contamination.

We present a symmetry projection technique for enforcing rotational and parity symmetries in nuclear-electronic Hartree-Fock wave functions, which treat electrons and nuclei on equal footing. The molecular Hamiltonian obeys rotational and parity inversion symmetries, which are, however, broken by expanding in Gaussian basis sets that are fixed in space. We generate a trial wave function with the correct symmetry properties by projecting the wave function onto representations of the three-dimensional rotation group, i.e., the special orthogonal group in three dimensions SO(3). As a consequence, the wave function becomes an eigenfunction of the angular momentum operator which (i) eliminates the contamination of the ground-state wave function by highly excited rotational states arising from the broken rotational symmetry and (ii) enables the targeting of specific rotational states of the molecule. We demonstrate the efficiency of the symmetry projection technique by calculating the energies of the low-lying rotational states of the H2 and H3+ molecules.

Transcorrelated density matrix renormalization group.

We introduce the transcorrelated Density Matrix Renormalization Group (tcDMRG) theory for the efficient approximation of the energy for strongly correlated systems. tcDMRG encodes the wave function as a product of a fixed Jastrow or Gutzwiller correlator and a matrix product state. The latter is optimized by applying the imaginary-time variant of time-dependent (TD) DMRG to the non-Hermitian transcorrelated Hamiltonian. We demonstrate the efficiency of tcDMRG with the example of the two-dimensional Fermi-Hubbard Hamiltonian, a notoriously difficult target for the DMRG algorithm, for different sizes, occupation numbers, and interaction strengths. We demonstrate fast energy convergence of tcDMRG, which indicates that tcDMRG could increase the efficiency of standard DMRG beyond quasi-monodimensional systems and provides a generally powerful approach toward the dynamic correlation problem of DMRG.

The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges.

In the past two decades, the density matrix renormalization group (DMRG) has emerged as an innovative new method in quantum chemistry relying on a theoretical framework very different from that of traditional electronic structure approaches. The development of the quantum chemical DMRG has been remarkably fast: it has already become one of the reference approaches for large-scale multiconfigurational calculations. This perspective discusses the major features of DMRG, highlighting its strengths and weaknesses also in comparison with other novel approaches. The method is presented following its historical development, starting from its original formulation up to its most recent applications. Possible routes to recover dynamical correlation are discussed in detail. Emerging new fields of applications of DMRG are explored, such as its time-dependent formulation and the application to vibrational spectroscopy.

Nuclear-electronic all-particle density matrix renormalization group.

We introduce the Nuclear-Electronic All-Particle Density Matrix Renormalization Group (NEAP-DMRG) method for solving the time-independent Schrödinger equation simultaneously for electrons and other quantum species. In contrast to the already existing multicomponent approaches, in this work, we construct from the outset a multi-reference trial wave function with stochastically optimized non-orthogonal Gaussian orbitals. By iterative refining of the Gaussians' positions and widths, we obtain a compact multi-reference expansion for the multicomponent wave function. We extend the DMRG algorithm to multicomponent wave functions to take into account inter- and intra-species correlation effects. The efficient parameterization of the total wave function as a matrix product state allows NEAP-DMRG to accurately approximate the full configuration interaction energies of molecular systems with more than three nuclei and 12 particles in total, which is currently a major challenge for other multicomponent approaches. We present the NEAP-DMRG results for two few-body systems, i.e., H2 and H3 +, and one larger system, namely, BH3.

Modern quantum chemistry with [Open]Molcas.

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

Optimization of highly excited matrix product states with an application to vibrational spectroscopy.

An efficient approximation to the full configuration interaction solution can be obtained with the density matrix renormalization group (DMRG) algorithm without a restriction to a predefined excitation level. In a standard DMRG implementation, however, excited states are calculated with a ground-state optimization in the space orthogonal to all lower lying wave function solutions. A trivial parallelization is therefore not possible, and the calculation of highly excited states becomes prohibitively expensive, especially in regions with a high density of states. Here, we introduce two variants of the DMRG algorithm that allows us to target directly specific energy regions and therefore highly excited states. The first one, based on shift-and-invert techniques, is particularly efficient for low-lying states but is not stable in regions with a high density of states. The second one, based on the folded auxiliary operator, is less efficient but more accurate in targeting high-energy states. We apply the algorithm to the solution of the nuclear Schrödinger equation but emphasize that it can be applied to the diagonalization of general Hamiltonians as well, such as the electronic Coulomb Hamiltonian to address X-ray spectra. In combination with several root-homing algorithms and a stochastic sampling of the determinant space, excited states of interest can be adequately tracked and analyzed during the optimization. We validate these algorithms by calculating several highly excited vibrational states of ethylene and demonstrate that we can accurately calculate prominent spectral features of large molecules such as the sarcosine-glycine dipeptide.

Theory meets experiment for unravelling the C1s X-ray photoelectron spectra of pyridine, 2-fluoropyridine, and 2,6-difluoropyridine.

High resolution X-ray photoelectron spectra of a series of substituted pyridines (pyridine, 2-fluoropyridine, and 2,6-difluoropyridine) have been recorded and rationalized by means of a quantum mechanical approach based on the density functional theory including vibronic effects at the Franck-Condon level. The significant chemical shifts of the C1s binding energies induced by fluorine atoms are reproduced quantitatively by our computational model, as well as the vibrational fine structure and the band shapes. Nonsymmetric normal modes play an important role due to the core-hole localization in the presence of equivalent carbon atoms in pyridine and 2,6-difluoropyridine.

Computational simulation of vibrationally resolved spectra for spin-forbidden transitions.

In this computational study, we illustrate a method for computing phosphorescence and circularly polarized phosphorescence spectra of molecular systems, which takes into account vibronic effects including both Franck-Condon and Herzberg-Teller contributions. The singlet and triplet states involved in the phosphorescent emission are described within the harmonic approximation, and the method fully takes mode-mixing effects into account when evaluating Franck-Condon integrals. Spin-orbit couplings, which are responsible for these otherwise forbidden phenomena, are accounted for by means of a relativistic two-component time-dependent density functional theory method. The model is applied to two types of chiral systems: camphorquinone, a rigid organic system that allows for an extensive benchmark, and some members of a class of iridium complexes. The merits and shortcomings of the methods are discussed, and some perspectives for future developments are offered.

Understanding the interplay between the solvent and nuclear rearrangements in the negative solvatochromism of a push-pull flexible quinolinium cation.

A detailed computational characterization of the one-photon absorption spectrum of a 2-((E)-2-[2,2']-bithiophenyl-5-yl-vinyl)-1-methyl-quinolinium cation in acetonitrile solution is presented. The main physico-chemical effects (solvation, vibronic progression) affecting the band position and shape are progressively introduced in the computational model, highlighting their relative role in the spectral profile. The reported results underline how an accurate reproduction of the experimental spectrum can only be obtained by going beyond oversimplified methods. Moreover, the deep interplay between the solvent effects and nuclear rearrangements permits the negative solvatochromism exhibited by hypsochromic molecules to be explained. This illustrates the potential of the computational investigation, which can shed light on the information hidden in experimental spectra.

The ionic states of difluoromethane: A reappraisal of the low energy photoelectron spectrum including ab initio configuration interaction computations.

A new synchrotron-based study of the photoelectron spectrum (PES) of difluoromethane is interpreted by an ab initio analysis of the ionic states, which includes Franck-Condon (FC) factors. Double differentiation of the spectrum leads to significant spectral sharpening; the vibrational structure observed is now measured with greater accuracy than in previous studies. Several electronic structure methods are used, including equation of motion coupled cluster calculations with single and double excitations (EOM-CCSD), its ionization potential variant EOM-IP-CCSD, 4th order Møller-Plesset perturbation theory (MP4SDQ) configuration interaction (CI), and complete active space self-consistent-field (CASSCF) methods. The adiabatic ionization energies (AIEs) confirm the assignments as band I, one state 12B1 (12.671 eV); band II, three states, 12B2 (14.259) < 12A1 (15.030) < 12A2 (15.478 eV); and band III, three states, 22B2 (18.055) < 22A1 (18.257) < 22B1 (18.808 eV). The three ionizations in each of the bands II and III lead to selective line broadening of the PES structure, which is attributed to vibronic overlap. The apparent lack of a vibrational structure attributable to both the 12A1 and 22A1 states in the PES arises from line broadening with the preceding states 12B2 and 22B2, respectively. Although these 2A1 states clearly overlap with their adjacent higher IE, some vibrational structure is observed on the higher IE. The effects of vibronic coupling are evident since the observed structure does not fit closely with the calculated Born-Oppenheimer FC profiles. Correlation of the lowest group of four AIEs in the PES of other members of the CH2X2 group, where X = F, Cl, Br, and I, clearly indicate these effects are more general.

A combined theoretical and experimental study of the ionic states of iodopentafluorobenzene.

A new synchrotron radiation photoelectron spectral (PES) study of iodopentafluorobenzene, together with a theoretical analysis of the spectrum, where Franck-Condon factors are discussed, gives detailed insight into the ionization processes, and this exposes the need for a reinvestigation of the vacuum ultraviolet spectral (VUV) assignments. We have calculated adiabatic ionization energies (AIEs) for several ionic states, using the equation-of-motion coupled cluster method for ionic states combined with multi-configuration self-consistent field calculation study. The AIE sequence is: X2B1 < A2A2 < B2B2 < C22B1 < D2A1 < E32B1. This symmetry sequence has a major impact on previous VUV spectral assignments, which now appear to be to optically forbidden states. Changes in the equilibrium structures for these ionic states are relatively small, but a significant decrease and increase in the C-I bond length relative to the X1A1 structure occurs for the X2B1 and C2B1 states, respectively. The PES shows major vibrational overlaps between pairs of ionic states, X with A, and A with B. The result of these overlaps is the loss of vibrational structure and considerable broadening of the higher energy PES state. Although the baseline is nearly re-established between the A and B states, where the two bands are nearly separate, the B state is also broadened by the A state. Only the C ionic state, which shows the most highly developed vibrational structure, can be regarded as free from vibrational coupling to a neighbor state. The Franck-Condon analysis of the PES bands X, A, B, and C is described in detail; the apparent simplicity of some of these bands is illusory, since almost all the observed peaks arise from super-position of several calculated vibrational states. The experimental AIE of the A state, which is submerged under the X state envelope, has been determined by the subtraction of the calculated X state envelope from the observed PES spectrum. The overlap of these PES bands and the apparent closeness of the potential energy curves describing them have been investigated, using the state-averaged, complete active space self-consistent field method. We have identified two structures, one where the potential energy curves for the X and A states cross and another for the A and B states. At these two conical intersections (ConInts), there is zero-energy difference within each pair of states. Although similar in energy, the ConInt for the crossing of the X with A states, and that for the A with B states, shows that the open-shell occupancies correspond to the 4 lowest AIE states, and all four states that are quite different from each other.

A combined theoretical and experimental study of the valence and Rydberg states of iodopentafluorobenzene.

A new ultraviolet (UV) and vacuum ultraviolet (VUV) spectrum for iodopentafluorobenzene (C6F5I) using synchrotron radiation is reported. The measurements have been combined with those from a recent high-resolution photoelectron spectroscopic study. A major theoretical study, which includes both Franck-Condon (FC) and Herzberg-Teller (HT) analyses, leads to conclusions, which are compatible with both experimental studies. Our observation that the VUV multiplet at 7.926 eV in the VUV spectrum is a Rydberg state rather than a valence state leads to a fundamental reassignment of the VUV Rydberg spectrum over previous studies and removes an anomaly where some previously assigned Rydberg states were to optically forbidden states. Adiabatic excitation energies (AEEs) were determined from equations-of-motion coupled cluster with singles and doubles excitation; these were combined with time dependent density functional theoretical methods. Frequencies from these two methods are very similar, and this enabled the evaluation of both FC and HT contributions in the lower valence states. Multi-reference multi-root configuration interaction gave a satisfactory account of the principal UV+VUV spectral profile of C6F5I, with vertical band positions and intensities. The UV spectral onset consists of two very weak transitions assigned to 11B1 (πσ*) and 11B2 (σσ*) symmetries. The lowest unoccupied molecular orbital of a σ*(a1) symmetry has a significant C-I* antibonding character. This results in considerable lengthening of the C-I bond for both these excited states. The vibrational intensity of the lowest 11B1 state is dominated by HT contributions; the 11B2 state contains both HT and FC contributions; the third band, which contains three states, two ππ*(11A1, 21B2) and one πσ*(21B1), is dominated by FC contributions in the 1A1 state. In this 1A1 state, and the spectrally dominant bands near 6.7 (1A1) and 7.3 eV (1A1 + 1B2), the C-I bond length is in the normal range, and FC components dominate.

General formulation of vibronic spectroscopy in internal coordinates.

Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption and emission one-photon, conventional and chiral spectroscopies has been extended to support various sets of internal coordinates. Thanks to the implementation of analytical first and second derivatives of different internal coordinates with respect to cartesian ones, both vertical and adiabatic models are available, with the inclusion of mode mixing and, possibly, Herzberg-Teller contributions. Furthermore, all supported non-redundant sets of coordinates are built from a fully automatized algorithm using only a primitive redundant set derived from a bond order-based molecular topology. Together with conventional stretching, bending, and torsion coordinates, the availability of additional coordinates (including linear and out-of-plane bendings) allows a proper treatment of specific systems, including, for instance, inter-molecular hydrogen bridges. A number of case studies are analysed, showing that cartesian and internal coordinates are nearly equivalent for semi-rigid systems not experiencing significant geometry distortions between initial and final electronic states. At variance, delocalized (possibly weighted) internal coordinates become much more effective than their cartesian counterparts for flexible systems and/or in the presence of significant geometry distortions accompanying electronic transitions.

Combined theoretical and experimental study of the valence, Rydberg, and ionic states of chlorobenzene.

New photoelectron (PE) and ultra violet (UV) and vacuum UV (VUV) spectra have been obtained for chlorobenzene by synchrotron study with higher sensitivity and resolution than previous work and are subjected to detailed analysis. In addition, we report on the mass-resolved (2 + 1) resonance enhanced multiphoton ionization (REMPI) spectra of a jet-cooled sample. Both the VUV and REMPI spectra have enabled identification of a considerable number of Rydberg states for the first time. The use of ab initio calculations, which include both multi-reference multi-root doubles and singles configuration interaction (MRD-CI) and time dependent density functional theoretical (TDDFT) methods, has led to major advances in interpretation of the vibrational structure of the ionic and electronically excited states. Franck-Condon (FC) analyses of the PE spectra, including both hot and cold bands, indicate much more complex envelopes than previously thought. The sequence of ionic states can be best interpreted by our multi-configuration self-consistent field computations and also by comparison of the calculated vibrational structure of the B and C ionic states with experiment; these conclusions suggest that the leading sequence is the same as that of iodobenzene and bromobenzene, namely: X(2)B1(3b1 (-1)) < A(2)A2(1a2 (-1)) < B(2)B2(6b2 (-1)) < C(2)B1(2b1 (-1)). The absorption onset near 4.6 eV has been investigated using MRD-CI and TDDFT calculations; the principal component of this band is (1)B2 and an interpretation based on the superposition of FC and Herzberg-Teller contributions has been performed. The other low-lying absorption band near 5.8 eV is dominated by a (1)A1 state, but an underlying weak (1)B1 state (πσ(∗)) is also found. The strongest band in the VUV spectrum near 6.7 eV is poorly resolved and is analyzed in terms of two ππ(∗) states of (1)A1 (higher oscillator strength) and (1)B2 (lower oscillator strength) symmetries, respectively. The calculated vertical excitation energies of these two states are critically dependent upon the presence of Rydberg functions in the basis set, since both manifolds are strongly perturbed by the Rydberg states in this energy range. A number of equilibrium structures of the ionic and singlet excited states show that the molecular structure is less subject to variation than corresponding studies for iodobenzene and bromobenzene.

Combined theoretical and experimental study of the valence, Rydberg and ionic states of fluorobenzene.

New photoelectron spectra (PES) and ultra violet (UV) and vacuum UV (VUV) absorption spectra of fluorobenzene recorded at higher resolution than previously, have been combined with mass-resolved (2 + 1) and (3 + 1) resonance enhanced multiphoton ionization (REMPI) spectra; this has led to the identification of numerous Rydberg states. The PES have been compared with earlier mass-analyzed threshold ionization and photoinduced Rydberg ionization (PIRI) spectra to give an overall picture of the ionic state sequence. The analysis of these spectra using both equations of motion with coupled cluster singles and doubles (EOM-CCSD) configuration interaction and time dependent density functional theory (TDDFT) calculations have been combined with vibrational analysis of both the hot and cold bands of the spectra, in considerable detail. The results extend several earlier studies on the vibronic coupling leading to conical intersections between the X(2)B1 and A(2)A2 states, and a further trio (B, C, and D) of states. The conical intersection of the X and A states has been explicitly identified, and its structure and energetics evaluated. The energy sequence of the last group is only acceptable to the present study if given as B(2)B2

Implementation of a graphical user interface for the virtual multifrequency spectrometer: The VMS-Draw tool.

This article presents the setup and implementation of a graphical user interface (VMS-Draw) for a virtual multifrequency spectrometer. Special attention is paid to ease of use, generality and robustness for a panel of spectroscopic techniques and quantum mechanical approaches. Depending on the kind of data to be analyzed, VMS-Draw produces different types of graphical representations, including two-dimensional or three-dimesional (3D) plots, bar charts, or heat maps. Among other integrated features, one may quote the convolution of stick spectra to obtain realistic line-shapes. It is also possible to analyze and visualize, together with the structure, the molecular orbitals and/or the vibrational motions of molecular systems thanks to 3D interactive tools. On these grounds, VMS-Draw could represent a useful additional tool for spectroscopic studies integrating measurements and computer simulations.

Interpretation of the photoelectron, ultraviolet, and vacuum ultraviolet photoabsorption spectra of bromobenzene by ab initio configuration interaction and DFT computations.

New photoelectron, ultraviolet (UV), and vacuum UV (VUV) spectra have been obtained for bromobenzene by synchrotron study with higher sensitivity and resolution than previous work. This, together with use of ab initio calculations with both configuration interaction and time dependent density functional theoretical methods, has led to major advances in interpretation. The VUV spectrum has led to identification of a considerable number of Rydberg states for the first time. The Franck-Condon (FC) analyses including both hot and cold bands lead to identification of the vibrational structure of both ionic and electronically excited states including two Rydberg states. The UV onset has been interpreted in some detail, and an interpretation based on the superposition of FC and Herzberg-Teller contributions has been performed. In a similar way, the 6 eV absorption band which is poorly resolved is analysed in terms of the presence of two ππ* states of (1)A1 (higher oscillator strength) and (1)B2 (lower oscillator strength) symmetries, respectively. The detailed analysis of the vibrational structure of the 2(2)B1 ionic state is particularly challenging, and the best interpretation is based on equation-of-motion-coupled cluster with singles and doubles computations. A number of equilibrium structures of the ionic and singlet excited states show that the molecular structure is less subject to variation than corresponding studies for iodobenzene. The equilibrium structures of the 3b13s and 6b23s (valence shell numbering) Rydberg states have been obtained and compared with the corresponding ionic limit structures.

Interpretation of the vacuum ultraviolet photoabsorption spectrum of iodobenzene by ab initio computations.

Identification of many Rydberg states in iodobenzene, especially from the first and fourth ionization energies (IE1 and IE4, X(2)B1 and C(2)B1), has become possible using a new ultraviolet (UV) and vacuum-ultraviolet (VUV) absorption spectrum, in the region 29 000-87 000 cm(-1) (3.60-10.79 eV), measured at room temperature with synchrotron radiation. A few Rydberg states based on IE2 (A(2)A2) were found, but those based on IE3 (B(2)B2) are undetectable. The almost complete absence of observable Rydberg states relating to IE2 and IE3 (A(2)A2 and B(2)B2, respectively) is attributed to them being coupled to the near-continuum, high-energy region of Rydberg series converging on IE1. Theoretical studies of the UV and VUV spectra used both time-dependent density functional (TDDFT) and multi-reference multi-root doubles and singles-configuration interaction methods. The theoretical adiabatic excitation energies, and their corresponding vibrational profiles, gave a satisfactory interpretation of the experimental results. The calculations indicate that the UV onset contains both 1(1)B1 and 1(1)B2 states with very low oscillator strength, while the 2(1)B1 state was found to lie under the lowest ππ(∗) 1(1)A1 state. All three of these (1)B1 and (1)B2 states are excitations into low-lying σ(∗) orbitals. The strongest VUV band near 7 eV contains two very strong ππ(∗) valence states, together with other weak contributors. The lowest Rydberg 4b16s state (3(1)B1) is very evident as a sharp multiplet near 6 eV; its position and vibrational structure are well reproduced by the TDDFT results.